EXPLORING BEST PRACTICES IN DEVELOPMENTAL MATHEMATICS
Dissertation
Submitted to
The School of Education and Allied Professions of the
UNIVERSITY OF DAYTON
In Partial Fulfillment of the Requirements for
The Degree
Doctor of Philosophy in Educational Leadership
By
Brian V. Cafarella, B.S., M.Ed.
UNIVERSITY OF DAYTON
Dayton, Ohio
May, 2013
EXPLORING BEST PRACTICES IN DEVELOPMENTAL MATHEMATICS
Name: Cafarella, Brian V.
APPROVED BY:
______Michele M. Welkener, Ph.D. Committee Chair
______A. William Place, Ph.D. Committee Member
______Carolyn S. Ridenour, Ed.D. Committee Member
______Aparna W. Higgins, Ph.D. Committee Member
______Kevin R. Kelly, Ph.D. Dean
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ABSTRACT
EXPLORING BEST PRACTICES IN DEVELOPMENTAL MATHEMATICS
Name: Cafarella, Brian V. University of Dayton
Advisor: Dr. Michele Welkener
Currently, many community colleges are struggling with poor student success rates in developmental math. Therefore, this qualitative study focused on employing best practices in developmental mathematics at an urban community college in Dayton, Ohio.
Guiding the study were the following research questions: What are the best practices utilized by a group of developmental mathematics instructors at an urban community college? How do these instructors employ such practices to enhance student learning?
Participants consisted of 20 developmental mathematics instructors from Sinclair
Community College in Dayton, Ohio who had taught at least six developmental math classes over a two-year period and who self-reported success rates of at least 60% during that time. This study employed a pre-interview document and a face-to-face interview as the primary research instruments. Using the constant comparison method (Merriam,
2002a), the researcher constructed findings from both approaches regarding best practices in developmental math. Such practices included communication with students, the art of organization, collaborative learning, frequent low stake assessments, technology
iii supplements, the use of mnemonics and memorable wording, and manipulatives, visualand real-life applications. When addressing the topic of acceleration, the participants reported that this strategy is a proper fit for some students but not all. The following conclusions were based on the study’s findings. Effective communication should be established between developmental math instructors and students as well as among developmental math instructors. Developmental math faculty ought to work with their students in developing their organizational skills. Developmental math instructors should couple the implementation of frequent low stake assessments with student outreach. Collaborative learning can be beneficial to some developmental math students, but instructors must take into account the composition of the class as well their own comfort level with collaborative learning. It is also important for developmental math instructors to employ some creativity in their classes. Accelerated instruction should be reserved for higher ability developmental math students with a strong work ethic. Lastly, college administrators must recognize and respect instructor comfort level. The findings from this dissertation will assist both new and veteran developmental math instructors with implementing practices that will enhance student success in their classes. This dissertation’s findings are also intended to aid community college leaders in gaining an understanding of the culture of developmental math and assist these leaders in the implementation of policy and practice regarding developmental math.
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DEDICATION
This is dedicated to my wonderful parents Margaret and John who never gave up on me when I was growing up and taught me to always reach for the stars. This is for my late aunt Mary Patricia Just who always believed in me and helped me to believe in myself. This is for Mr. Buck Showalter and the 2012 Baltimore Orioles who showed this country that success can be achieved through resilience, hard-work, and dedication.
Finally, this work is dedicated to my beautiful wife Lisa who showered me with love and support when completing this dissertation and this doctoral program.
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ACKNOWLEDGEMENTS
I would like to acknowledge my dissertation chair, Dr. Michele Welkener for working tirelessly with me throughout this entire process. Dr. Welkener’s patience, expertise, and attention to detail played a major role in the completion of this dissertation.
I also wish to acknowledge my other committee members, Dr. Carolyn Ridenour, Dr.
William Place, and Dr. Aparna Higgins for their time and dedication to helping me complete this project.
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TABLE OF CONTENTS
ABSTRACT…………………………………………………………………….iii
DEDICATION………………………………………………………………….v
ACKNOWLEDGEMENTS…………………………………………………….vi
CHAPTER
I. BACKGROUND OF THE STUDY…………………….……....…….....…..1
Introduction………………….………….……………….…....…...... ……1
Definition of Key Terms…………………...…………..……………………1
Statement of the Problem…………………….……………………...….…...4
Significance of the Problem……..…………….…………….………………7
Research Purpose…………………………………………………………..11
Delimitations…………………………………………………………...…..11
Chapter Summary…………………….…………………………..………..12
II. LITERATURE REVIEW………………………………………....…….…13
Introduction………………………………………………………..….…...13
Overview of the History of Developmental Education………..……..……14
Literature on Developmental Mathematics Students………….…….……..21
Literature on Developmental Mathematics Faculty…………..……………27
Literature on Best Practices in Developmental Mathematics……………...30
Course redesign………………………..….…….………..……..……...31
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Compressed courses………………………….………..……….…32
Acceleration…………………………………………...………….33
Statway and quantway………………………….……………...... 35
Technology in developmental mathematics………………….……….38
Partially and fully computer-based courses……….….…...... …..39
Distance learning………………….…………………..……..…...41
Calculator usage…………………….…….…….…….………….43
Best practices that supplement traditional instruction……...…...... 45
Supplemental instruction…………………..…………………….45
Learning communities………….………..………………………49
Student outreach…………….……………….…………………..52
Classroom activities and strategies……….……………...……...54
Similar Best Practice Studies………………………………….…….…….60
Chapter Summary……………………………………...……..……...... 64
III. METHODOLOGY, METHODS AND DATA COLLECTION
PROCEDURES…………………………………….………….…….…….68
Introduction……………………………………………………..…...... 68
Methodology of Study………………………………………….……...... 68
Method of Study……………………………………………….…...... 69
Role of the Researcher………………………………………….……...... 70
Setting of the Study……………………………….…………….……...... 75
Rationale for Site Choice……………………………………..……….…..86
Participant Selection………………...……………….…………..…….….88
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Data Collection Procedures……………………………..…….…...... 91
Method of Data Analysis……………………..……..….…...………...... 98
Strategies to Ensure Trustworthiness……….……………….…………...98
Limitations……………………………………...……………………….106
Chapter Summary……………………………………………………….107
IV. FINDINGS…………….……….……………………………………….108
Introduction……………………………………………………………..108
Inhibitors to Students Success in Developmental Mathematics…...... 108
Severe underpreparedness…………………………………..…...... 109
Behaviors that thwart success…………………….…….…………...112
External issues………………………...……………....…………….116
General Best Practices…………………………………………………..117
Communication with students…………………………...…...... 117
Communicate with students regularly regarding their progress.…118
General meaningful interaction…………..…….…...………...... 123
The art of organization…………………………………..…...…...... 126
The development of student organizational skills..……….….…..127
Departmental organization………………...………….……..……135
Collaborative learning…………………..…………….………...... 136
General group work………………..…………...…….…..………136
Guided inquiry………………………...……..………….…..……139
Frequent low stake assessments……...……….…………..…...... 144
Technology supplements………………....……..…………………..149
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Content-Specific Best Practices………………….…….………..……....151
Mnemonics and memorable wording……….…………..……….……152
Manipulatives, visuals, and real-life applications……….……………156
Accelerated Instruction…………………………..….……………….….164
Acceleration: a good fit……………………….……………………...165
Acceleration: a poor fit……………………….…………….…...... 166
Acceleration: the bottom line……………….…………..…….….…..168
Improving Institutions to Enhance Student Learning in Developmental
Math……...………………………………………………………………170
Sharing of best practices………………………………...... ………….170
Less administrative interference……………………….….….……….171
Early intervention……………………………………...... ……….…..174
Chapter Summary………………………………….....………………….175
V. DISCUSSION OF FINDINGS…………………………....……...... 178
Introduction…………………………….….……..………...….…………178
Conclusions, Implications, and Recommendations…………...…...... 179
Communication with students …………..….….…….…...………….179
The importance of student and instructor organization……...... 181
Frequent low stake assessments coupled with student outreach……..183
The muddy waters of collaborative learning……………..…………..184
Appropriate technology supplements…………...………..…………..187
Go the extra mile with creativity………………...………..…...... 188
Policy implications………………....…………………………...... 189
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Mandatory advisement…………………………...………………..189
A certain degree of uniformity…………………………………….190
Acceleration: a best practice but not a universal quick fix………..191
The importance of respecting instructor comfort level and input…194
Professional development……………………………...…...……..197
The limitations of best practices………….……………………….199
Reactions from the Researcher……………………………….……...... 202
Ideas for Future Research………………………………...….………….204
Chapter Summary……………………………………...….…………….207
Concluding Comments……………………..…….……..…………...... 209
REFERENCES……………………………….………………………………211
APPENDICES
Appendix A- Invitation to Interview……………………………..…….….236
Appendix B- Initial Self-Report Questionnaire …………...…….………..238
Appendix C- Pre-Interview Questions…………………...……….…….…240
Appendix D- Faculty Demographics Form…………………………..……242
Appendix E- Face-to-Face Interview Questions……………….……….…243
Appendix F- Invitation for Member Checking………………….……..….246
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CHAPTER I
BACKGROUND OF THE STUDY
Introduction
In this dissertation, I address a national crisis in American higher education: student success rates in developmental mathematics. Furthermore, this work highlights and describes best practices in developmental mathematics to assist community college leaders and faculty in coping with this issue. In this chapter, I identify key terms, the research purpose and questions, and elaborate on the significance of the problem of developmental mathematics.
Definition of Key Terms
According to Boylan and Bonham (2007), “Developmental education refers to a broad range of courses and services organized and delivered in an effort to retain students and ensure the successful completion of their post-secondary goals” (p. 2). Boylan and
Bonham (2007) pointed out that developmental courses consist of content that is below college level and usually contain course numbers that are below 100 (i.e., Math 099).
The terms “developmental”, “remedial” and “college preparatory” are often used interchangeably in post-secondary education. Therefore the aforementioned terms are used interchangeably in this dissertation and refer to courses below college level. The term “remediation” refers to the efforts that lead to successful completion of a developmental mathematics course or course sequence.
1 Developmental mathematics refers to courses that the individual institution considers to be below college-level mathematics. Content in developmental mathematics generally consists of arithmetic and algebra (Boylan, 2011; Fulton, 1996; Hagedorn,
Siadat, Fogel, Nora & Pascarella, 1999). However, it is noteworthy that some content may vary between institutions (Boylan, 2011). This is especially true for higher level algebra concepts. For example, some institutions consider quadratic equations to be developmental course content while other institutions place them in college-level mathematics. The structure of developmental mathematics courses may vary between institutions as well. In some institutions developmental mathematics courses are combined with developmental reading and English courses to form a stand-alone department of developmental education. In other institutions, developmental mathematics courses are paired with college-level mathematics courses to form a department of mathematics.
Developmental mathematics course grades generally appear on students’ transcripts. Some institutions include developmental mathematics courses when calculating a student’s quarterly or semester grade point average (GPA). However, developmental mathematics courses usually do not count toward degree program requirements or graduation GPA.
The site of focus for this dissertation is a community college. Community colleges are public, two-year institutions that provide open access to all students.
Mission statements are generally broad as community colleges tend to offer something for all students. In a community college, it is common to see a diverse group of classes such as welding, philosophy, fire safety, and English. Community colleges offer a
2 plethora of associate degrees but also certificates as well. A high school or equivalency diploma may or may not be required for admission to a community college (Thelin,
2004). Arenson (2006) reported that as of 2004, there were nearly 400,000 students who were enrolled in an institution of higher education who did not possess a high school diploma or an equivalency degree. This accounts for 3% of all community college students.
Community colleges are generally composed of very diverse student populations from various ethnic backgrounds; many of these students possess limited English proficiency. Community college students have often experienced a lack of success in their previous academic pursuits. Many community college students are employed full- time with family commitments and limited time and resources. Consequently, community colleges offer flexible scheduling, low tuition, financial aid, and a plethora of student support services (Phillippe & Sullivan, 2005).
Throughout this dissertation, the term “faculty” generally refers to those who teach developmental mathematics courses. Community college faculty generally teach part-time or full-time. Each institution sets the teaching load requirement for an employee to be considered full-time. In this study, the terms part-timers and adjuncts are used synonymously. Adjuncts have their contracts renewed each quarter or semester and generally do not carry a full teaching load. Often adjuncts hold more than one job. Full- time faculty may be either contingent, tenure-track, or tenured. Contingent faculty carry a full-time teaching load but have their contracts renewed each year. Tenure-track faculty are individuals who carry a full-load and are on the path to tenure. The number of years in which a faculty member is eligible for tenure varies among institutions. Tenured
3 and tenure-track faculty are often referred to as permanent faculty. The term “instructor” also refers to those who teach developmental mathematics classes; instructors and faculty will be used as synonyms.
The term “students” represents individuals who pay for a class and receive a grade, or individuals who register for a class and withdraw. This term does not include individuals who audit a class.
Success rates signify the percentage of students who have passed a class, a course sequence, or a degree program successfully. Each institution defines the specific grade requirements for a student to be successful in a class or a degree program. Retention rates refer to the percentage of students who enrolled in a course and completed the course through the final exam. This excludes students who withdrew from the course.
Graduation rates specifically refer to the percentage of students who have successfully graduated from an institution.
Lastly, the term “best practices” describes methods, techniques, or strategies that have consistently shown positive results such as increased student success rates and student retention.
Statement of the Problem
Most degree programs in community colleges contain some sort of mathematics requirement. Therefore, students must pass a certain number of mathematics courses to obtain a degree (Hall & Ponton, 2005). Mireles (2010) articulated that most degree programs require at least one college-level mathematics course in order to graduate.
Each year, however, many students who enter a community college place into a developmental mathematics class. Sixty percent of the institutions that offer
4 developmental mathematics courses contain sequences of at least two courses. Some developmental mathematics course sequences are as high as four classes (National Center for Education Statistics [NCES], 2003).
In 2006, Noel-Levitz reported that nationally, 75% of all community college students enroll in at least one developmental mathematics course. More specifically, the
Virginia Community College System has reported as many as 61% of incoming students require a developmental mathematics course (Curtis, 2002). Biswas (2007) asserted that more than 80% of incoming students consistently place into developmental mathematics at Housatonic Community College in Bridgeport, Connecticut. According to Corash,
Baker, and Nawrocki (2006), in the fall of 2004, the Colorado Community College system witnessed a total of 83% of their first-time students placing into developmental mathematics. In Arizona, this has been the case for at least 91% of the incoming students in the Maricopa and Pima Community College Districts (Puyear, 1998). In 2006, data from 35 community colleges that participated in Achieving the Dream, a national initiative geared toward improving community college success rates, revealed that at least
61% of students at those colleges were required to take at least one developmental mathematics course. At some of those colleges, as many as 89% of the students needed at least one developmental mathematics course (Ashburn, 2007).
Unfortunately, the student success rates for developmental mathematics classes are particularly low. In a national study which drew on college transcript data, Attewell,
Lavin, Domina, and Levey (2006) reported that only 30% of all students pass all of the developmental mathematics courses in which they enroll. Several community college systems have been struggling with student success rates in developmental mathematics.
5 In the fall of 2006, only 58% of the students succeeded in developmental mathematics in the Wyoming Community College system (The Wyoming Community College
Commission and the University of Wyoming, 2011). Also in the fall of 2006, overall success rates in developmental mathematics courses in the Indiana Community College system were as low as 53%. More specifically, success rates for developmental mathematics in the community colleges in the Indianapolis region of Indiana were a paltry 29% (Office of Institutional Research and Planning, 2007). According to Hinds
(2009), in 2007, success rates in developmental mathematics for the New York City community colleges were as low as 36%. The Virginia Community College System has witnessed success rates as low as 29% in the lowest level developmental mathematics class (Waycaster, 2001). In a study of 107 California community colleges, Bahr (2008) revealed that 75% of students who attempted a developmental mathematics course were not successful.
Many students who place into a developmental mathematics class do not persist in college. Overall retention rates are particularly dreadful for developmental mathematics students. In fact, Bahr (2008) found that 81.5 % of students who attempted a developmental mathematics course did not complete a degree or transfer to another school. In 1997, Boylan reported that the one-year retention rate for students who did not pass their first developmental mathematics course was 9.6%. This was in sharp contrast to the one-year retention rate of 66.4% for those students who successfully passed their first developmental mathematics course. In 2008, Fike and Fike confirmed that students who are not successful in their first developmental mathematics course are very likely to withdraw from college within one year. Bailey, Jeong and Cho (2010) revealed that only
6 33% of the students who are referred to a developmental mathematics class complete the required sequence within a three-year period. Their study revealed that in a required sequence of three courses or more, only 17% of students successfully completed the sequence in three years. Boylan (2011) mentioned that only 12% of students who attempt a developmental math sequence of three courses or more pass each of the three courses the first time.
Significance of the Problem
Lack of success in developmental mathematics is discouraging for students. It also becomes expensive for students to repeat courses as they spend money and accumulate debt. Students receiving financial aid are often required to carry a certain number of credit hours and maintain a certain GPA. Therefore, when students continue to fail their developmental mathematics courses, the government discontinues their financial aid (Bailey, 2009). Students also begin to doubt their academic ability. These deficits in turn affect their persistence, and they often drop out of college entirely
(Boylan, 2011).
The low developmental mathematics success rates are becoming particularly detrimental to the community college and to society overall. The fact that so many students require developmental mathematics courses and need to repeat them because of failure means that more and more courses must be offered. This reality has become quite costly. In 2009, Roueche and Waiwaiole reported that the annual cost of developmental education in community colleges is between $1.9 billion and $2.4 billion. It is noteworthy that while tuition accounts for community college revenue, it is only a small portion. According to Weisbrod, Ballou, and Asch (2008), state and local appropriations
7 are the largest source of revenue for community colleges. Local appropriations include local tax levies as citizens within the community college taxing district pay property taxes to fund the operation of local community colleges (Waller, Glasscock, Glasscock &
Fulton, 2006). In short, developmental mathematics has become costly to state and local taxpayers.
The cost of developmental mathematics is eating into an already shrinking operating budget for most community colleges. This is because public support for community colleges has been on the decline for quite some time. According to the
American Council on Education (2004), between 1980 and 2000 the state support for public four-year colleges and community colleges decreased from 46% to 34%. State funding has continued to decrease over the first decade of the 21st century. Alexander
(2006) articulated that all of the states have been hit hard by funding reductions.
According to Hebel (2010), since 2008, Alabama, South Dakota, New Mexico, South
Carolina, Florida, Arizona, Virginia, Nevada, Utah, and West Virginia have received the largest cutbacks in higher education funding. Hebel (2010) maintained that the main reason for this is that Medicaid has simply exploded and consumed much of the states’ budgets. Rizzo (2006) stated that “Medicaid costs have skyrocketed as a result of large increases in caseloads, escalating prescription costs, and lagging support from the federal government” (p. 5). Hebel (2010) and Rizzo (2006) asserted that escalating prison costs have been another factor in decreased funding for higher education. According to the
American Council of Higher Education (2004), state spending on corrections grew six times the rate of spending on higher education between 1985 and 2000.
8 Community colleges have been struggling financially for a variety of reasons.
Certainly, the decline in state funding has been damaging; however, community colleges have also faced increased costs to support soaring enrollment. Again, student tuition is only a minor source of revenue for community colleges as it is so low. According to
Mullin and Phillippe (2009), the number of community college students in America increased by 11.4% from 2008 to 2009 and 16.9% from 2007 to 2008. Overall, full-time student enrollment increased by 24.1% between 2007 and 2009 in community colleges.
The low success rates in developmental mathematics have gained national attention. Boylan (2008) warned that governors and state legislators are running out of patience and are putting pressure on institutions to raise student success rates. Apling
(1993) stressed that remediation is costly to tax-payer dollars. Bahr (2008) pointed out that that many have argued that tax-payers should not have to pay so much for students to learn the same material twice since all of the material in developmental mathematics is covered in elementary or high school. Weisbrod et al. (2008) asserted that many states have begun to impose funding formulas on public institutions of higher education. More specifically, schools need to show higher success and retention rates to receive more funding. Both state legislators and higher education boards are making institutions more accountable for successful remediation of students (Arendale, 2003). Therefore, to continue to receive adequate state funding, community colleges must explore ways to improve student success rates in developmental mathematics classes.
Despite the discouraging statistics, developmental mathematics can have a positive impact on students. Bailey et al. (2010) articulated that students who successfully completed developmental mathematics requirements are more likely to pass
9 their college-level mathematics requirements. McClenney (1997) and Lesik (2007) reported that participating in a developmental mathematics course has an overall positive impact on student retention as students who complete their developmental mathematics course requirements are more likely to persist in college. Higbee and Thomas (1999) claimed that as students proceed to pass their developmental mathematics courses, their math anxiety decreases. Bahr (2008) even went as far as to articulate that developmental mathematics “has the capacity to fully resolve the academic disadvantage of math skill deficiency” (p. 442). In summary, developmental mathematics is certainly a valid cause, and it is worthwhile to explore methods of improvement.
Future research must be devoted to improving developmental mathematics.
According to Bahr (2008), “Identifying methods of increasing the successful remediation in mathematics should be a topic of central concern to all stakeholders in the community college system” (p. 446). Furthermore, it is imperative to examine the best practices by developmental mathematics faculty. Wheeler and Montgomery (2009) found that students generally view their teacher as the most important factor in learning mathematics. Wheland, Konet, and Butler (2003) stated that “instructors must develop effective methodologies to help underprepared students” (p. 26). Depree (1998) also stressed the importance of investigating teaching methods that may improve course completion rates in developmental mathematics. As far as setting, Ashby, Sadera, and
McNary (2011) suggested that a best practice study for developmental mathematics should be conducted at a community college as community colleges offer the greatest amount of developmental mathematics classes. As students continue to place into developmental mathematics at a high rate in community colleges, it is imperative to
10 identify and gain an in-depth understanding of best practices in developmental mathematics to help future students find success.
Research Purpose
In this study, my purpose was to gain an in-depth understanding of the best practices utilized by a group of developmental mathematics instructors at an urban community college. Through qualitative research, I garnered a comprehensive description of the methods, techniques, and strategies that a group of developmental mathematics instructors believe increase student learning. I also examined how one sample of developmental mathematics instructors employed such practices to enhance student success. It is worthy of note that I did not categorize or identify many of these practices in advance; such practices emerged from interviews with developmental mathematics faculty. My findings from this study are intended to contribute to the knowledge base of developmental mathematics and post-secondary education. Guiding this study were the following research questions: What are the best practices utilized by a group of developmental mathematics instructors at an urban community college? How do these instructors employ such practices to enhance student learning?
Delimitations
This study took place at Sinclair Community College in Dayton, Ohio. My rationale for this setting is explained in Chapter Three. The population was restricted to part-time and full-time developmental mathematics faculty. Furthermore, the study included only part-time and full-time faculty who have taught at least six classes since the beginning of fall term in September 2010. Faculty who have consistently fostered student success were given priority for selection. More specifically, this included faculty
11 who regularly have student success rates of 60% or higher. The rationale for this specific percentage is explained in greater detail in Chapter Three.
Chapter Summary
Clearly, the student success rates in developmental mathematics constitute a national crisis in American higher education. The majority of students who enter a developmental mathematics course do not complete the course or the required sequence of courses. The low success rates in developmental mathematics are certainly discouraging for students but have also become increasingly expensive for students, colleges, and taxpayers as students must repeat their courses several times. This situation is extremely detrimental for colleges as state legislators and other officials are losing patience with developmental education. The future success rates of developmental mathematics will no doubt have an effect on the state funding of institutions. Therefore, to assist community college faculty and administrators with better serving developmental math students, the research purpose of this dissertation was to gain an in-depth understanding of the best practices utilized by a group of developmental mathematics instructors at an urban community college.
12 CHAPTER II
LITERATURE REVIEW
Introduction
In this chapter, I review relevant literature related to developmental mathematics.
First, I will provide context by outlining the history of developmental education. The focus is on how developmental education has evolved since the inauguration of American higher education. Next, I analyze literature that focuses on developmental mathematics students. This literature review highlights why such a high number of students place into developmental mathematics classes and why there are such high failure rates. Because developmental mathematics faculty served as the participants for this study, I then examine works relating to the profile of developmental mathematics faculty. Next, I review writings on the existing best practices in developmental mathematics. Existing best practices are split into three categories: overall course redesign, technology in developmental mathematics, and practices that supplement traditional instruction.
Finally, I review various studies that relate closely to the study conducted in this dissertation, and I discuss how this dissertation adds to the knowledge base of developmental education.
13 Overview of the History of Developmental Education
The practice of developmental education can be traced back to the birth of
American higher education. Institutions of higher education have been serving underprepared students since Harvard opened its doors in 1636 (Boylan & White, 1987).
In the 17th century, most courses were instructed in Latin, and most books were only available in Latin (Thelin, 2004). According to Boylan and White (1987), “the learning of an academic language was not a high priority for colonists attempting to carve a homeland in the wilderness” (p. 3). As a result, many students entered college underprepared.
For students to be successful in their studies, they needed to understand Latin.
Harvard College began to provide tutors in Latin for these underprepared students.
Tutors were typically young men who had recently received a baccalaureate degree and were preparing for a career in the ministry. Tutors were generally with their students throughout the day as they ate in the same dining halls and slept in the same chamber
(Brubacher & Rudy, 1976). According to Boylan and White (1987), tutorials in Latin persisted well into the 18th century as Latin continued to be the language of instruction, and scholarly works were generally available only in Latin. In the 17th and 18th century, programs for underprepared students were simply labeled “tutoring” (Arendale, 2002).
However, Brubacher and Rudy (1976) conveyed that after the American Revolution, college course instruction and literature were generally in English.
The need for remediation continued into the 19th century as more colleges continued to open. It is notable that there were no universal college entrance requirements until the late 19th century (Brubacher & Rudy, 1976). According to
14 Brubacher and Rudy (1976), colleges at that point in time were generally tuition-driven.
Therefore, anyone who had the funds to attend college was able to do so without prior preparation. However, as colleges continued to grow, tutors were not able to meet the high demand of students in need of remediation (Boylan & White, 1987). Therefore, the
University of Wisconsin established the nation’s first formal college preparatory program in 1849. The program provided formal remedial courses in reading, writing, and arithmetic for students who lacked a sufficient background to succeed in their college courses (Brier, 1986). It is also noteworthy that by the mid-19th century, the label for programs for underprepared students was no longer tutoring. Colleges referred to such programs as pre-collegiate, college preparatory, and remedial. (Arendale, 2002). The need for remedial education grew in the late 19th century as higher education continued to expand. In 1862, the Morrill Land Grant Act was passed. This bill allotted land in several states to develop institutions of higher education to promote a liberal and practical education. Furthermore, the emphasis of instruction was to be on agriculture and mechanical arts (Goodchild & Weschler, 1997). Geiger (2005) maintained that this led to diversification of higher education institutions and, more importantly, a larger and more heterogeneous student body. According to Brier (1986), other colleges began to adopt the model from the University of Wisconsin, and by the late 19th century, more than 80% of the colleges and universities in the United States offered college preparatory programs.
In an attempt to raise academic standards and reduce the amount of college preparatory courses offered, the College Entrance Examination Board was established in
1890. However, many students were still not college ready; therefore, colleges and universities continued to offer college preparatory courses. However, colleges and
15 universities did begin to reduce the number of college preparatory courses offered as junior colleges emerged (Boylan, 1988). The purpose of a junior college was to provide students with a liberal arts preparation prior to enrolling in a bachelor’s degree program at a four-year college or university. Consequently, junior colleges offered remedial classes (Thelin, 2004). By 1940, 11% of all college students were enrolled in junior colleges (Geiger, 2005). In fact, Boylan (1988) stated that “by the 1940s, the college preparatory program had been largely replaced as a fixture in American higher education by junior colleges and college divisions within universities” (p. 2). According to
Maxwell (1997), college divisions were separate programs offered by various universities to prepare students who were deemed unfit for its regular program. Geiger (2005) specified that the University of Minnesota was the first to use a college division in 1932.
In 1944, the U.S. Government passed the Servicemen’s Readjustment Act, also known as the G.I. Bill of Rights. The government was concerned about the millions of veterans who were returning to potential unemployment. Therefore, the government allotted millions of dollars for the education and training of these war veterans (Thelin,
2004). Overall, several millions of the returning American war veterans from World War
II used the G.I. Bill to enroll in college (Olson, 1974). According to Boylan (1988), colleges and universities had become more selective by the middle of the 20th century in terms of admissions. However, many admissions officers preferred to give the veterans a chance rather than deny them access. As a result, colleges provided a greater variety of study skills and reading classes to accommodate the needs of veterans.
During the 1960s, for the first time in the history of higher education, colleges and universities were able to be highly selective in their admissions process. Admissions
16 offices were swarmed with a plethora of applicants who were college ready. Therefore, many colleges and universities were able to reduce the number of college preparatory courses that they offered. Despite this, programs for underprepared students surged in the late 1960s and early 1970s. Boylan (1988) claimed that at that point in time, colleges were referring to these programs as developmental, remedial, and learning assistance.
More specifically, however, by the early 1970s the term “developmental education” was born and was becoming more widely utilized as there was an increased focus on student development (Arendale, 2002; Boylan & Bonham, 2007). Public community colleges, which were open access and offered a variety of remedial courses, opened at a rate of one per week between 1965 and 1972 (Geiger, 2005). This resulted in part from the Higher
Education Act of 1965, which stemmed from President Lyndon Johnson’s War on
Poverty (Gladieux, King, & Corrigan, 2005). According to Boylan (1988), the nation began to focus on the poor and underserved. The government provided need-based aid for minorities and others who had been previously underrepresented in higher education.
Community and junior colleges greatly expanded their efforts to provide developmental education to all students. However, at this point, private junior colleges were losing ground to open admissions community colleges (Weisbrod et al., 2008).
During the 1970s and 1980s developmental education gained recognition as an academic discipline. According to Spann (1996), in 1976, the National Association of
Developmental Education (NADE) was funded from the W.K. Kellogg Foundation at
Appalachian State University. In 1980, NADE sponsored the establishment of the
Kellogg Institute for the Training and Certification of Developmental Educators at
Appalachian State University. This was the nation’s first professional development and
17 certification program specifically for developmental educators (Spann, 1996). Boylan and Bonham (2007) reported that in 1984, the National Center for Education Statistics
(NCES) published its first report on developmental education. This was important as the
U.S. Department of Education was finally acknowledging that developmental courses were significant enough to include in national research. Boylan and Bonham (2007) also mentioned that during the 1970s and 1980s NADE began to release several developmental education publications such as the Journal of Developmental Education and Research and Teaching in Developmental Education. Also, in 1986, the nation’s first doctoral program in developmental education was established at Grambling State
University in Alabama.
The recognition of developmental education continued to grow throughout the
1990s and into the next millennium. In 1990, the first national study of developmental education was conducted by NADE. The study gathered information from over 5,000 students from 120 institutions of higher education. Researchers identified relationships among methods, courses, services, organizational structures, and student outcomes
(Boylan, Bonham, Claxton, & Bliss, 1992). Boylan and Bonham (2007) stated that, “this study made a major contribution to improving practices in the field and enhancing the professionalism of developmental educators” (p. 3). Developmental education continued to surge at the turn of the 21st century. In 2003, NCES reported that developmental courses were offered at 98% of the nation’s community colleges and 80% of the nation’s public, four-year institutions. However, developmental classes were only offered at 59% of the nation’s private, four-year institutions.
18 As the 21st century has progressed, developmental education has become an endangered species at many four-year colleges and universities. Arendale (2001) claimed that many officials believe that developmental education is simply too costly and furthermore can water down the standards of a four-year college or university. Because students who enroll in developmental courses produce low success and retention rates, developmental education has a negative impact on the retention rates of four-year institutions (Bettinger & Long, 2004). Jacobs (2012) cited that since 2007, more than a dozen states, including Oklahoma, Nevada, Colorado, South Carolina, Louisiana, and
Tennessee, have restricted funding for developmental education at four-year institutions.
In 2014, Ohio will cease funding developmental classes at four-year institutions. Jacobs
(2012) further revealed that students who place into developmental courses in the aforementioned states are referred to or will be referred to community colleges. Bettinger and Long (2004) specified that since community colleges have traditionally served underprepared students, many officials believe that community colleges are a better fit for developmental students.
The turn of the century saw the beginning of non-government funded grants to improve dismal student success rates in developmental education. In 2003, the Lumina
Foundation, a private, Indianapolis-based group, assembled several dozen of the nation’s experts on community colleges. The discussion focused on improving student success and graduation rates at community colleges. Along with several other private foundations such as the W.K. Kellogg Foundation, the Boston Foundation, and the
Knowledge Works Foundation, the Lumina Foundation provided millions of dollars to community colleges across the country. The initiative was named Achieving the Dream:
19 Community Colleges Count (Ashburn, 2007). Immerwahr and Friedman (2005) mentioned that Achieving the Dream focuses on enhancing the “achievement of community college students, especially those facing the greatest obstacles” (p. 2).
Achieving the dream provides attention to low-income students and students of color.
Colleges that participate in Achieving the Dream examine their data and success rates and identify gaps and areas that need improvement. Community college experts, also known as coaches, then work with community college leaders and faculty in implementing strategies and change initiatives to increase student success.
The Gates Foundation has also become involved in improving developmental education. Melinda Gates, co-chairman of the Bill and Melinda Gates Foundation, has reported pledging $110 million to improve developmental education. This money was allotted to develop groundbreaking models for developmental education (Ashburn, 2007).
According to Collins (2011) in 2009, the Gates Foundation teamed with the Lumina
Foundation to form the Developmental Education Initiative (DEI). Several community colleges have begun to participate in DEI grants. Through DEI grants, philanthropic organizations such as Gates and the Lumina Foundation are supporting community colleges to redesign their developmental education programs to increase student success.
Collins (2011) further articulated that developmental education programs are searching for ways to move their students faster through their developmental courses. The focus has been on developmental English and mathematics courses. However, developmental mathematics has received the greatest amount of attention because of the low success rates. The DEI has even been nicknamed Achieving the Dream Phase Two as many of the institutions who took part in Achieving the Dream are now part of the DEI.
20 Literature on Developmental Mathematics Students
While public community colleges are open access, incoming students are generally still required to take some sort of placement test as is imperative to accurately place students into the courses in which they have the maximum chance for success
(Boylan, 2008; Diaz, 2010; Donovan & Wheland, 2008). The three most common placement tests that are currently utilized are Compass, Accuplacer, and American
College Testing (ACT). James (2006) asserted that the predictive validity of a placement test is the degree to which the test scores predict a performance score at a later time. The placement test results are directly correlated with course performance. Furthermore,
James (2006) found Accuplacer to be a reliable predictor of student success in developmental mathematics and therefore a reliable instrument. Similarly, Donovan and
Whelen (2008) claimed that both the Compass and ACT exams are good predictors of student success. It is worthy of note, however, that placement requirements for specific courses vary among institutions. Therefore, it is likely that the same student could place into a developmental mathematics course at one institution and a college-level course at another (Boylan, 2011).
Why do so many students place into developmental mathematics courses?
Hagedorn et al. (1999) claimed that students in remedial classes reported studying less in high school and achieved lower high school grade point averages (GPA) than their peers who placed into college-level classes. Also, remedial students received less encouragement to study in high school and enroll in college than students who placed into college-level mathematics. Students in remedial classes also reported receiving less support from their teachers and counselors than students in college-level classes. This is
21 especially true for minority students. Redden (2010) articulated that many students who place into a developmental mathematics course have been out of school for many years and simply do not retain the content.
In a New York Times article, educational journalist Winerip (2011) mentioned that there are students who excel in their high schools but still place into developmental mathematics classes. For example, the graduation rate in the New York City Public High
Schools has risen significantly; however, more students are placing into developmental mathematics courses. According to Winerip (2011), many students felt underprepared when taking their college placement test. Furthermore, many students become calculator-dependent in high school; however, on their college placement exams, they are forbidden to use the calculator (Boylan, 2011; Hopkins, 1977). Winerip (2011) further conveyed that many students believed that the main goal of high school was to simply push them through. Stigler, Givven, and Thompson (2010) also found that many students who place into developmental mathematics did pass algebra in high school, but these do students do not pass the arithmetic and algebra portions of their college placement test.
Stigler et al. (2010) concluded that many of these students were simply taught how to conduct the mathematical procedures; however, they never achieved a conceptual understanding of the material. Rather than thoroughly understanding the material and how it relates to real life, students temporarily memorized a set of procedures that they soon forgot.
Howell (2011) found that many developmental students successfully passed their high school classes. Furthermore, Howell discovered a significant relationship between high school teachers’ attributes, such as experience and educational attainment, and
22 remediation rates of college students. More specifically, Howell asserted that students who had high school mathematics teachers who did not possess master’s degrees and were operating under emergency credentials or teacher waivers were more likely to test into a developmental mathematics course.
There seems to be a variety of reasons for students’ lack of success in developmental mathematics classes. Poor attendance certainly is a key factor. Smith et al. (1996) and Merseth (2011) maintained that many students report feeling bored in class. Because the content is basic, some students may feel that they do not need to attend class. However, Smith et al. (1996) also noted that after missing several classes, some students may fall behind and either fail or withdraw from the class. Boylan (2011) stated that the design of developmental mathematics is linear. For example, students must master the material in the second chapter before progressing to the third chapter.
Therefore, poor attendance may create gaps that thwart the mastery of content. This is consistent with the findings of Gupta, Harris, Carrier, and Caron (2006) as well as those of Wheland et al. (2003) that students who miss more classes have lower success rates.
Gonzalez (2010) stated that many students simply become frustrated when placing into a developmental mathematics class and lose their drive for a college education. According to Redden (2010), this is especially true of students who scored on the high end of the placement test and narrowly missed placing into a college course.
These students, who knew most of the material, still placed into a developmental mathematics class. Therefore, they become bored and frustrated. Wheland et al. (2003) mentioned that there is a unified belief among students that developmental mathematics
23 classes will have little impact on their college career. Consequently, students do not put forth maximum effort.
Researchers have cited student apathy as another reason for failure or non- completion of developmental mathematics courses. On the one hand, Stigler et al. (2010) concluded that students who place into developmental mathematics classes seem to understand that they need to pass the class in order to earn a degree or achieve their career goals; some students also have the potential and ability. However, many developmental math students lack the motivation needed to succeed. Students’ low motivation and overall poor attitude negatively affect their success rates in developmental mathematics (Ferren & McCafferty, 1992; Higbee & Thomas, 1999). Ferren and
McCafferty (1992) claimed that many students will fall into a pattern of not completing some of the required work, failing a test or multiple tests, and then cease trying.
Lack of student engagement has also been associated with non-success. Smith et al. (1996) found that students who exhibited loner behavior had higher failure and attrition rates. That is, students who did not interact as much with their classmates or the instructor and who sat in the back of the room had lower success rates than their peers who interacted regularly with others and sat in the front of the room. Merseth (2011) specified that many unsuccessful developmental mathematics students have weak ties with their peers and with faculty. This is consistent with Tinto’s (1993) finding that isolation is positively associated with first-year student non-success and attrition.
Study and work habits seem to impact student success in developmental mathematics classes as well. Higbee and Thomas (1999) mentioned that many developmental mathematics students simply never learned how to study. Smith et al.
24 (1996) revealed that many unsuccessful students in developmental mathematics classes never take notes. Stigler et al. (2010) conveyed that many developmental mathematics students simply do not learn and study mathematics in the most effective ways. Students will memorize formulas and facts, but they do not know how to make connections among topics. Pang (2010) pointed out that many students never formed the necessary work habits when studying arithmetic; therefore, arithmetic continues to be a constant barrier.
This is consistent with Miles’ (2000) claim that at one time, poor arithmetic skills were a minor problem in developmental mathematics; now they are a major problem. According to Boylan, Saxon, and McLeod (2006), the number of students placing into developmental courses has not changed significantly over the years. The level of under preparedness has simply increased. Burley, Butner, and Cejda (2001) noted that many developmental students have various learning deficiencies that hinder their ability to be successful in mathematics. Colleges must have tests and facilities in place to accommodate these students.
Researchers have discovered that math anxiety is very common in developmental mathematics students and is often a barrier to success. Richarson and Suinn (1972) described math anxiety as “feelings of tension and anxiety that interfere with the manipulation of mathematical problems in a wide variety of ordinary life and academic situations” (p. 551). Woodard (2004) found that “math-anxious students display symptoms such as nervousness, inability to concentrate, a blank mind, and a feeling of sickness when they are confronted with taking a math test” (p. 1). Taylor and Brooks
(1986) argued that these feelings can lead to poor performance in or even avoidance of a mathematics class. Diaz (2010) articulated that past experiences, such as intimidating
25 teachers and poor academic performance, can lead to math anxiety. Female students have exhibited higher levels of math anxiety than male students (Campbell & Evans,
1997; Woodard, 2004). Smith (1979) mentioned that many women believe that they are unable to succeed in mathematics because of their gender. Furthermore, many women believe mathematics is a male-dominated world (Taylor & Brooks, 1986). Findings for math anxiety in relation to student age have been mixed. Royce and Rompf (1992) claimed that students 25 and older exhibit significantly more math anxiety than students under 25. Woodard (2004), however, contradicted this finding and reported no significant difference in math anxiety levels between students under 25 and students 25 and older.
Employment obligations are another aspect researchers and faculty have posited for a lack of student success and attrition. According to Johnson, Rochkind, Ott, and
DuPont (2009), 60% of community college students who fail to graduate mentioned that they had to work full-time to support themselves and other family members. Many of these students reported getting little to no financial assistance from their parents.
Immerwahr, Friedman, and Ott (2005) also noted that balancing work and school simply becomes too much for these students; many students in developmental courses are enrolled in two or three classes when they do not have sufficient time for one class.
As far as gender, in years past failure rates among women were higher than males in developmental mathematics classes. There is still an overrepresentation of women in developmental mathematics (Hagedorn et al., 1999; Topper, 2008). However, Topper
(2008) conveyed that women are now outperforming men in developmental mathematics.
More specifically, women have higher GPAs and are completing more courses.
26 In terms of ethnicity, Hagedorn et al. (1999) asserted that there is an overrepresentation of Black and Hispanic students in developmental mathematics classes.
Adelman (2004) estimated that 46% of Black students and 51% of Hispanic students enroll in at least one developmental mathematics course. This contrasts sharply to 31% of White students and 29% of Asian students. Overall, Bahr (2010) found that that White students are 60% more likely to pass a developmental mathematics class than Black or
Hispanic students. Bahr (2010) mentioned that Black and Hispanic students have the lowest achievement rate among all ethnic groups, in mathematics from kindergarten through twelfth grade. Therefore, Bahr (2010) suggested that these students simply carry this disadvantage into postsecondary developmental mathematics.
Literature on Developmental Mathematics Faculty
The academic background of developmental mathematics faculty varies greatly.
Because there are very few pre-service programs in this country that are geared specifically toward developmental education, many developmental mathematics faculty have academic backgrounds in mathematics or education but not specifically developmental mathematics. Consequently, any training faculty receive toward developmental studies tends to be more in-service rather than pre-service (Breneman &
Haarlow, 1998). This has been an area of concern. Boylan (2008) maintained that developmental education is not the placement for inexperienced faculty who have not worked with underprepared students, and search committees should seek faculty members with specific experience and training in developmental mathematics. Boylan and Saxon (2005) argued that it is crucial for inexperienced developmental education faculty to receive intense and thorough training and mentoring.
27 The collegiate background of developmental mathematics faculty has been debated as well. Developmental mathematics faculty either possess a bachelor’s or a graduate (master’s or Ph.D.) degree. This requirement is generally set internally by the specific institution. Fike and Fike (2007) found that developmental mathematics students taught by faculty members with only a bachelor’s degree achieve lower grades than students taught by faculty with graduate degrees. Fike and Fike (2007) stated that
“mathematics faculty with advanced degrees may have a better understanding of mathematical principles and concepts and convey this understanding in their instruction”
(p. 7). However, this conclusion contradicted the findings of Gupta et al. (2006), who reported that developmental mathematics students who were taught by a faculty member with a bachelor’s degree received higher grades than those students taught by faculty members with a graduate degree.
Like most community college faculty, developmental mathematics faculty are composed of part-time (or adjunct) and full-time faculty (contingent and permanent).
However, in recent years, there has been an increase in the number of adjunct faculty and a decrease in the number of permanent faculty in community colleges (Levin, Kater, &
Wagener, 2006; Townsend & Twombly, 2007). Of course, this issue has affected all institutions of higher education. Nationally, public and private four-year schools and public two year schools have seen a significant decrease in the number of permanent faculty over the past 20 years (Altbach, 2005; Ehreberg & Zhang, 2006; Weisbrod et al.,
2008). Weisbrod et al. (2008) specified that many higher education leaders claim it is more cost-effective to employ adjunct faculty. Permanent faculty are costly in that their salaries increase significantly over time and because of escalating health benefits. With
28 state funding for public institutions steadily declining, many higher education leaders feel this is a necessary move.
The increased reliance on adjunct faculty and the overall employment status of developmental mathematics faculty has drawn some attention. In community colleges, only 42% of developmental mathematics courses are taught by full-time faculty, whereas
91% of advanced level mathematics courses are taught by full-time faculty (American
Mathematical Association of Two-Year Colleges [AMATYC], 2006). Fike and Fike
(2007) found that there is no significant difference in student success rates between adjunct and full-time faculty. More specifically, students are not adversely impacted by the increased numbers of adjunct faculty. However, this contradicts the findings of
Penny and White (1998) that students who are taught by full-time faculty have higher success rates. Boylan and Saxon (2005) argued that developmental mathematics courses should be taught primarily by permanent faculty, and that developmental education must be considered a priority by the institution. Because developmental education students are the most at risk, they therefore require the best instruction. Permanent faculty possess the most experience and training when working with developmental education students; therefore, those courses should be taught by permanent faculty (Boylan & Saxon, 2005).
Developmental mathematics faculty have expressed frustration over the abysmal success rates of their students. McClenney (2009) conveyed that developmental mathematics faculty feel a sense of helplessness in regard to success rates. Many faculty members believe that students are not successful because they are underprepared.
Immerwahr and Friedman (2005) conveyed further frustrations of developmental mathematics faculty. Faculty are frustrated that students may not seem to be aware of
29 what it takes to achieve a passing grade. Some students may fail all exams and not complete homework assignments but still be surprised that they failed the course. Both
McClenney (2009) and Immerwahr and Friedman (2005) stated that many faculty members believe that some student failure is acceptable. Immerwahr and Friedman
(2005) specified that some faculty members believe that failure can be a learning experience for students.
Literature on Best Practices in Developmental Mathematics
Pedagogical beliefs of developmental mathematics vary. There are some faculty who believe that fundamental skills should be presented as step-by-step procedures and then reinforced by drill and practice. These faculty members believe that this is the most effective means of gaining fundamental skills (Krantz, 1999). However, Johnson and
Johnson’s (1991) findings challenge this belief as they discovered that non-traditional instructional methods such as collaborative learning impact student learning more than rote memorization. Boylan (2002) articulated that lecture is the most common form of instruction in developmental mathematics. He further claimed that developmental students are a diverse group and expressed concern that the diversity of the group is not being accommodated by the heavy reliance on lecture-based instruction. However,
Boylan (2002) specified that lecture need not be abandoned as it can lead to student learning; it simply should not be the sole source of instruction. According to Boylan
(2002), best practice instructors use a vast array of pedagogical practices. Mireles (2010) and Epper and Baker (2009) echoed this belief and maintained that developmental mathematics students need to gain both concrete and abstract problem-solving skills.
30 Course redesign.
In an effort to move students through their developmental mathematics course sequence and into their college-level mathematics courses quicker, many institutions have initiated redesign projects for their developmental mathematics courses. As a result, more developmental mathematics programs now offer compressed and accelerated courses. According to Edgecombe (2011) compressed courses allow students to complete multiple courses in one semester or quarter. Again, in a traditional developmental mathematics course sequence, students may be required to complete stand-alone arithmetic and multiple algebra classes. A compressed course may allow students to study both arithmetic and algebra in one class and complete their developmental mathematics requirements sooner. Edgecombe (2011) clarified that acceleration involves the reorganization of instruction and curricula in ways that expedite the completion of coursework or credentials. Acceleration is similar to compression; however, in acceleration students can complete the required material in less than one semester or quarter. Acceleration usually involves classes that are self-paced in a lab setting. Students meet their requirements when they have completed their work.
Accelerated and compressed courses have certainly been emphasized by the Gates
Foundation in an effort to improve student success (Collins, 2011; Killough, 2009).
Some individuals are concerned that developmental math sequences are too long.
More specifically, Edgecombe (2011) warned that there is mounting evidence that suggests that the traditional sequence of developmental mathematics courses hinder community college students from entering college level courses. This evidence is based on Bailey et al.’s (2010) findings that only 33% of students referred to developmental
31 mathematics courses complete their required course work within three years, and only
17% of students successfully complete a developmental mathematics course sequence of three courses or more. This study included a sample of over 250,000 students from 57 different community colleges in seven states. Therefore, many developmental mathematics programs are abandoning the belief that all students require the same curriculum (Gonzalez, 2011). Redden (2010) maintained that many developmental mathematics educators are realizing that there must be differing instructional methods for different students.
Compressed courses.
Many developmental mathematics programs have had success with compressed courses. In 2008, New York City implemented the Start program (Redden, 2010).
Rather than a multiple-course sequence of developmental mathematics courses, Start combines several concepts of arithmetic and algebra into an intensive course that meets five hours a day and five days a week. Many more students have completed this course and have moved on to college-level work. Redden (2010) reported that other institutions, such as South Texas College, have had increased success rates in compressing a traditional three-course sequence into two courses and increasing the amount of time students spend using mathematics software in the computer lab. Bergen Community
College in New Jersey has begun to offer a compressed arithmetic and algebra course for students who score on the high end of the placement test. This allows students to complete their developmental mathematics requirements in one semester. Students who score on the low to mid-range of the placement test can opt to take the traditional course
32 sequence. As a result, the success rates in developmental mathematics at Bergen
Community College have increased by fifteen percentage points (Redden, 2010).
Overall research has favored the use of compressed courses for developmental mathematics. Sheldon and Durdella (2010) concluded that there is an advantage to offering developmental mathematics courses in a compressed format as opposed to a traditional design. They further articulated that “developmental students are quite capable of assimilating course material in a shorter time when the material is presented in a more intense and compressed format” (p. 52). Based on their quantitative study, which utilized a group comparison design between a group of students in a compressed course and a group of students in a traditional course, Woodard and Burkett (2010) also recommended that developmental mathematics courses should be offered in a compressed form and added that compressed courses not only increase student success but also reduce the chance of burnout for many students.
Acceleration.
Many institutions have noticed increased success rates by offering accelerated instruction. Squires, Faulkner, and Hite (2009) noted that Cleveland State Community
College (CSCC) in Cleveland, Tennessee, through a grant provided by the Tennessee
Board of Regents, segmented all of the content in their mathematics courses into modules. For each module, students complete online homework assignments, quizzes, and exams using the Pearson software program, MyMathLab (MML). Squires et al.
(2009) reported that students are provided with video instruction from faculty as well.
Students work in a lab setting with a lead faculty member and professional tutors who can provide them with individualized instruction. Students have deadlines for modules;
33 however, the students can complete the modules before the deadlines. As a result, students can finish multiple courses in one semester. If students do not complete a course, they can complete it the next semester. Students also take an online pre-test before each module. If they score high enough, they are able to test out of that module, and their requirements for that module are waived. This program allows students to focus on the material that is troublesome. Since the start of this redesign, success rates in developmental mathematics, according to Squires et al. (2009) have risen 18 percentage points.
The Community College of Denver (CCD) has also seen increased student success rates using an accelerated program entitled FastStart (Epper & Baker, 2009).
Similar to the program at CSCC, FastStart utilizes MML. In FastStart, many students are completing in one quarter what was previously two levels of developmental mathematics.
Moreover, CCD has seen a significant increase in the number of developmental mathematics students who are now passing college-level mathematics.
Other schools have also been implementing accelerated courses. Passport
Mathematics, which originated at Collin College in Dallas, Texas, is another individualized and flexible program that allows students to accelerate through their developmental mathematics material. Similar to CSCC’s and CCD’s program, students can begin where they need to and focus solely on the material that they need to (Diaz,
2010). Gonzalez (2011) reported that the entire Virginia Community College (VCC) system has also begin to utilize self-paced math modules; this started in the fall of 2012 and included all 23 community colleges in Virginia. Their program is similar to CSCC’s,
CCD’s, and Passport Mathematics in that students are able to move through their
34 developmental mathematics requirements at an accelerated pace using computer software. Students also focus solely on the material that they have not mastered.
However, the program at the VCC system differs slightly in that students only focus on material that is required for their individual majors. More specifically, students who are majoring in liberal arts will not be required to complete as much mathematics course work as students who are majoring in science, technology, or engineering. Gonzalez
(2011) pointed out that accelerated mathematics programs are changing the role of the faculty member. Faculty members are becoming facilitators rather than lecturers as the students progress at their own pace. Boylan, (2002) warned that students should be screened prior to entering compressed or accelerated courses to determine if they are candidates for such intensive instruction.
Statway and quantway.
According to Merseth (2011), in September of 2009, the Carnegie Foundation for the Advancement of Teaching launched a $13 million initiative, which is funded by six organizations, to improve student success rates in developmental mathematics. This initiative will create two alternative pathways for developmental mathematics students:
Statway and Quantway. Merseth (2011) articulated that the goal of the initiative is “to double the proportion of students who in a 1-year course sequence are mathematically prepared to succeed in further academic study” (p. 32).
Hern and Snell (2010) pointed out that many students who require a developmental mathematics course generally do not major in a field of mathematics.
These students will most likely need a college-level statistics class to complete their overall mathematics requirement. In fact, Schield (2008) estimated that statistics is the
35 quantitative requirement for 40% of undergraduate majors. However, developmental mathematics courses are algebra intensive, laying the groundwork for courses in trigonometry and even calculus. Many developmental mathematics students will never take such courses. Byrk and Treisman (2010) voiced that course content in statistics requires rigorous skills that students are not being prepared for in traditional developmental mathematics courses. Merseth (2011) claimed that developmental mathematics courses in arithmetic and algebra do not prepare students for a society saturated with quantitative information. Therefore Byrk and Treisman (2010) suggested that many of these students could just as easily be served by another pathway. The proposed alternative is Statistics Pathway (or Statway), a six-unit course that focuses primarily on statistics and would allow students to complete their institutional mathematics requirements in one year.
Statway is geared toward students who do not plan to enter a mathematics related or intensive field such as science, technology, engineering, or mathematics (Merseth,
2011). Students who successfully pass the course sequence would receive college credit, and the course is designed for transfer as well. Rather than algebra concepts, Statway focuses on computing percentages, interpreting graphs, and evaluating formulas (Hern &
Snell, 2010). Merseth (2011) pointed out that students who successfully complete
Statway will understand various ways of interpreting data. Byrk and Treisman (2010) asserted that Statway focuses on math in the real world and math that will help students in everyday life. The Carnegie Foundation for the Advancement of Teaching is organizing a group of faculty members and researchers from community colleges and various professional groups to further develop Statway. Over the next few years, the goal
36 is to expand Statway to more than 100 community colleges nationwide. Hern and Snell
(2010) noted that Statway has already been piloted in the California Community College system. While the sample size was very small, Hern and Snell mentioned that the descriptive statistics were promising. The success and retention rates were encouraging, suggesting that Statway could positively impact student learning in the future.
Quantway will be another pathway for students who do not plan to enter a mathematics related or intensive field. According to Merseth (2011), Quantway began in early 2010 with the work of AMATYC. The Carnegie Foundation has continued to build on this effort. Merseth (2011) further articulted that “in Quantway, students will focus on understanding and applying the mathematical concepts needed to facilitate their quantitative literacy rather than memorizing seemingly disconnected processes and procedures” (p. 33). The content covered in Quantway will be similar to the content covered in Statway; however, there the course will focus more specifically on quantitative reasoning with an emphasis on numeracy, equations, functions, and proportional reasoning (Asera, 2011). Merseth (2011) specified that Quantway will be a one-semester course, and upon completing the course, students will have the option of taking a quantitative reasoning course at their college or entering a vocational program that requires the mastery of developmental mathematics.
Both Statway and Quantway will target at-risk students at the community college level. These students may have a weak K-12 preparation, face language barriers, and possess low self-efficacy in mathematics. Also, since many of these students face language barriers, course creators will make a solid effort to ensure that the course material is clear and concise (Merseth, 2011). Asera (2011) also stated that many
37 students change curricular directions after entering college. Therefore, course creators will construct bridges between the two pathways. More specifically, this will allow a student who has started on the Statway path to transfer to Quantway. Finally, Asera
(2011) asserted that Statway and Quantway are not the ultimate answer for the abysmal success rates in developmental mathematics. However, these pathways might be the answer for the right group of students.
Technology in developmental mathematics.
Similar to the rest of higher education, there has been an infusion of technology into developmental mathematics. Some developmental mathematics courses have become entirely computer-based while others have incorporated software and online components. Other developmental mathematics courses are offered online as a distance learning course. Results and opinions have been mixed. Holton, Muller, Oikkonen,
Valenzuela, and Zizhao (2009) reported that students at Virginia Tech who were enrolled in a technological version of a developmental mathematics course performed half a grade better than those students who were enrolled in a traditional course with lecture-based instruction. However, drawing from the results of a group comparison study,
Benedickson (2004) concluded that success rates for students in technological versions of developmental mathematics courses were significantly lower than for students in traditional classes. Schwartz (2007) argued that technology has made mathematics more precise. Computer software can control for sloppy errors. However, Schwartz (2007) also has expressed concern that developmental mathematics students may rely too much on technology and this may be leading to diminished proficiency in basic arithmetic skills. Overall, AMATYC (1995) called for more infusion of technology into
38 developmental mathematics classes and also stressed that material should be applicable to true-to-life situations. AMATYC then reiterated this belief in 2006.
Developmental mathematics programs have experimented with and utilized several interactive online software programs such as Carnegie and PLATO. However, the most commonly utilized mathematics software seems to be MyMathLab (MML).
MML is an interactive course design that is distributed by Pearson. MML provides multimedia instructions along with online homework, quiz, and practice test problems
(Kodippili & Senaratne, 2008). According to Speckler (2008), whose research was published by Pearson, retention and success rates have improved, with some exceptions, in developmental mathematics courses that utilize MML in some capacity.
Partially and fully computer-based courses.
Trenholm (2006) studied several developmental mathematics programs that used various computer software in a “casual-comparative quasi-experimental study” (p. 51).
These are programs that have used computer software as both supplementary course components and as the entire modality of instruction. Trenholm (2006) articulated that developmental mathematics students enter class on the first day with a broad range of skills. Some students are on the high end of developmental math ability and may become bored with traditional lecture. Other students, however, are on the low end and may not keep up with their class. Courses that are completely computer-based can speed up or slow down instruction to meet various student needs. Zavarella and Ignash (2009) specified that computer-based instruction can be a viable alternative for some students.
Overall, Trenholm (2006) and Blackner (2000) concluded that developmental
39 mathematics classes that utilized computer-based instruction showed higher retention and success rates than traditionally-taught students.
Jacobson (2006) conducted a study to determine the impact of computer homework on a group of developmental mathematics students. He also collected some qualitative data in the form of student evaluations regarding computer homework.
Overall, the findings consisted of mixed results utilizing computer-based homework in a traditional class. The exact software type was undisclosed; it was simply a computer software program that accompanied the students’ textbooks. Jacobson (2006) mentioned that students found the software to be helpful. However, students also expressed frustration that the software was extremely meticulous in accepting answers. More specifically, students complained that they would input the correct answer; however, their answer was rejected because the number of symbols may not have been entered correctly.
Overall, Jacobson (2006) claimed that the use of online homework did not increase student success rates.
Zavarella and Ignash (2009) led a group comparison study between students enrolled in a traditional class with lecture and students enrolled in a class with computer- based instruction. They also collected some written feedback from students. According to their findings, the withdrawal rate for students in a course that consisted fully of computer-based instruction was double the amount than for students enrolled in a traditional class with lecture-based instruction. Overall, Zavarella and Ignash (2009) found that numerous students simply had many misconceptions when beginning a computer-based course. Students believed that the course material would be more comprehensible in a computer-based class. Students also believed that the computer-
40 based classes would be less time consuming. Many students simply found learning math via computer software to be difficult. Both Zavarella and Ignash (2009) and Trenholm
(2006) argued that computer-based instruction does have some promise and can provide some building blocks for faculty to implement effective courses. However, Zavarella and
Ignash (2009) pointed out that that faculty and college leaders must increase the lines of communication with students to understand how computer-based instruction can be implemented more efficiently.
Distance learning.
Nationally, fully online courses have been growing exponentially. Between 1999 and 2005, the number of students taking one or more online classes went from 744,000 to over three million (Weisbrod et al., 2008). Between the fall of 2008 and the fall of 2009, the number of students taking at least one online course grew by one million (Phillip,
2011). According to Weisbrod et al. (2008), most of the growth in online courses has been for students seeking an associate’s degree or taking post-baccalaureate courses.
Allen and Seamon (2007) mentioned that the growth of online courses offered at community colleges has exceeded the growth of online classes overall in higher education. Online courses in developmental mathematics have been rising as well, and
Epper and Baker (2009) articulated that developmental mathematics faculty must continue or begin to explore strategies that will increase student learning in the distance learning environment.
Online developmental mathematics courses have often helped to increase student learning. Potocka (2010) maintained that when students had to engage in independent learning, it improved their knowledge and mathematical skills. Students also learned
41 responsibility and time management. They learned that if they did not complete the assignments in a timely manner, they would not pass the class. Students also liked the idea of being able to work ahead in the material. Epper and Baker (2009) suggested that online classes create a more democratic environment for students. More specifically, students who were leery about asking questions in a traditional class were more likely to pose questions in online discussion groups, which increased their likelihood to persist.
Wadsworth, Husman, Duggan, and Pennington (2007) argued that online courses can be a good fit for developmental mathematics students who already possess stellar computer skills and may have scored on the higher end of the math placement test. The findings from Epper and Baker (2009) and Diaz (2010) suggested that each generation is becoming more comfortable with technology and is more adept at finding resources when needed. In fact, according to Hawkins and Rudy (2006), computer ownership among community college students rose 26 percentage points between 2002 and 2005.
There have also been some negative findings from online developmental mathematics courses. Ashby et al. (2011) claimed that developmental mathematics classes have significantly lower retention rates than traditional face-to-face classes. Both
Phillip (2011) and Boylan (2002) warned that developmental mathematics students lack the time management skills and autonomous learning ability that are imperative in many online courses. Potocka (2010) posited that these deficits make it easier for students to procrastinate and, as a result, fall behind in their studies. Potocka (2010) added that while online instruction can foster independent learning, it can be difficult for students who lack very basic skills. Boylan (2002) also pointed out that it is the developmental mathematics instructors who have traditionally discussed learning problems with
42 students, made referrals to student services, and provided social reinforcement.
Computers cannot handle these imperative tasks; Boylan (2002) suggested that such issues are the major limitations to distance learning.
Wadsworth et al. (2007) maintained that it is the college’s responsibility to determine if an online developmental mathematics course is suitable for a particular student. Wadsworth et al. (2007) further asserted that students need the correct learning strategies, self-efficacy, concentration, information processing, and self-testing skills to succeed in an online developmental mathematics course. Advisors should screen students accordingly before they are placed.
Calculator usage.
The use of the calculator in developmental mathematics has been a widely and long-debated topic. There have been two contradicting beliefs as to whether the calculator increases or inhibits student learning in developmental mathematics.
According to Vasquez and McCabe (2002), many educators believe that the calculator should be prohibited because developmental mathematics students need to learn the very fundamental skills that the calculators can already perform. Hopkins (1977) argued that the calculator can reduce the students’ ability to discover errors and can even reduce the motivation of students. Martin (2008) articulated that many educators feel that students simply become dependent on the calculator and lose their own logical thinking skills.
However, professional organizations such as AMATYC (1995, 2006) have maintained that technology should permeate the curriculum and instruction of all mathematical classes. Darken (1991) found that calculators can make problem solving more realistic by allowing students to work with true-to-life numbers. Furthermore, students can place
43 attention on the idea behind the problem without getting bogged down in heavy arithmetic. Davidson, Donaldson, Hardin, and McGill (1996) posited that calculators can help students become more computer literate. Vasquez (2003a) asserted that the calculator can help students interpret information. For example, students can interpret graphs based on linear and quadratic equations using a graphing calculator.
Developmental mathematics students have had competing views on the calculator as well. Martin (2008) led a mixed methods study that focused on the impact of the calculator on a group of developmental mathematics students, but she also collected qualitative data on student reactions to the calculator. According to Martin (2008), students found the calculator useful for clarifying problems, but many felt that the cost of a calculator does not justify its use. Some of the graphing calculators can cost over one hundred dollars. Vasquez and McCabe (2002) reported on a similar study and conveyed that students did find the calculator useful when dealing with arithmetic; however, the calculator only complicated matters in algebra. Martin (2008) concluded that some students felt that the calculator made mathematics so confusing that it actually heightened their overall math anxiety.
Educators have conflicting views on how to use the calculator to enhance student learning. Martin (2008) suggested that developmental mathematics faculty should teach the fundamental skills of basic mathematics and algebra and then use the calculator as a tool to enhance those skills through applications. Furthermore, students should be instructed exactly how to use the calculator. This instruction will alleviate confusion and ensure that students acquire the basic fundamental knowledge. Conversely, Vasquez
(2003a) recommended that faculty not give students specific instructions as to how to use
44 the calculator. Faculty should allow students to experiment and determine the best possible method of calculator usage. The calculator should also be used when teaching all topics from the beginning. This practice will allow students to develop more abstract thinking skills.
Studies on the relationships between calculator usage and student learning in developmental mathematics classes have generally shown that the calculator does not impede student learning. Vasquez and McCabe (2002) found that “calculator usage neither positively nor negatively affected the attainment of basic skills for developmental mathematics students” (p. 33). Davidson et al. (1996) also reported no significant difference in student success rates between students who used the calculators and those who did not. Martin (2008) even discovered that developmental mathematics classes that used a graphing calculator with more abstract problem solving had higher success rates than non-calculator classes that simply emphasized drill and practice of mathematical facts. In her findings, Martin (2008) noted that the withdrawal rate for developmental mathematics classes that used the calculator was lower than non-calculator classes. She speculated that students may find calculator classes more interesting as they involve more true-to-life problem solving applications rather than repetitious drill.
Best practices that supplement traditional instruction.
Supplemental instruction.
Supplemental Instruction (SI) is a widespread practice that has been utilized in developmental mathematics. According to Finney and Stoel (2010), SI can be utilized inside and outside of class. It starts with a student who has successfully completed a developmental mathematics class. That student may then be hired as an SI leader. As an
45 SI leader, the student attends a future developmental mathematics course, listens to the lectures, takes notes, and even takes part in the classroom discussion. The SI leader then works with the current students in the class and will usually lead workshops outside of class. The SI leader tutors students and leads group discussions regarding the content. In mathematics classes that are in lab settings, this may be even done during class. It is noteworthy, however, that an SI leader is more than simply a peer tutor. Wright, Wright, and Lamb (2002) mentioned that SI leaders receive extensive training for working with developmental education students. Finney and Stoel (2010) noted that most colleges generally pay SI leaders about $10 a day.
SI was first introduced by Deanna Martin in 1973 at the University of Missouri in
Kansas City and has been adopted at a variety of institutions (Phelps & Evans, 2006).
According to Arendale (2002), the major goals of SI include improving grades in target courses, reducing attrition rates, and improving the graduation rates. Arendale (2002) noted that there are generally four key people who are involved with SI. First, there is the supervisor; this is usually a faculty or staff member who is trained in SI and oversees the entire program. Then, there is the course instructor. There is the trained SI leader, the former student who works with the current students. Finally, there are the participating students. Wright et al. (2002) specified that SI is generally used for classes with high withdraw and failure rates.
As Wright et al. (2002) mentioned, SI leaders receive extensive training. In developmental mathematics, SI leaders are trained in techniques for alleviating math anxiety. These could include simple breathing techniques as well as proper study habits.
SI leaders also develop more interpersonal skills through role-playing and other
46 interactive activities. As Finney and Stoel (2010) noted, SI leaders attend classes with the students. This way SI leaders become familiar with a specific faculty member’s teaching style. For example, if a faculty member is teaching linear equations, the SI leader can work with the students utilizing the same methodology as the faculty member.
Phelps and Evans (2006) stated that SI leaders are model students. SI leaders act as role models by taking notes in class and participating actively in class discussions.
As Phelps and Evans (2006) mentioned, SI sessions can take place inside or outside of the classroom. However, SI sessions are simply not a lecture review of the previous class. SI leaders may lead a discussion of the class notes and then clarify any misconceptions. It is quite common for SI leaders to utilize group activities when dealing with difficult mathematics content. Many of these activities promote more abstract reasoning skills. More specifically, in an SI session, it is common to find students working with real-life applications rather than simply completing repetitious drills.
Martin and Arendale (1993) posited that SI engages students in thinking behavior which facilitates connections between, notes, textbooks, and problem solving. Martin and
Arendale (1993) further noted that SI sessions help students learn to study, which Higbee and Thomas (1999) stated is a major issue for developmental mathematics students.
Phelps and Evans (2006) specified that an SI session is typically 50 minutes. There is generally a ten-minute warm up activity, a thirty-minute group interaction activity, and a
10-minute closing activity. Maxwell (1997) reported that there are normally a minimum of two SI sessions each week.
SI sessions can also combat isolation, which Tinto (1993) noted is a major reason for attrition in college. Phelps and Evans (2006) mentioned that through SI, students
47 make connections with other students. SI sessions also help students realize that they are not alone in struggling with concepts such as fractions, algebraic equations, and expressions.
Overall, SI sessions have had a positive impact on student success. McCarthy and
Smuts (1997) revealed that class sections that utilized SI showed improved student performance and retention rates. SI was adopted by Valencia Community College, an urban community college in Orlando, Florida. The implementation of SI was funded through the Achieving the Dream initiative. As a result of SI, students reported a higher confidence level in developmental mathematics and a lower level of anxiety. Moreover, students who participated in SI sessions showed higher success rates in their developmental mathematics classes (Phelps & Evans, 2006; Finney & Stoel, 2010).
Finney and Stoel (2010) also claimed that faculty, in general, have embraced the concept of SI and have expressed more interest in implementing it into their classes.
An issue with SI has been attendance as many SI sessions take place outside of class. Again, attendance is an issue for developmental mathematics students. Attendance in SI sessions is lower for developmental mathematics students than for college-level students (Wright et al., 2002). Therefore, Wright et al. (2002) suggested utilizing SI more during class sessions. More specifically, they suggested that the faculty member should alternate between short periods of lecture and short periods of individual work.
During these periods of individual work, the SI leaders can circulate and lead smaller sessions.
48 Learning communities.
Learning communities are a popular and prominent practice that is being implemented across the nation (Weissman et al., 2011). Specifically, the use of learning communities has also become a common practice for many developmental mathematics courses. Learning communities may take several forms and are used widely in many programs by many institutions. However, Tinto (1998) gave one definition of learning communities as “a kind or co-registration or block scheduling that enables students to take courses together. The same students register for two or more courses, forming a sort of study team” (p. 169). Tinto (1998) further explained that by requiring students to register for courses together, they form a cohort and can form a support network early in their college career. Because two courses are linked together, students explore and discuss related topics between both courses, which helps students develop more abstract thinking skills. According to Powell (1981), the origin of learning communities can be traced back to 1927 when Alexander Meiklejohn designed the two year Experimental
College at the University of Wisconsin. Students read and discussed Greek literature and compared and connected it to contemporary American literature. The overall belief in the
Experimental College was that undergraduate college studies should teach students to become active citizens with the intellectual skills to participate in a democratic society
(Powell, 1981).
Learning communities have been viewed as a strategy to help students with the adjustment process to college. Weissman et al. (2011) reported that proponents of learning communities believe that they will lead to two positive outcomes. First, relationships among students will be strengthened, and students will make more
49 meaningful connections with their instructors. This is based on the finding that students who make connections early in their college career with peers and faculty are more likely to be successful and persist (Tinto, 1998). Second, learning communities will enhance how material is taught. Traditional lecture can be supplemented with collaborative learning and group discussion. Finney and Stoel (2010) argued that establishing community and informing students that they are in a learning community on the first day is imperative. Instructors should also discuss the various support systems on campus. In a developmental mathematic class, this may involve discussing campus-wide academic support and tutorial centers. Students should also become acquainted with each other.
According to Visher, Schneider, Wathington, and Collado (2010), each institution generally has a learning community liaison. This is a paid person who is responsible for managing all of the campus-wide learning communities.
Various institutions have implemented learning communities as a way to improve student learning and ultimately student success in developmental mathematics classes.
According to Weissman et al. (2011), Queensborough Community College (QCC), a large urban community college in New York City, linked several developmental mathematics courses with college-level mathematics courses. Edgecombe (2011) referred to these as paired courses. Weissman et al. (2011) revealed that QCC’s goal was to expose students to both developmental and college-level mathematics and how the concepts relate. Two additional goals were to increase student learning and to accelerate students’ progression through their required mathematics courses. Weissman et al.
(2011) also referenced Houston Community College (HCC), another large urban community college in Texas, and their work with learning communities. HCC linked
50 their lowest level developmental mathematics classes with student success classes.
Student success classes are designed to prepare students for the demands of college.
Students could learn proper study and work habits and apply them to the challenges and demands of their mathematics classes. Visher et al. (2010) noted that other institutions such as Kingsborough Community College in New York City, Hillsborough Community
College in Florida, and Merced Community College in California have implemented learning communities into their developmental mathematics classes and have followed the trend set by HCC and QCC.
The findings from an experimental study conducted by Weissman et al. (2011) and a mixed methods study led by Visher et al. (2010) conveyed that overall success rates in developmental mathematics courses are higher in classes that utilize learning communities than those that do not. Students also reported feeling supported both academically and personally. Visher et al. (2010) also specified that the learning community cohorts led to strong relationships among students. Students believed that the social connections increased their learning.
There have been some negative findings from learning communities. Learning communities have not always been linked to persistence in college. More specially, while students in developmental mathematics learning communities are more likely to have higher success rates in their specific math courses, they are no more likely to persist through the rest of their college courses than their peers who were not involved in learning communities (Weissman et al., 2011). Ashburn (2007) also mentioned that it is difficult for many schools to increase the number of learning communities because of the complications of community college schedules. Community college students are often
51 commuter students with employment and family obligations and therefore do not possess flexible schedules. Visher et al. (2010) maintained that it can be challenging to combine material from two separate courses effectively. For example, it can be difficult to find common threads between a developmental mathematics class and a sociology class. That is why Tinto (1998) stressed that courses in a learning community should be related.
Student outreach.
Because attendance and study habits can be an issue for developmental mathematics students, some faculty members have started to reach out to students outside of the classroom. In his quantitative study that focused on the impact of email reminders on a group of developmental math students, Jacobson (2005) found that sending email reminders to students regarding attendance, assignments, and exams had a positive impact on student learning and student success. When students missed a class, he would email the student inquiring why he or she missed class. Jacobson (2005) would also email the entire class to remind them of an assignment at least 36 hours before the due date.
Jacobson (2005) warned that simply sending email reminders is not enough.
Students may go through the motions of coming to class, but they may not exert any other effort. Developmental mathematics students require motivation. Therefore, when discussing his findings, Jacobson (2005) recommended that faculty members use some sort of teaser in their communications. For example, an email reminder may include the first part to a math puzzle or riddle. Students can get the answer only when they come to class. This is consistent with Tanner’s (2005) findings that making class more enjoyable
52 can increase student learning. Email reminders can also include some sort of extra credit problem that students can only receive if they come to the next class.
Jacobson’s (2005) use of email notifications resembles a practice that many schools have institutionalized college-wide. Over the last decade, many community colleges have implemented Early Alert programs. According to Thorton (2004), the
Early Alert Initiative encourages faculty to identify at-risk students in their courses and refer them electronically to the college counseling and retention services. At-risk students may include students who have missed an excessive number of classes, possess a failing grade, or are exhibiting some sort of emotional or behavioral problem. Faculty can refer students through an internal software program within the first two or three weeks of class. Donnelly (2010) noted that counselors and retention specialists can then assemble an intervention program to assist these students. Hudson (2006) conveyed that students have reacted positively to Early Alert Initiatives. Students were amazed that faculty cared enough to refer them for assistance, and overall, Early Alert Initiatives have led to increased student retention.
Some schools have initiated student outreach even before their admittance to the institution. El Paso Community College and the University of Texas at El Paso have worked closely with their area’s 12 school districts. Using the Accuplacer exam, the college evaluates high school juniors and seniors on their mathematical ability. Students with low scores can participate in tutorial programs to help them become more college ready in mathematics (Killough, 2009). These intervention tutorials may include summer courses at the college while they are still in high school (Gonzalez, 2010). Roueche and
Waiwaiole (2009) reported that faculty at El Paso Community College are working with
53 local high school teachers to close academic gaps. According to Miller (2011), these college readiness programs have reduced the number of students placing into developmental mathematics courses. Even the students who place into developmental mathematics are more academically prepared. These actions echo the recommendations of Wheland et al. (2003) in that community colleges must establish liaisons with local high schools to better prepare students for college-level mathematics. As a result, many other community colleges have begun partnering with local high schools to implement similar college readiness programs through the DEI (Collins, 2011).
Classroom activities and strategies.
Many faculty members have found the use of group activities blended with traditional lecture beneficial in their developmental mathematics classes. Phoenix
(1990/1991) articulated that developmental mathematics faculty should provide guided practice for students while encouraging class discussion. Student questions should be accepted and praised. Phoenix (1990/1991) suggested that after the faculty member has introduced a concept to the class, students should work cooperatively in a group of three to five on some applications involving the content covered. Woodard (2004) along with
Galbraith and Jones (2006) maintained that group activities help students to feel more relaxed and can relieve math anxiety. There is consistency in the findings among
Woodard (2004), Phoenix (1990/1991) and Phelps and Evans (2006) in that when students work together to problem solve, they realize that they are not alone in struggling with mathematics. Woodard pointed out that the use of group activities can help students feel less embarrassed about struggling as students are more likely to seek help from their peers than their instructor. She concluded that this technique improves student learning
54 and student success. DePree (1998) conducted a quasi-experimental study that investigated the impact of small-group work on the confidence levels and achievement on a group of development mathematics students. Her findings were similar to those of
Woodard (2004) and Phoenix (1990/1991) in that small-group activities increased course completion rates. Boylan (2002) also stated that collaborative learning can increase critical thinking skills, a best practice in developmental education. Together, students can develop their own problem-solving skills and protocols.
Group activities can increase the self-efficacy of developmental mathematics students. Hall and Ponton (2005) have posited that educators must raise the mathematical self-efficacy of all students as high self-efficacy is a pre-requisite for success. Hall and
Ponton (2005) further asserted that developmental mathematics educators must create an environment that encourages students to ask questions and be pro-active in their struggles. Ashburn (2007) reported that group activities do indeed improve the self- efficacy of developmental mathematics students. Students felt more comfortable discussing math problems with each other, and as a result, their confidence increased.
Overall, the data have shown improved student learning and success rates with group activities.
There was agreement in the findings of both Vasquez (2003b) and Schurter
(2002) that there should be a certain structure to teaching a developmental mathematics class. When introducing new concepts, Vasquez (2003b) stressed the Algorithm
Instructional Technique (AIT). An algorithm is a step-by-step procedure for calculating a solution to a problem. The AIT consists of the instructor initially modeling to the class effective step-by-step strategies to solving math problems of a specific topic. In other
55 words, the instructor utilizes guided practice by modeling how to attempt and solve a certain problem. Vasquez (2003b) argued that students should then practice the novice material. Instructors should also give feedback early and often. Practice problems can be completed in small groups; however, Vasquez (2003b) asserted that in the final step, students should achieve independence. More specifically, students should be able to complete the math problems independently without assistance from peers or their instructor. Schurter (2002) also posited a structured approach to teaching developmental mathematics, but it was geared specifically toward solving word problems, a topic of difficulty in both arithmetic and algebra. Schurter (2002) referred to this process as a modified and simplified version of George Polya’s (1945) Strategy for Solving Word
Problems. In this process, students should first attempt to understand a problem, devise and carry out a plan, and finally, reflect on their answer. Drawing from the results of an experimental study, Schurter (2002) reported that the use of Polya’s (1945) Strategy for
Solving Word Problems had a positive impact on student learning.
Vasquez (2003b) and Schurter (2002) stressed the psychological importance of such structure in a developmental mathematics class. Vasquez (2003b) articulated that
“if students become anxious and cannot solve a problem then they can rely on the algorithm for support and guidance” (p. 17). Algorithms can be another strategy to combat math anxiety as they provide a reliable structure to math problems. Vasquez
(2003b) further claimed that the AIT models structured behaviors for students. The modified and simplified version of Polya’s (1945) Strategy for Solving Word Problems, posited by Schurter (2002), emphasizes the use of metacognition. Metacognition refers to a person’s own knowledge in relation to that person’s cognitive processes and
56 products. Furthermore, metacognition refers to the active monitoring of these processes
(Flavell, 1976). In relation to mathematical word problems, the use of metacognition allows students to keep track of what they have accomplished and their next course of action. Metacognition also allows students to make connections between their own work and their overall knowledge of the subject matter (Finkel, 1996).
Boylan (2002) articulated that best practice instructors utilize a wide variety of active learning techniques. The use of mathematical games has proven effective in the classroom. Tanner (2005) conveyed that implementing mathematical activities such as relay races and mathematical bingo as in-class review tactics motivated more students to come to class and in the long run improved student success. When implementing a relay race, a class may be broken into teams of five. Each team would be given a five-part question. An example would be solving a linear or quadratic equation. Each member of the team completes one part of the question and then passes the question to the next person. The team that reaches the correct answer first wins. This activity makes class more enjoyable, according to Tanner (2005), and furthermore, students do not want to disappoint their teammates. Therefore, students come to class better prepared. This makes them more accountable to their classmates. When employing a mathematical game or activity, Tanner (2005) suggested that faculty use questions from the previous class’s homework assignment for the games. This will motivate students to be more meticulous in completing their homework.
Some developmental mathematics faculty have also focused on classroom skills such as strategic note-taking in developmental mathematics classes. Isaacs (1994) found that there is a strong and positive correlation between students who take quality notes and
57 review them and positive outcomes on exams. Furthermore, Isaacs (1994) and
Grossman, Smith, and Miller (1993) reported that note-taking enhances short-term and long-term memory of lectures. Again, Smith et al. (1996) maintained that many who do not take notes in developmental mathematics classes are often unsuccessful.
Eades and Moore (2007) have advocated quality note-taking in developmental mathematics classes. They further asserted that it is up to the faculty member to endorse note taking. First and foremost, faculty must model quality and organized note-taking.
According to Darken (1991) many developmental mathematics students often do not know how to take notes; therefore, their notes are often disorganized and incomplete.
Eades and Moore (2007) suggested that faculty members model this on the board or overhead and work with their students. Students’ notes should be clearly labeled with the date, topic, and corresponding textbook pages. They posited that a faculty member must first help students realize the benefits of quality note-taking. To get students to understand the importance of quality note-taking, Eades and Moore (2007) suggested that faculty members inform students that an upcoming exam will consist of math problems that are in their notes or even allow students to use their notes during a test or quiz.
Based on their findings from a mixed methods study that examined incorporating study habits into a developmental mathematics class, Mireles, Offer, Ward, and Dochen (2011) even suggested that students engage in a peer review process and evaluate each other’s notes for constructive feedback.
A major myth that developmental mathematics instructors must debunk is that mathematics is a spectator sport. Eades and Moore (2007) mentioned that many students come into a developmental mathematics class with the belief that they can simply learn
58 by sitting and watching the instructor. They do not realize that mathematics is a hands-on and participatory course. Grossman et al. (1993) argued that when students engage in note-taking, they stay more alert and focused in class.
Developmental mathematics faculty have also incorporated various study strategy sessions into their classes. Mireles et al. (2011) recommended that faculty members have students analyze their test preparation for a past exam and then discuss how they could better prepare for the next exam. Students could be divided into groups and predict upcoming test questions based on the material they have studied. Mireles et al. (2011) found that the use of these study sessions increased attitude, concentration, motivation and overall student learning in developmental mathematics classes.
Assessment is an important component to developmental mathematics or any other discipline. Long (2002) articulated that effective teaching is often defined by its result: learning. Student learning is often measured by paper and pencil tests. Boylan
(2002) pointed out that frequent assessment is necessary for developmental students.
However, Galbraith and Jones (2006) and Boylan (2002) maintained that developmental mathematics students are generally poor test takers. The aforementioned researchers also stressed that paper and pencil tests are not the sole form of assessment. Boylan (2002) argued that best practice instructors find alternate methods of assessment such as individual projects, written paper reports, and class presentations. Galbraith and Jones
(2006) reported that many developmental mathematics faculty have witnessed an improvement in student success rates by implementing the aforementioned alternative assessments throughout the term as opposed to traditional paper and pencil exams. These instructors do, however, still often administer a traditional paper and pencil final exam to
59 measure their students’ overall progress. Boylan (2002) also stressed that frequent assessment should lead to frequent and timely feedback and added:
Clear feedback on what students have failed to master, how they have failed to
master it, and what they can do to improve their performance is essential for
developmental students if they are to adjust their study and learning behaviors. (p.
84)
Similar Best Practice Studies
In this literature review, I referenced several best practices studies in developmental mathematics. The research purposes in many of these studies mildly compare to the purpose in my study in that they aimed to identify a best practice in developmental mathematics. However, the purposes of these studies also sharply contrast with my study in that they have generally sought to identify the impact or effect of a best practice on a group of developmental mathematics students. These studies have also measured students’ success rates while comparing one practice to another. In general, many of the studies that have focused on best practices in developmental mathematics have utilized a primarily quantitative approach. Other studies have utilized a mixed methods approach in that there was an experimental or quasi-experimental design with a small qualitative component. More specifically, very few studies have fully examined the “how” or “why” when exploring best practices in developmental mathematics. My study, however, employed qualitative methods that highlighted and described a broad range of best practices in developmental mathematics. Also, the populations in many of these studies contrast sharply to my study. In general, the participants utilized in most of these studies have been students. My participants were a
60 group of developmental mathematics instructors. The setting of some of these studies differed from mine as well. While a few of the best practice studies referenced took place in community colleges, many were set in either public or private four-year colleges.
Again, my study took place in a large urban community college with an ethnically diverse student population. In summary, there have been very few emergent studies that have identified and described a wide range of best practices utilized by a group of developmental mathematics instructors that have been set in an ethnically diverse community college. There are, however, two best practice studies that somewhat resemble my research purpose, setting, and method.
In 2010, Finney and Stoel conducted a qualitative case study in which their purpose was to explore the implementation and overall reception to a best practice in developmental mathematics, Supplemental Instruction (SI), in Valencia Community
College (VCC), an urban community college in Florida. Finney and Stoel’s findings were based on an interview with one faculty member from VCC who oversaw the implementation of SI.
The researchers chose to study SI because it was a new instructional practice at
VCC. In their study, the faculty participant mentioned that SI was an effective practice in developmental mathematics as it increased student learning. This effectiveness was determined by the fact that developmental mathematics courses with an SI component at
VCC had a higher success rate than developmental mathematics courses that did not.
Finney and Stoel (2010) discussed the implementation process of SI. Reactions to SI were positive as the authors reported that SI was well-received by students and faculty.
According to their participant, students enjoyed the sense of community that SI created.
61 Faculty members also embraced the idea of SI and requested more classes with an SI component.
The research purpose of Finney and Stoel’s (2010) study slightly compared to my study in that both sought to explore best practices in developmental mathematics.
Furthermore, both studies focused specifically on best practices utilized by faculty that increase student learning. Finney and Stoel (2010), however, entered the study with the intention of examining only one practice. My study highlighted and described a broad range of best practices in developmental mathematics. The methods used in each study are similar in that they were both qualitative and also utilized interviewing as the primary source of data collection. However, Finney and Stoel (2010) used only one participant in their data collection. For the purpose of identifying and describing multiple best practices in developmental mathematics and to add richness to the overall findings, I interviewed 20 participants. The settings and demographics for both studies were similar in that both took place in an urban community college with a diverse population.
In 2006, Galbraith and Jones led a case study in developmental mathematics.
Their research purpose was to examine effective in-class activities in a developmental mathematics classroom in a small and rural community college that increased student learning. Their data collection method consisted of a series of interviews with one developmental mathematics instructor during an academic term. Galbraith and Jones
(2006) identified several activities that improved student learning. Activities that the instructor believed led to an increase in student learning were deemed effective. To measure student learning, the instructor in their study collected written and verbal feedback from her students regarding in-class activities. Galbraith and Jones (2006)
62 reported several valuable in-class strategies such as a “no paper and pencil test philosophy” (p. 22). More specifically, the instructor in the study would dispense pre- and post-tests at the beginning and end of the academic term; however, throughout the term, the instructor would utilize alternative methods of assessment such as group presentations and class projects related to developmental math content. The instructor also separated her classes into small groups based on their pre-test scores. This allowed the students who were more advanced to work at an accelerated pace and allowed the other students to work together and with the instructor on content they found difficult.
Working in small groups relieved initial math anxiety and also allowed students to realize that they could learn from each other as well as their instructor. Galbraith and Jones also
(2006) discovered that relating developmental mathematics concepts to real-world situations improved student learning. For example, the instructor in the study linked the managing of personal finances such as checkbook balancing and configuring pay per hour to developmental math content.
There were some similarities and differences between Galbraith and Jones’ (2006) study and my study. Both of our research purposes focused on identifying best practices utilized by faculty in developmental mathematics. However, Galbraith and Jones (2006) limited their study to examining effective in-class activities. My study was open to a broader range of best practices including course redesign in developmental mathematics.
A community college was the setting for both of our studies; however, Galbraith and
Jones (2006) conducted their study in a small and rural institution whereas my study took place in a large and urban community college. Our studies were both emergent and used interviewing as the primary data collection method. However, Galbraith and Jones
63 (2006) reported on a case study in which one developmental mathematics instructor was the sole source of data collection. To gain richer discoveries, I interviewed 20 developmental mathematics instructors, and my findings consisted of themes derived from data across participants.
My study shared a common research purpose with the both the Galbraith and
Jones (2006) and Finney and Stoel (2010) studies in that all three works focused on exploring best practices in developmental mathematics from the instructor’s frame of reference. The method utilized in all three studies was emergent, and all three studies utilized interviewing as the source of data collection. However, the purpose of Finney and Stoel’s (2010) study was limited to one effective best practice and while the research purpose in Galbraith and Jones’ (2006) bore more resemblance to mine, their study was limited to effective in-class strategies. My study sought to identify and describe a broader range of best practices in developmental mathematics. Also, both Finney and
Stoel (2010) and Galbraith and Jones (2006) utilized only one faculty participant in their studies whereas I interviewed 20 participants. In summary, my study identifies and describes a broader range of best practices in developmental mathematics than previous studies. Furthermore, by collecting data from 20 faculty members my study potentially adds richness to the knowledge base of best practices in developmental mathematics. My findings identify best practices and elaborate and shed new light on existing best practices.
Chapter Summary
Since the beginning of American higher education, institutions have been serving underprepared students. Throughout the 17th and 18th centuries, tutors aided
64 underprepared college students. In the 19th century, the University of Wisconsin implemented the nation’s first formal college preparatory program to assist students in reading, writing and arithmetic. Other institutions continued to adopt this model throughout the 19th and 20th centuries as more institutions implemented college preparatory programs. By the 1970s the term “developmental education” was born as more institutions began to focus on student development while remediating students.
During the latter part of the 20th century developmental education became a recognized academic discipline. Through various studies and national initiatives such as Achieving the Dream, an increased amount of data has been collected on developmental education, and it has become apparent that developmental mathematics is a major obstacle for some students. As a result, student success rates in developmental math are quite low.
Each year, institutions serve large numbers of developmental math students. In general, these students enter these courses based on the results of their college placement exam. Students who place into a developmental math course report studying less in high school and lower GPAs than their peers who place in college-level classes.
Developmental math students who are unsuccessful also display poor attendance and are unable to keep up with the class. Many of these unsuccessful students also experience math anxiety and appear unmotivated and do not engage with their peers or the instructor.
Many faculty members and institutions have responded to underprepared students by implementing various practices to increase student success. Some institutions have redesigned some of their developmental mathematics courses or the entire course sequence by implementing accelerated instruction or compressed courses. These actions align with the goal of the Bill and Melinda Gates Foundation, which is to move students
65 through their developmental mathematics course sequence and into their college level courses at a faster pace. As a result, many of these schools have witnessed an increase in the number of students who are successfully completing their developmental math courses.
While technology in higher education is not new, faculty members have been incorporating various types of technology into their developmental mathematics classes.
Some developmental classes have become fully computer-based or even online, while others simply include online or computer-based components. The use of the calculators in developmental mathematics classes continues to be a major debate as well.
Many faculty members have utilized various practices to supplement traditional instruction. Such practices include supplemental instruction (SI) in which a trained SI leader works with developmental math students during and outside class to better understand the material. Various institutions have also executed learning communities.
In general, learning communities involve the linking of a developmental math course with a college level math course or another course such as student success. Learning communities have two major goals: The first is to strengthen the relationship among students and to strengthen the relationship between students and their instructor. The second is to enhance the learning experience of the students by supplementing traditional lecture with collaborative learning and group discussion. Instructors and institutions have also implemented different forms of student outreach. These strategies include increased email communication and reminders, The Early Alert Program, and connections with local high schools that will assist students in becoming more college ready. Lastly, several instructors are employing various classroom activities and strategies to enhance
66 student learning. Such activities and strategies include group activities, mathematical structure which included the Algorithm Instructional Technique (AIT) and a simplified version of George Polya’s Strategy for Solving Word Problems, the use of mathematical games, and an emphasis on note-taking and study sessions.
Finally, I compared my study to other studies that have focused on developmental math. Most studies that have centered on best practices in developmental math have utilized primarily quantitative or mixed methods approaches whereas my study was a basic interpretive qualitative study. There have been other qualitative studies that have been similar to mine; however, they have utilized only one participant or focused on only one best practice. My study, however, included 20 participants and identifies a broad range of best practices in developmental math.
67 CHAPTER III
METHODOLOGY, METHODS AND DATA COLLECTION PROCEDURES
Introduction
In this chapter, I address the overall design of this study. First I provide a description of the methodology for this study, and I also describe and give a rationale for my choice of method. Next, I discuss my role as the researcher. I then share the demographics and history of Sinclair Community College (SCC), which was the site of this study. Thereafter, I shift focus to the math area in the Academic Foundations
Department at SCC as this is where I selected my participants. I then explain my participant selection process as well as my data collection methods. Next, I elucidate my method of data analysis. Lastly, I describe strategies that I employed to ensure trustworthiness in the study.
Methodology of Study
The genre that I chose is a basic interpretive, qualitative study. Merriam (2002b) articulated that in a basic interpretive qualitative study, “the researcher is interested in understanding how participants make meaning of a situation or phenomena” (p. 6).
Merriam (2002b) further asserted that the researcher seeks to understand the perspective and worldviews of the people involved. The strategy is inductive and the process is descriptive. To gain an in-depth understanding of best practices in developmental mathematics, it was imperative that I better understood how my participants, a group of
68 developmental mathematics instructors, construct meaning of their best practices. My data analysis methods were inductive as I sought to understand the individual perspectives and views of my participants. My findings consisted of a thick, rich description (Krathwohl, 2009; Merriam, 2002a; Patton, 2002; Ridenour & Newman,
2008) of the construction of meaning of best practices in developmental mathematics.
The details of a thick, rich description are discussed later in this chapter.
Method of Study
In this study, my purpose was to gain an in-depth understanding of the best practices utilized by a group of developmental mathematics instructors at an urban community college. The research questions were: What are the best practices utilized by a group of developmental mathematics instructors at an urban community college? How do these instructors employ such practices to enhance student learning? In any study, the research purpose and question must support the method (Merriam, 2002b; Krathwohl,
2009; Patton, 2002). Therefore, I chose a qualitative method because the research purpose and questions of the study called for an inductive and emergent study.
According to Patton (2002), “Qualitative methods facilitate study of issues in depth and detail” (p. 14). To identify and understand emerging and existing best practices in developmental mathematics, this issue must indeed be studied in depth. Merriam (2002b) specified that “the key to understanding qualitative research lies with the idea that meaning is socially constructed by individuals in interaction with their worlds” (p. 3). In this study, I endeavored to understand how faculty members construct the ideas behind the best practices that increase student learning.
69 Certainly, both types of research methods, qualitative and quantitative, are valuable to the discipline of developmental mathematics. In fact, the results from several quantitative studies have added to the knowledge base of best practices in developmental math. However, researchers must continue to discover new best practices rather than simply corroborate hypotheses on existing best practices. Krathwohl (2009) articulated that qualitative studies “describe complex and personal phenomena that would be impossible to portray with quantitative research’s single scale dimensions” (p. 237).
Krathwohl (2009) added that qualitative research “provides examples that put meat on statistical bones” (p. 237). Therefore, the rich and detailed findings from this study should enhance educators’ understanding of existing best practices.
Role of the Researcher
I have been employed as a developmental mathematics faculty member at SCC, the site of this study, since the fall of 2003. Prior to that, I taught middle school and high school mathematics for four years. I entered SCC as an assistant professor. In 2007, I received a promotion to associate professor; in 2008, I was granted tenure, and in 2012, I received another promotion to professor. As a full-time faculty member, I am required to teach at least fifteen credit hours each term, which totals at least four classes. I also serve on various departmental and college-wide committees related to assessment, curriculum design, and other areas as needed.
As a professor of developmental mathematics at SCC, I am an insider to the profession and the site of study. I believe that the major benefit for me as an insider was cooperation from faculty. Considering that the discipline of developmental mathematics has fallen under scrutiny for low success rates, there is a sense of mistrust among faculty.
70 If I were an outsider, faculty may not have been as willing to participate in this study because of that mistrust. More specifically, they may have feared that I was out to evaluate them as instructors and to expose various weaknesses. If they did participate, these instructors may not have been as candid or as forthcoming in their responses.
However, most of the developmental mathematics faculty at SCC were well aware that I was a doctoral candidate conducting a dissertation and not an outsider looking to evaluate them. Consequently, I believe the developmental mathematics faculty at SCC were more likely to participate in the study and be more open and honest in their responses.
Being an insider did create some challenges for me in this study. As a result of my position, certain biases emerged. In fact, biases are likely to emerge in a qualitative study as the researcher is the primary instrument (Merriam, 2002a; Patton, 2002).
However, Patton (2002) articulated that the researcher must reveal and minimize potential sources of bias. In my years at SCC, I have utilized several instructional modalities: blended lecture with small-group work, computer-based instruction in laboratory settings, inquiry-based instruction, distance learning, and accelerated instruction. Over time, I have employed various best practice strategies based on research. I have also incorporated best practice strategies based on feedback from my colleagues. Based on my student success rates and overall student reactions, I do carry personal opinions, and I hold certain practices in higher regard than others. For example, when teaching I prefer to employ interactive lecture-based instruction. I strive to establish an interactive atmosphere where students can ask questions and share their thoughts while I am explaining a concept. I also try to mix my lecture with independent student activities and a small amount of group work. Since 2008, I have also developed
71 several online courses, and I have taught these courses on a regular basis. Employing these modalities consistently over time has helped me to develop a high comfort level with each modality. My success rates have also been high when employing these styles.
Conversely, I have also taught classes where I have utilized large amounts of group work, and I witnessed lower success rates than I did with blended lecture and online learning. I believe that this resulted from my comfort level being lower and my overall lack of experience with group activities.
Considering that my goal was to explore and describe the best practices utilized by a group of developmental mathematics instructors, when analyzing the raw data, I did struggle with separating my own personal opinions from my participants’ responses.
Therefore, when coding the data, I was careful to ensure that my own personal biases did not skew my interpretations. I achieved this through the process of reflexivity, which is explained later in this chapter.
As an insider to SCC, my participants were my peers. Some of my participants were individuals whom I have known for several years and consider friends. I considered some of my other participants to be acquaintances; others, I did not know well at all. As a result, there was a variation in my comfort level as I conducted face-to-face interviews.
I was more at ease interviewing participants whom I considered friends. However, interviewing participants who I was closer to did create some challenges. More specifically, in the preliminary interviews, it was difficult not to drift into unrelated conversation. For example, in my first interview, the participant began to complain about the internal politics of SCC. I had to refrain from joining in since this participant and I normally discuss SCC politics during regular conversations. However, during the
72 interview, I made it a point to stay on task. In another case, I was interviewing a participant who was a longtime friend. When answering questions, she would often ask,
“don’t you think so?” or “don’t you agree?” This was most likely due to the fact that in my hundreds of casual conversations with this participant, we could enjoy such exchange.
However, during the interview, I was a researcher looking to collect data. Therefore, I had to pause during the interview and politely explain that I wanted to focus on others’ views during the interview. The participant was very understanding, and we continued.
Some of my participants whom I knew well provided vague answers at times.
This may have been due to the fact that they assumed that I knew what they were referring to when answering a question and did not feel they needed to elaborate. For example, when I posed the question, “Currently, the country is struggling with success rates in developmental mathematics classes as so many students are simply not passing their developmental math requirements. Based on your opinion, why are so many students struggling in developmental mathematics courses?” the participant responded,
“They are lacking basic computation skills.” Being an insider to developmental mathematics, the participant most likely assumed that I understood exactly what she meant. Truth be told, I did. However, I wanted my findings to reflect her view and not my own personal knowledge or opinions about developmental mathematics. I was tempted to leave this question alone because I did understand what she meant. However,
I employed this probe: “How are they lacking basic computational skills?”
As a mathematician, I tend to be a very linear thinker. I prefer organization, structure, and movement in a straight line. Therefore, a struggle for me throughout the first few interviews was to accept the messiness of conversation as a data source. For
73 example, during my third interview, I posed my final question: “Is there anything else that you would like to add about best practices in developmental mathematics?” I originally designed this question with the intent of obtaining some basic concluding comments. I assumed that I would not need any follow-up questions or probes.
However, when answering this question, this particular participant began discussing another best practice. Therefore, I quickly realized that I needed to utilize the follow-up questions that I had employed for the previous “best practice” questions and quickly devise probes based on the participant’s responses so that I could obtain rich data. This caught me off guard. Also, my questions were also arranged to identify one best practice at a time. However, there were a few participants who described two best practices when answering the same question. Rather than interrupt the participant, I simply allowed him or her to speak, and I made sure to employ my follow-up questions and probes when necessary.
When I designed my original questions, I intended to use probes such as “Could you explain that a little more?” or “Why is that?” I learned very quickly that those were not always the appropriate probes, and when employing probes, I needed to think and react quickly. For example, during one interview I inquired about a practice that did not work. The participant responded that some students are simply “not good group workers.” I needed more clarification so I asked, “What are the characteristics of that group of students?” This was not on my original list of probes and follow-up questions, but I had to think fast and construct a probe that would allow me to gain richer data.
As a professor, I do not possess a superior or subordinate role to any of my participants. However, some of the adjunct faculty may have viewed me as a superior
74 because I am a permanent faculty member and possess a higher rank. To reduce this potential issue, I explained in my initial invitation to interview (see Appendix A) that as a full-time faculty member, my position is in no way superior to any other faculty member in the department.
In a qualitative study, the researcher must establish credibility. Therefore, as the researcher, I utilized various trustworthiness strategies to ensure that my interpretation of the data was based on the raw data and that any biases did not skew the findings. These trustworthiness strategies minimized the potential biases discussed in the previous paragraph. In fact, I employed the strategy of reflectivity to examine my own feelings and struggles throughout the study. This strategy allowed me to reveal and examine the issues that I discussed earlier in this section. Reflexivity and other trustworthiness strategies are explained in detail later in this chapter. My objective was to enter this study with openness to hearing participants’ stories. According to Patton, (2002) the investigator does not set out to prove a particular perspective or manipulate the data to arrive at predisposed truths” (p. 51). Throughout the study, I acknowledged, as Patton
(2002) described, qualitative heuristics. More specifically, I remained open to new concepts and was cognizant of the idea that this research was emergent and may change during the process.
Setting of the Study
This site for this study was Sinclair Community College (SCC). SCC is an urban community college in downtown Dayton, Ohio in Montgomery County with an average enrollment of 24,000 students each term (SCC, n.d., Project Profile). According to SCC
College History (n.d.), SCC can be traced back to the Dayton YMCA in the 19th century.
75 In 1887, the YMCA started offering classes in bookkeeping and mechanical drawing to a small group of young men. This program was known as the YMCA College. In the late
19th and early 20th century, the YMCA College grew and started offering more classes and a broader curriculum. In 1929, the YMCA College moved to a larger facility and included the Dayton Law School, the Dayton Technical School, and a school of liberal arts. In 1948, the YMCA College was renamed Sinclair College after David A. Sinclair, a Scottish immigrant who founded the original educational program at the YMCA. In
1965, a plan for Sinclair College to become a community college was implemented, and in 1966, the charter for SCC was approved. Since then, SCC has expanded to 20 buildings across downtown Dayton. The curriculum has also grown to offer more than
100 programs, which include both degree and certificate programs.
In 2006, SCC began to provide satellite campuses for students in suburbs. In addition to the main downtown Dayton campus, SCC has four other campuses; two are in
Montgomery County, and there is one campus each in Preble and Warren Counties (SCC, n.d., College History). The two campuses in Montgomery County are located in Huber
Heights and Engelwood, Ohio, and are 15 and 14 miles respectively from the main campus in Dayton. The campus in Warren County is in Mason, Ohio and is 34 miles from the main campus. Preble County’s campus is located in Eaton, Ohio and is 27 miles from the main campus. The satellite campuses are significantly smaller than the main campus. Unlike the main campus, which has 20 buildings and is spread across downtown
Dayton, Ohio, each satellite campus consists of only one building which contains all classrooms, offices, and facilities. All campuses are a part of the entire organization of
Sinclair Community College.
76 Like most public community colleges, SCC provides low tuition and relies heavily on the state government and local tax levy for financial support. As of 2012,
Montgomery County residents pay $92.37 per credit hour. Out of county residents pay
$266.40 per credit hour (SCC, n.d., Student Services). SCC heavily relies on the Sinclair tax levy, which accounts for roughly 20% of the budget. The Sinclair tax levy has successfully passed each time it has gone on the ballot (Ohio Board of Regents, 2009).
SCC is a commuter college that serves a diverse student population on all campuses. According to the Ohio Board of Regents (2009), 71% of the student population is White, and 16% is African American. Other ethnic groups include
Hispanics and Asians. The average age of the SCC student is 32, and 54% of the entire student body is 25 or older. As for financial assistance, 56% of the first-time, degree seeking, full-time students receive some sort of financial assistance (i.e., need-based grants, loans, and work-study). Specifically, 34% of first-time, degree-seeking, full-time students receive a federal grant (Ohio Board of Regents, 2009). Many SCC students are first generation college students from low socioeconomic backgrounds. Several SCC students also hold full-time employment to support families. SCC’s mission statement is
“We help individuals turn dreams into achievable goals through accessible, high quality, affordable learning opportunities” (SCC, n.d., Mission and Vision).
At SCC, there are a total of 397 full-time faculty. This includes the faculty who teach on the satellite campuses as well. Slightly more than half of the full-time faculty are female, and only 12% are from minority groups. Over 80% of the full-time faculty possess graduate degrees (master’s degrees or higher). There are also an estimated 600 part-time faculty members (Ohio Board of Regents, 2009). This number can increase or
77 decrease significantly based on student enrollment and the need for more classes. Full- time faculty at SCC consist of annually contracted faculty (ACF’s), tenure-track, and tenured faculty (permanent faculty). ACF’s receive a contract renewal each year and are generally referred to as “instructors.” Permanent faculty members, however, are part of a professorial ranking system. Permanent faculty are usually hired as assistant professors.
After four consecutive years, these individuals are eligible for a promotion to associate professor. To receive a promotion, faculty members must demonstrate a strong commitment to SCC. This commitment is evidenced by exemplary teaching skills, a commitment to student development, scholarly and professional growth, and a vigorous amount of community service to SCC. After a permanent faculty member’s fifth year, he or she is eligible for tenure status. To receive tenure, the faculty member must have received a promotion and demonstrate an ongoing commitment to SCC. After nine years, a faculty member is eligible for professor. To receive the promotion to professor, a faculty member must demonstrate all of the characteristics required for associate professor as well as model leadership skills. Each promotion results in a significant increase in pay.
Since its inauguration, SCC has offered developmental courses in reading,
English, and mathematics. Such courses have traditionally formed SCC’s developmental education program, which has always been a stand-alone department. When students complete their requirements in developmental mathematics and English, they proceed into the Mathematics and English departments respectively. The developmental reading faculty have the task of preparing students for all courses that require college-level reading. Through 2007, the department was known as Developmental Studies. In 2007,
78 the name of the department was changed to Academic Foundations. However, the course identification codes have retained the developmental title (i.e., DEV 084, DEV 085). The
Academic Foundations Department is one of 21 departments that is currently under the
Liberal Arts, Communications, and Social Sciences Division. This division is overseen by one dean and one assistant dean.
The Academic Foundations Department is supervised by one chair. The individual areas are managed by faculty coordinators, otherwise known as area coordinators. Area coordinators are generally permanent, senior faculty members who have the responsibility of overseeing policy and practice and communicating with full and part-time faculty. The area coordinator is a rotating position; a new faculty member accepts the responsibility every two years. Area coordinators usually receive a small amount of reassigned time for their work. For example, if an area coordinator received four credit hours of reassigned time, that would be four fewer hours that he or she would be assigned to teach, or if the area coordinator taught a full load, he or she would receive a monetary stipend equivalent to four credit hours. The amount of reassigned time varies each year based on the budget.
From SCC’s conception in 1966 through the summer of 2012, the school operated on quarter terms: fall, winter, spring, and summer terms that each ran 11 weeks in length.
However, in the fall of the 2012, SCC, in compliance with a mandate from the Ohio
Board of Regents, converted to semester terms: fall, spring, and summer terms that are 16 weeks in length. However, since I began collecting data at the conclusion of spring quarter of 2012, all findings were based on the quarter structure. The math area in the
Academic Foundations Department has consisted of content in arithmetic and beginning
79 algebra. While content has been rearranged slightly to accommodate the transition to semesters, the actual content of arithmetic and algebra has remained intact.
While on quarters, there was a three-course sequence in the math area. The content from DEV 084, the lowest course, consisted of operations with whole numbers, fractions, and decimals. DEV 085, the middle course, entailed arithmetic topics such as operations with fractions, decimals, ratios, proportions, word problem applications, percentages, and integers. DEV 108, the exit course, was comprised of beginning algebra topics such as operations with rational numbers, simplifying and evaluating expressions, solving linear equations, word problem applications, basic laws of exponents, and very basic factoring. Incoming students place into a course via the Accuplacer placement test.
Most SCC degrees require completion of at least one college-level mathematics course.
According to the director of SCC’s Research, Analytics, and Records Department
(personal communication, March 14, 2012), 5260 (over 60%) first-time students placed into a developmental mathematics course during the 2010-2011 academic year.
Therefore, many students must complete the highest level developmental math course in order to take a college-level mathematics course. It is worth noting that the Mathematics
Department is not only a separate department from developmental mathematics, but it is in another academic division. The Mathematics Department is part of the SME (Science,
Mathematics, and Engineering) division. There is also speculation that the math area may eventually become a separate department and become part of the SME division.
SCC offers three modalities for the highest two developmental mathematics courses. This was the case for quarter terms and is still the case for semester terms. All three courses offered a traditional modality in which faculty members generally possess
80 pedagogical academic freedom. Faculty may utilize traditional lecture and mix in group- work or even technological components. However, DEV 085 and DEV 108 also offered accelerated and online instruction. In the online sections, all assignments and exams are completed via distance education. The online sections utilize the software program,
MyMathLab.
There are two types of accelerated modalities. The first is titled “the math academy.” In the math academy, students work at their own pace in a lab setting and can finish their developmental mathematics course work early. More specifically, students may complete two courses in one academic term. The class takes place in a computer lab, and each class is staffed with a lead instructor and one or two tutors to assist students. The lead instructor is either a full-time or adjunct faculty member, and the tutors are individuals who hold at least a bachelor’s degree but do not necessarily teach their own classes. Similar to online instruction, the math academy utilizes MyMathLab as the primary software program. The content covered is the same as in the face-to-face classes; however, students work at their own pace. There are, however, certain deadlines within the course. For example, tests must be completed by certain dates; otherwise, there is a 10% penalty for that exam. Students report to class for a total of four hours per week (the same contact time as the face-to-face classes). However, students can access the software from any location; therefore, they can complete their work outside of the classroom as well. During class, students work independently on their math while the lead instructor and tutors circulate throughout the lab and assist students. The math academy sections are very similar to those courses offered at Cleveland State Community
College (CSCC) and the Community College of Denver (CCD), which were discussed in
81 Chapter Two. The second accelerated modality is titled “boot camp.” Boot camps run for three hours a day for five days (one week). Each boot camp covers the content of one developmental math course. Basically, students can complete a developmental math course in one week. Boot camps run for a week in August, a week in November, and a week in March. Boot camps may employ traditional instruction (lecture and guided practice) or blended instruction (lecture and group work); it depends on the instructor.
The accelerated courses are part of the Developmental Education Initiative (DEI), which is funded by the Bill and Melinda Gates Foundation.
Originally, the courses in both types of accelerated modalities were only intended for students who placed on the high end on the Accuplacer. During its inaugural term, the math academy was only accessible for students who were at most 15 points away from placing into a higher level developmental math or college math class. More specifically, if a student missed placing into DEV 108 by 15 points or less, he or she could enroll in a DEV 085 math academy section. However, the math academy has become open to all students who enroll in the two highest developmental math classes regardless of their Accuplacer scores. When the boot camps were originally designed, they were also geared toward students who placed on the cusp of a specific developmental math course. For example, a student who missed DEV 108 by five or ten points on the Accuplacer was an ideal candidate for DEV 108 boot camp. However, like the math academy, the boot camps are now open to all students.
All three instructional modalities follow the same curriculum. There are also uniform unit tests and a final exam. In the online and accelerated classes, all faculty must follow the same formula to configure a student’s final grade. In the traditional classes,
82 however, faculty enjoy the freedom to employ their own formulas to configure a student’s final grade. However, students must pass the final exam in any of the courses with a grade of 75% to successfully pass the course. That is true in all three modalities as well. It is noteworthy that developmental math classes are also offered at each of the satellite campuses. Developmental math courses that are conducted on satellite campuses are assigned to both full and part-time faculty. These faculty members may teach some of their courses on a satellite campus and teach the rest on the Dayton campus; others may teach all of their courses on the satellite campus. Also, the instructors who teach on satellite campuses must follow the same curriculum, materials, and grading polices as the instructors on the Dayton campus.
Traditionally, the math area in the Academic Foundations Department has struggled with student success rates but has seen improvement in recent years. In the
Academic Foundations Department student success rates are computed by dividing the number of students who receive a letter grade of “C” or higher by the number of students who are enrolled in a class the second week of the term. Therefore non-successful students include those who fail the course or withdraw after the first week of the term.
This is how academic units across SCC’s campus compute and determine success rates.
Between September of 2008 and June of 2011, the average success rate for DEV 084 was
50%. The average success rates for DEV 085 and DEV 108 were 51.3% and 55.94% respectively. It is worthy of note, however, that in a five year span (2006-2011), the success rate for DEV 085 has increased by six percentage points. The success rate for
DEV 108 has increased by fourteen percentage points in that time span. DEV 084 has remained pretty consistent (SCC, n.d., Research Analytics, and Reporting). No
83 experimental studies have been conducted to determine why the success rates in certain courses have risen. However, in an attempt to enhance student learning in developmental math, the department began to offer multiple modalities of instruction (traditional instruction, accelerated instruction and online) to students. Also, instructors have been implementing various best practices in their classes. Therefore, I speculate the use of multiple modalities and the employment of various best practices has led to an increase in student success.
The success rates in developmental mathematics courses at SCC are certainly well below those in other academic departments across campus. Considering that and the dismal national success rates of developmental mathematics courses, the SCC administration has set different standards for the math area in the Academic Foundations
Department than other academic departments. A 70% success rate or higher in an overall class is considered excellent. Student success rates between 60-69% are considered good. Student success rates between 55-59% are considered respectable but improvement is needed. Student success rates between 50 and 54% require improvement. Student success rates below 50% are unacceptable (SCC, n.d., Quarterly
Status Reports). Please note that these percentage categories are not based on national data; they are based on administrator feedback from the Achieving the Dream initiative.
Between 2006 and 2009, student success rates were computed each quarter for every
SCC developmental mathematics course. The Achieving the Dream director and several senior level administrators collaborated to comment on the data. When SCC took part in
Achieving the Dream, the administration and the faculty agreed that overall success rates of 70% or higher in developmental mathematics was a reasonable goal. This is due to the
84 reality that some students will either enroll but never attend class or withdraw for personal reasons. Therefore, when success rates were 70% or higher, feedback was extremely positive. Success rates between 60-69% also resulted in positive feedback.
When the success rates were between 50-59%, the overall comments indicated that improvement was needed; however, the comments were more positive when the success rates were in the high 50s. Success rates below 50% were deemed unacceptable.
As of the summer of 2012, there are 16 full-time faculty members in the developmental mathematics area: 10 are permanent and six are ACF’s. Of the ten permanent faculty members, 8 have received tenure. Each of the full-time faculty members possesses a graduate degree. There are also 53 part-time faculty members.
Again, this number can increase or decrease significantly depending on the student enrollment and the number of developmental mathematics classes that are needed. Upon hire at SCC, all full-time faculty are subject to an interview by a search committee. The search committee may interview as many as 10 candidates and then recommend two or three to the division dean. The division dean and the SCC provost make the final hiring decision. The hiring process for part-time faculty is generally internal among the math area. Applications are sent from Human Resources to the math area coordinator, who usually interviews the candidates independently. If there are class sections that are unstaffed with classes about to commence, the Academic Foundations Department chair may unilaterally hire part-time faculty. Adjunct faculty who teach on a satellite campus must undergo the same hiring process as those who teach on the Dayton campus.
85 Rationale for Site Choice
I did not choose SCC as the setting for this study out of convenience. I chose
SCC because of the institution’s commitment to developmental education and student success. College administrators and faculty have devoted a great deal of time working to improve student success rates in developmental education. Also, administrators and faculty have been able to travel around the country to study best practices in other institutions with similar demographics. Nationally, SCC has gained a reputation for being an innovative and effective institution. In a New York Times article, Greenhouse
(2009) articulated that SCC is “widely acclaimed as one of the best colleges in the nation” (At Sinclair Community College, Focus is Jobs section, para. 7).
Since 1989, SCC has been a part of the League for Innovation for Community
Colleges (SCC, n.d., College History). The League of Innovation is an international organization that is committed to improving community colleges. According to College
History (n.d), in 2001, SCC became one of the League’s vanguard colleges. “Vanguard is a term designated by the League to recognize the top twelve two-year institutions in
North America that focus constantly on student and learner access and success” (History section, para 7).
Over the past decade, SCC has been involved in the nation’s two premier initiatives to improve developmental education: Achieving the Dream and the
Developmental Education Initiative (DEI), which I discussed in Chapter Two. SCC received these grants because of college’s recognized stellar work in helping students succeed (Ruiz, 2009). Furthermore, Ruiz (2009) reported that SCC was one of only 15 community colleges in the United States to receive to receive the DEI grant. More
86 specifically, SCC was only one of five community colleges in Ohio to receive this grant; the others were North Central State College, Cuyahoga Community College, Zane State
College, and Jefferson Community College. Much of the grant money has gone into constructing and implementing accelerated instruction in developmental mathematics.
In 2011, SCC received another multi-million dollar grant from the Gates
Foundation entitled “Completion by Design.” Completion by Design has become the third major national initiative to increase student success rates in developmental education. According to Jobs for the Future (n.d.), through Completion by Design, community colleges will examine the overall college experience for students ages 17 through 26. Furthermore, these institutions will work to increase completion rates for these students. SCC was one of only 23 colleges nationwide to receive the Completion by Design grant. In Ohio, only two other community colleges received this grant: Lorain
County Community College and Stark State Community College. During the first year of
Completion by Design, college officials have studied the college experience for students ages 17 through 26 and examined data associated with those students as well. During the
2012-2013 academic year, officials at SCC will begin to design actual initiatives based on their findings to improve student success.
Nationally, there are only three community colleges that have received the
Achieving the Dream, DEI, and Completion by Design grants: El Paso Community
College, South Texas College, and Sinclair Community College (Jobs for the Future, n.d.; Ruiz, 2009). In short, I conducted this study on best practices in developmental mathematics at SCC because it has been recognized as a best practice institution.
87 Participant Selection
For this study, I utilized purposive sampling. According to Krathwohl (2009),
“Purposive sampling is most often used in qualitative research to select those individuals or behaviors that will better inform the researcher regarding the current focus of the investigation” (p. 172). Patton (2002) pointed out that purposive sampling involves intentionally selecting participants who will add depth and understanding to a study; it is a technique that involves seeking “information-rich” (p. 172) cases.
I sought faculty participants who have shown consistency in student success rates.
Upon completing and analyzing my pilot studies, I emailed all faculty who were currently teaching developmental math. This included the faculty who teach some or all of their courses on the satellite campuses as well. In this email, I asked them to answer two questions: First, I inquired how many developmental mathematics classes that they have taught since the beginning of fall term in September of 2010. I wished to recruit participants who have taught on a consistent basis for the previous two years. Therefore,
I considered faculty members who answered six classes or more as those who have taught consistently over a two-year span. I chose six because that would be equivalent to teaching a fall, winter, and spring term each academic year. In my second question, I requested that my potential participants calculate their average student success rate in that time period. I asked them to choose from the following categories when reporting their success rates: 70% or higher, between 60- 69%, between 55- 59%, between 50- 54%, or below 50%. It is quite possible that due to a variety of reasons, one class section with a low success rate could conceivably lower the overall average for an instructor with otherwise good success rates. Therefore, I allowed the potential participants to exclude
88 the class section with the lowest success rate from their calculation. Each quarter faculty are asked to calculate their success rates for each class section and submit these results to the math area coordinator and department chair and retain a copy for themselves; therefore, they had this information available. Please see Appendix B (Initial Self-Report
Questionnaire) for complete details on this procedure. Faculty members have varying methods for calculating final grades in the traditional courses; however, whether a student passes or fails the course is ultimately determined by the course final exam. It is noteworthy, however, that faculty members grade their own final exams. I asked my participants to self-report because, ethically, it would not have been appropriate for me to search through any academic data files without their consent.
My goal was to include at least 20 participants in this study. I believe this number was reasonable for obtaining enough participants with good success rates who have taught developmental mathematics consistently for a two-year period and large enough to acquire rich findings. By inviting all eligible developmental math faculty to participate, I was striving to ensure that both full-timers and part-timers and men and women were equally represented in the study. I wanted to be sure that my findings represent various members of the developmental mathematics faculty and not simply one group.
Within one week of emailing the entire group of developmental math faculty (69 instructors), I received a total of 35 responses. Out of the 35 responses, 22 reported success rates of at least 60% and taught at least six developmental mathematics classes since the beginning of the fall of 2010. Again, success rates of 60% are considered good by the SCC administration. Therefore, I invited these 22 faculty members to participate in the study (see Appendix A-Invitation to Interview). All 22 instructors agreed to be
89 involved, but two eventually withdrew their names because they could not commit their time to the study. I then worked with each individual faculty member to arrange an interview time and place. My participants included nine full-time faculty (Jose, Ann,
Robyn, Jenny, Brenda, Jeff, Verne, Daniela, and Casey) and eleven adjunct faculty
(Dylan, Andrea, Megan, Jerry, Sally, Larry, Blake, Frankie, Katie, Taylor, and Kelly).
Note: The names above are pseudonyms. There were a total of 11 female and nine male participants. The ages of the participants ranged from late 20’s to late 50’s. The participants’ races consisted of White and African American/Black. Their experience in teaching developmental math ranged from two years to over thirty.
Informed consent and confidentiality are two factors that must be addressed when conducting a study with human participants. According to Kvale and Brinkmann (2009),
“Informed consent entails informing the research participants about the overall purpose of the investigation and the main features of the design, as well as of any possible risks and benefits from participation in the research project” (p. 70). In my initial email communication, I informed the potential participants that the purpose of my study was to gain an in-depth understanding of the best practices employed by a group of developmental mathematics instructors. More specifically, I explained that I was attempting to bring to light effective strategies and techniques to add to the knowledge base of developmental mathematics. I ensured that only the professional transcribers and
I would have access to the actual interview recordings and transcripts. However, I explained that the final report, which included raw data from the interviews, would be available to the public. Therefore, I addressed confidentiality, which according to Kvale and Brinkmann (2009), “implies that private data identifying the participants will not be
90 disclosed” (p. 72). Consequently, I assigned participants a pseudonym to protect their identities. This pseudonym was used on all paper documentation (pre-interview questions and demographics form) and during the interviews so that even the professional transcriber was not aware of the participant’s true identity. To further protect the identity of my participants, I locked away all pieces of information (i.e. questionnaires, transcripts, and field notes) relating to this study in a desk drawer. Only I had access to this information.
Data Collection Procedures
In order to ensure that my interview questions would elicit target data, I tested my interview protocol on two developmental math faculty members from SCC who would not be a part of the actual study. I did not use any of these interviewees’ responses in my findings. The purpose of these trial interviews was to evaluate my interview questions. My study consisted of pre-interview questions, which originally consisted of four questions that would be used in the face-to-face interview. I asked faculty to respond in writing to these questions within a week of the face-to-face interview. The study also consisted of a face-to-face interview, which originally consisted of eight lead questions with various follow-up questions and probes. My rationale for choosing each of these data collection procedures and a more in-depth explanation of each data collection method is explained in detail later in this chapter.
Based on results from the test interviews, I made some slight changes to my protocol. The largest change was the elimination of one question. It was originally the first question on both the pre-interview questionnaire and the face-to-face interview: “We are going to be discussing your experiences teaching developmental mathematics. Please
91 tell me what the term ‘developmental’ means to you.” First, I found that when employing this question, the interviews ran too long. Each ran for slightly more than 60 minutes, and this question consumed at least ten minutes of each interview. Faculty are quite busy, and I made a conscious effort to be considerate of their time. Second, I did not feel that their responses to this question in any way related to the concept of best practices in developmental mathematics. In fact, there was some overlap in their responses from this question and the second question: “Currently, the country is struggling with success rates in developmental mathematics classes as so many students are simply not passing their developmental math requirements. Based on your opinion, why are so many students struggling in developmental mathematics courses?” The test interviewees’ responses to the latter question connected more with the concept of best practices in developmental mathematics. Therefore, I eliminated the former question from both the pre-interview questions and the face-to-face interview and added the latter question on the list of pre- interview questions.
After conducting the trial interviews, I also decided to soften some of the language of my questions. For example, one of my original follow up questions was “Do you feel that all developmental mathematics instructors could successfully implement this practice or strategy?” When I posed this question, both interviewees paused and asked
“all?” One mentioned that the term “all” is very strong and could apply to every developmental mathematics instructor on the planet. Therefore, I opted to change the term “all” to “most.” To be consistent, I did that in every other follow-up question that originally utilized the term “all.”
92 There was also a lead question that I needed to reword in the face-to-face interview. Originally, my next to last question was “In your opinion, and based on your experience, please describe how Sinclair and community colleges in general could better accommodate the diverse needs of developmental mathematics students.” One interviewee became agitated after I posed this question, and asked “accommodate?” I nodded in the affirmative, and he answered the question. However, in our discussion after the interview, he suggested that I consider rewording that question since he and other community college faculty have become increasingly frustrated with the administrative concept of student consumerism. More specifically, he and other faculty members feel strongly that administrators cater to students solely for the purpose of bringing more income into the college. Consequently, I reworded the question to “In your opinion, and based on your experience, please describe how Sinclair and community colleges in general could do a better job of increasing student success in developmental mathematics.”
Finally, I asked both interviewees if they had any other suggestions for how I could improve my interview. One mentioned that when asked about best practices, it can be difficult for faculty to “think on their feet.” I had already asked faculty about general best practices that they employ in their classes on the list of pre-interview questions, but he also suggested asking faculty to think in advance about best practices that were content-specific. As a result, I added a fifth question to my list of pre-interview questions: “Please describe a content-specific best practice that you have utilized that increased student learning. More specifically, this is a practice that you use or have used to help students with developmental math content. For example, this practice could help
93 students with fractions, decimals, or linear equations.” This was already a follow-up question during the face-to-face interview.
Within one week before each interview, I assigned each participant five pre- interview questions. I asked each participant to reflect on each question, write a response and submit the document to me upon our face-to-face interview. The five questions were selected from the face-to-face interview. The purpose of this pre-interview exercise was to allow the participants to begin reflecting on their own teaching, policies, and practices.
More specifically, this allowed the participants to be better prepared for the face-to-face interviews, which resulted in richer and more descriptive data. For the complete list of pre-interview questions, please see Appendix C.
Prior to the face-to-face interview, I emailed a demographics form to my participants. It was included in the same communication as the pre-interview questions.
In this form, I asked my participants to answer background questions regarding their age and race and how many years they have been teaching overall and at SCC. Patton (2002) referred to these as background/demographic questions. My rationale for these questions was to garner information from which to create a profile of participants. More specifically, I was able to obtain background information such as the participants’ ages, ethnic backgrounds, and years of experience teaching developmental math. For more details on the demographics questionnaire, please see Appendix D (Faculty
Demographics Form).
Face-to-face interviews were the primary data collection method. Patton (2002) stated the following about interviews:
94 The purpose of interviewing, then, is to allow us to enter the other person’s
perspective. Qualitative interviewing begins with the assumption that the
perspective of others is meaningful, knowable, and able to be made explicit. We
interview to find out what is in and on someone else’s mind, to gather their
stories. (p. 341)
Kvale and Brinkmann (2009) pointed out that interviews have the purpose of producing knowledge.
I utilized a standardized, open-ended interview. Patton (2002) articulated that standardized, open-ended questions are carefully worded and are very specific. Each participant received the same lead question in the same order. Patton (2002) has also referred to this as a structured interview. He argued that a major advantage of the standardized open-ended interview is that because the interview is highly focused, the participants’ time is used efficiently. This was imperative as my participants are college faculty whose time is limited. Kvale and Brickmann (2009) also mentioned that when an interview is more structured, the later analysis of the interview will be more straightforward. However, the nature of the questions will still allow for rich and detailed responses. Each participant was asked a total of seven lead questions and various follow- up questions. My probes, however, varied as I utilized appropriate probes based on the responses from my participants. To ensure accuracy and allow verbatim transcription, each interview was audio recorded; however, I did take field notes during the interview process.
As Patton (2002) suggested, I began the interview with a rapport builder. More specifically, before moving to the interview questions, I attempted to create a welcoming
95 environment with informal conversation. For example, I may have asked the participants if they were enjoying the hot weather or I may have inquired about their summer plans. I believe this allowed my participants to become more at ease and talk freely during the actual interview.
I allowed the participants to choose the site of the interview. Several of the interviews were completed on the Dayton campus. Some took place in my office and others were conducted in the participants’ offices. Either way, all of the interviews on the Dayton campus were completed in a private office. I also conducted a few of the interviews at the Mason, Englewood, and Huber Heights campuses. Since faculty members do not have private offices at the satellite campuses, I conducted the interviews in an empty classroom. I also completed one interview at a coffee shop in the Dayton area. The length of each interview ranged from 35 to 51 minutes.
Over the course of the interview, I employed various types of interview questions such as opinion and values, experience/example and basic descriptive questions
(Janesick, 2004). I asked my participants to reflect on their own teaching experiences by asking experience/example questions such as, “Please give me an example of a student who did not pass your developmental math class.” Drawing from the participant’s experience led to richer data. The face-to-face interview also included basic descriptive questions such as, “Please describe a best practice that you have utilized in a developmental math class that has increased student learning.” This question was the heart of the study; I wanted to obtain a rich description of best practices that increase student learning. I also tried to gain an understanding of my participants’ emotions by posing feeling questions (Patton, 2002) such as “Many schools, including Sinclair, are
96 attempting to help students complete their developmental math requirements by offering accelerated and compressed course (if needed, I provided the definitions of the two aforementioned terms). As an educator, how do you feel about that?”
As both Kvale and Brickmann (2009) and Patton (2002) suggested, I employed follow-up questions and probes when necessary. For example, after the lead question in which I inquired about a best practice that the participant utilized, I followed up with this question: “Let’s say you were mentoring another faculty member who was about to employ this practice. How would an instructor go about using this practice to enhance student learning?” Another follow-up question (to the aforementioned lead question) was
“Do you feel that most developmental mathematics instructors could successfully implement this practice or strategy?” However, this kind of question is what Patton
(2002) labeled a dichotomous response question, which he warned could simply yield a
“yes” or “no” response. Therefore, there were some cases when I needed to employ the following probe after that question: “Why or Why not? Please explain that a little more.”
This merely allowed me to extend the discussion on the topic and obtain a richer description from my participants. The probes that I utilized varied based on the responses that I received. For example, when I asked one of the participants about a practice that did not work well, she simply replied “MyMathLab.” Obviously, I needed more information; therefore, I asked, “Can you talk about MyMathLab a little more?”
More importantly, all questions were singular because as Patton (2002) noted, “Multiple questions create tension and confusion because the person being interviewed doesn’t really know what is being asked” (p. 364). For the complete list of face-to-face interview questions, please see Appendix E (Face-to-face Interview Questions).
97 Method of Data Analysis
Upon completion of the interviews, recordings were professionally transcribed to ensure accuracy. I then began to read and reread the written information from the pre- interview questions and the interview transcripts, and more importantly, I began to code the data. According to Kvale and Brinkmann (2009), “Coding involves attaching one or more keywords to a text segment in order to permit later identification of a statement” (p.
202).
The overall method that I utilized to analyze the raw data was constant comparison. According to Merriam (2002b), constant comparison is when units of data that the researcher believes to be meaningful are compared with each other in order to generate tentative categories. I accomplished this by rereading both the transcripts and the pre-interview questions and writing memos, notes and other insights. I did this by hand in the margins of the documents and on a blank page next to each page of interviews. My first reading was simply aimed at developing the coding categories or classification system. I then started the coding process in a more formal way and transitioned to sorting, searching for common threads and ideas across the memos and notes. This in turn allowed me to generate tentative categories with the common ideas that emerged across the data. I continued to engage in constant comparison until I reached a point where no new insights and interpretations emerged from further coding.
Strategies to Ensure Trustworthiness
Qualitative research contrasts sharply with quantitative research in that data are in the form of words rather than numbers. Therefore, terms such as internal validity, the ability to infer a causal relationship, and external validity, the ability to statistically
98 generalize to a certain population (Shadish, Cook, & Campbell, 2002), are generally not used to evaluate qualitative research. Instead qualitative researchers often utilize terms such as credibility, transferability, and trustworthiness. Patton (2002) articulated that the credibility of qualitative research relies on the methods that the researcher uses while conducting the study. More specifically, did the researcher utilize methods that would lead the reader to believe that high quality data were collected?
Patton (2002) claimed that the credibility and authenticity of a study are determined by the actions of the researcher. For example, did the researcher conduct the study in an ethical manner? Ethical issues are bound to arise in qualitative studies.
Merriam (2002a) maintained that a trustworthy qualitative study is one that is conducted in an ethical manner. Operating a study in an ethical manner increases the reader’s confidence in the findings. Some ethical issues are clear cut. For example, Kvale and
Brinkmann (2009) and Patton (2002) stated that major ethical guidelines to follow when interviewing include obtaining the participants’ informed consent, securing confidentiality and discussing possible risks with the participants. As mentioned earlier in this chapter, I satisfied all of the aforementioned tasks before each interview. Merriam
(2002a), however, suggested that in many cases, no specific guideline can inform a researcher how to proceed ethically. Therefore, I engaged in journaling and self- reflection after each interview and throughout the study.
While conducting this study, I was not confronted with many ethical dilemmas.
The major ethical predicament that I faced consisted of a conflict in my role as the researcher and being an insider to the study. As permanent faculty members, we are encouraged to inform our department chairs when it comes to our attention that an
99 adjunct faculty member is either doing a stellar job in the classroom or is struggling mightily. That is because adjunct faculty may teach in the evenings or off the main campus and are not as visible to the department chair as full-time faculty.
As I was conducting interviews with the part-time faculty participants, I became impressed with the practices that many were employing in their classrooms. I was truly awestruck by the creativity and dedication of this group. As a faculty member, my first reaction was to pass this information along to my department chair so that we can be sure to retain these instructors. As a veteran faculty member, I am very well aware that we need to preserve quality adjunct faculty for the benefit of our students. However, I had to repeatedly remind myself that in this role I was a researcher not a faculty member.
Moreover, if I mentioned anything to my department chair, I would be breaching confidentiality. As I was reflecting on and struggling with this dilemma, I constructed a solution. I could ask the adjunct faculty members if I could inform our chair that they were employing some very innovative practices in their classroom. By obtaining their permission, I would not violate confidentiality. Also, it is not unusual for me to relay this kind of information to my department chair. In the past, when I have casually observed adjunct faculty members displaying exemplary teaching skills, I generally informed my chair. I contacted some of the adjunct faculty members and asked if I could share with my department chair that it had come to my attention they are doing a stellar job in the classroom. I specified that I would not mention that they were in my study. I simply explained that “it came to my attention.”
During the data collection and data analysis stages of this study, I engaged in reflexivity. According to Patton (2002), “Reflexivity has entered the qualitative lexicon
100 as a way of emphasizing the importance of self-awareness, political/cultural consciousness, and ownership of one’s perspective” (p. 64). Patton (2002) further articulated that reflexivity involves an ongoing examination of self-awareness. Lincoln and Guba (2000) specified that reflexivity involves reflecting critically on the self as the researcher. Ridenour and Newman (2008) suggested that researchers can engage in reflexivity by keeping a daily journal. Therefore, I maintained a daily journal in which I reflected on my thoughts and feelings after each interview.
I utilized my journal when making decisions throughout the study and how my beliefs and attitudes tied into my decision making. The process of reflexivity was imperative as I needed to identify and deal with potential biases. By identifying any potential or existing biases, I was able to judge whether any biases skewed my findings.
In my journal, I would reflect on each practice that the participants discussed. I would examine my own feelings and experiences with regard to the practices. For example, when a participant discussed using email communication to help students, I noted that I had success with this practice and felt very positive toward the use of this practice. Some of the participants noted that they had a negative experience with the software program,
MyMathLab (MML). I noted that this conflicted with my experience and feelings as I have utilized MML on a regular basis; furthermore, I have found the program to be beneficial to my students. When analyzing the raw data (interview transcripts and pre- interview documents) to construct my findings, I would constantly compare the raw data with my journal. This process helped me to separate my own feelings from the participants’ feedback. Maintaining a journal also allowed me to reflect on the ethical issue that I discussed earlier and to derive a solution. Again, my goal was to ensure that
101 my findings were grounded in the data that I collected. I believe that my ongoing examination of myself as the researcher through journaling allowed me to lucidly convey the ethical issue and biases that I encountered during my study.
By using both the pre-interview document and face-to-face interviews, I employed the strategy of triangulation. More specifically, I used the data from both the interviews and the pre-interview document to construct my findings. Merriam (2002a) described triangulation as the use of multiple methods of data collection in a study.
Ridenour and Newman (2008) claimed that the use of triangulation can help the researcher obtain a fuller and richer interpretation. Most of all Patton (2002) pointed out that through triangulation, “Researchers can make substantial strides in overcoming the skepticism that greets singular methods, lone analysts, and single-perspective interpretations” (p. 556). While the pre-interview document employed some of the questions from the face-to-face interviews, the two approaches did at times yield different types of data. The interviewees’ responses to the pre-interview questions tended to be shorter and not as descriptive and rich as the responses during the face-to-face interview.
This was most likely due to the fact that I was able to employ various follow-up questions and probes during the face-to-face interview. The data from the pre-interview document were, however, easier to code. In answering the pre-interview questions, the responses tended to be linear, concise and to the point as opposed to the data from the face-to-face interviews where the responses were not always straightforward and at times contained extraneous information.
Member checking was another salient trustworthiness strategy that I utilized.
Merriam (2002a) suggested that member checking should be conducted after the
102 researcher has begun to interpret and analyze the data. Krathwohl (2009) specified that member checking involves asking the “study participants to read the researcher’s report to determine whether it has portrayed them accurately” (p. 346). Therefore, after I constructed tentative findings, I contacted my participants via email, and I asked them if they felt that my findings were grounded in their responses. For further details, please see Appendix F (Invitation for Member Checking). If any of my participants did not feel that my findings were grounded in their responses, I would have re-examined my findings and compared those findings again with my raw data. However, my participants concurred with my findings; therefore, I proceeded with the study.
After analyzing and interpreting the data, I engaged in peer debriefing. According to Merriam (2002a), peer debriefing involves “asking a colleague to scan some of the raw data and assess whether the findings are plausible based on the data” (p. 26). Ridenour and Newman (2008) asserted that in a qualitative study, researchers may begin to develop feelings or become somewhat attached to their participants and as a result, interpret data based on their own feelings. Therefore, it is imperative for researchers to ask other professionals to examine their construction of meaning. I asked two colleagues to review my interview transcripts and the participants’ responses to the pre-interview questionnaires as well as my tentative finding. My peer debriefers did not have a background in developmental mathematics; however, they completed qualitative dissertations that consisted of interviews as the primary data collection method. I provided them with a thorough and detailed outline of my findings that were arranged in categories and sub-categories. I asked the peer debriefers the following questions: Do you feel that the raw data from the transcripts and the pre-interview responses are
103 evidenced in my findings? Do you feel that the categories I have constructed accurately reflect the data I have collected? Is there any extraneous information in my findings?
The peer debriefers reported that the findings were indeed grounded in my data and that I did not include any extraneous information. However, they did suggest that I reword and slightly rearrange some of my sub-categories. I reviewed their suggestions along with my findings and decided to alter some of my sub-categories accordingly.
To ensure further trustworthiness, I provided an audit trail. According to
Krathwohl (2009), “Researchers argue that leaving a clear audit trail helps critics to track the steps of qualitative method and is likely to provide for greater methodological rigor”
(p. 331). Merriam (2002a) specified that an audit trail is dependent upon the researcher engaging in reflexivity throughout the study. As stated earlier, I kept a reflective journal through the duration of the study. In this report, I have addressed how I arrived at my findings and the struggles and ethical issues that I encountered along the way. I also appended various documents, such as the pre-interview questions, the face-to-face interview questions, and other communications to the participants to the final report.
This will assist other researchers in understanding the details of the study.
As stated earlier, I sought diversity in my sample of developmental mathematics instructors: part-time, full-time, male, and female. Merriam (2002a) referred to this strategy as “maximum variation” (p. 31). I purposely pursued diversity in my selection to allow for a greater range of findings. I achieved this by including a balanced number of full-time and part-time faculty in my study as well as an evenhanded number of men and women.
104 In my face-to-face interviews, I pursued negative cases. That is, I sought out data that disconfirmed existing data. This was imperative as I needed to take all data into account before presenting my findings. Ridenour and Newman (2008) stated that in negative case analysis, “The researcher expands and reshapes interpretation until all outliers are included” (p. 58). Even though at times there were findings that emerged because a majority of participants regarded them as best practices, there still might have been a small number of participants who struggled with such a practice. Therefore, I included this information in my findings to provide the reader with the whole picture.
Merriam (2002a) articulated that “the researcher must be submerged or engaged in the data-collection phase over a long enough period to ensure an in-depth understanding of the phenomenon” (p. 26). Qualitative researchers often refer to this strategy as prolonged on-site engagement. Ridenour and Newman (2008) pointed out that if a researcher fails to remain in the data collection process for sufficient time, he or she may only see part of the picture. Consequently, the researcher will not collect high quality, rich, and even accurate data. Merriam (2002a) posited that there is no specific guideline that can inform any researcher a time length for the data collection process. My original goal was to include a minimum of 20 participants in this study so that I could achieve thick, rich data. I was able to achieve this goal with the 20 interviewees who took part in this study.
Ridenour and Newman (2008) stressed the importance of transferability in a qualitative study. Transferability refers to the likelihood that the findings of the study will hold up in another setting or situation. The reader must be able to judge this and come to a conclusion. I allowed my readers to do this by providing a thick, rich
105 description of the setting and my findings. Patton (2002) conveyed that “thick, rich description provides the foundation for qualitative analysis and reporting” (p. 437).
Again, qualitative findings are not generalizable; however, it is important for researchers to be able to determine whether findings from a study are transferrable to another context.
Merriam (2002a) posited that providing a thick, rich description will allow readers to determine how closely situations match and whether findings can be transferred. Patton
(2002) argued that studies that are rich and detailed open up a world to the reader.
Ridenour and Newman (2008) claimed that a thick, rich description can place the reader within the scenario of the story. Therefore, the presentation of my findings was detailed and should provide enough information for other researchers to determine transferability.
Also, Krathwohl (2009) maintained that a researcher can provide a thick, rich description by including excerpts of raw data into the findings. I included specific quotes from interviews to convey detail to the readers.
In summary, a researcher must utilize various strategies to ensure overall trustworthiness in a study. Ridenour and Newman (2008) articulated that trustworthiness refers to the “truth value” of a study. In other words, the reader should be able to conclude that the findings of a study are believable.
Limitations
Despite my best efforts, certain limitations were inevitable in this study. This study was limited to 20 faculty participants who identified and described best practices in developmental math. Consequently, there were faculty members who did not participate in this study and thus it is possible that these instructors who did not participate may have not found success with some of the methods and strategies that the participating faculty
106 identified as best practices. In summary, the findings from this study are not absolute; they are based on the feedback from the 20 participating faculty members.
As mentioned earlier in this chapter, I related to my part-time faculty participants that as a permanent faculty member, I do not consider myself superior to anyone else.
Nonetheless some of these part-time faculty participants may have still viewed me as a superior and chose not to participate in the study. As for the part-time faculty who did participate, this may have affected their answers to various interview questions.
Time may have been an issue as well. Due to teaching loads and other responsibilities, faculty are generally quite busy. This may have limited their available time to devote to the interview and furthermore may have limited the richness of their responses.
Chapter Summary
This was a qualitative study that utilized a basic interpretive design. Thus, I, the researcher, was the main instrument in this study. I am currently a professor of developmental mathematics at Sinclair Community College (SCC), the site of this study.
SCC is a large urban community college in Dayton, Ohio. The participants in this study were full-time and part-time developmental mathematics faculty who have taught at least six developmental mathematics classes since the beginning of fall term in September of
2010 and have reported average success rates of 60% or higher. My data collection methods consisted of a pre-interview exercise and face-to-face interviews. Using the constant comparison method, I analyzed these data. I also employed various strategies to ensure the trustworthiness of the study.
107 CHAPTER IV
FINDINGS
Introduction
In this chapter, I present the findings from this study. The findings are based on the data I collected from 20 participants through face-to-face interviews and the pre- interview questionnaires. In presenting my findings, I first discuss the inhibitors to student success in developmental math. Then, I describe the various best practices that developmental math instructors employ. Such practices will be divided into two main categories: general best practices and content-specific best practices. After discussing the general and content-specific best practices, I examine developmental math instructors’ views and experiences with accelerated instruction. I specifically asked the participants about acceleration because currently it is a salient topic in developmental math. Finally, I discuss the various institutional improvements that developmental math faculty feel are necessary to enhance student learning in developmental math.
Inhibitors to Student Success in Developmental Mathematics
I began each interview by asking the faculty participants to discuss some of the deterrents to student success they recognize in teaching developmental mathematics.
Before discussing best practices, I felt it was salient to bring these inhibitors to light.
Based on the feedback from the faculty participants, I grouped the major inhibitors to
108 student success into three major categories: severe underpreparedness, behaviors that thwart success, and external issues.
Severe underpreparedness.
Developmental education has always served the underprepared student.
However, several of the participants reported that many incoming developmental math students are too far behind academically when they enter community college and that it is difficult to help them achieve success even in a developmental math class. The faculty participants asserted that many incoming developmental math students lack very basic computational skills. Again, students place into developmental math because they lack basic skills; however, these students often lack the most vital of the basic skills.
When beginning their teaching assignments some of the participants were astonished at the skill level of their students. Frankie recalled:
On my first day of teaching DEV 085, I asked a student, ‘OK what is three times
five?’ The student paused and, after what seemed like an eternity, tentatively
answered ‘eight?’ I couldn’t believe it; this is college and she couldn’t multiply!
Casey was just as surprised:
On the first day of a DEV 084 class, I asked the class to turn to page 24. I had a
student who did not understand what I meant. He had no understanding of double
digit numbers. He couldn’t identify numbers past nine!
Kelly recalled an incident when she asked a group of students, “‘If I had a dollar, how many 40 cent stamps can I buy?’” Kelly mentioned that she would get answers anywhere from “1 to 20”. When she asked, “why did you say 20?” the students’ general response was “‘well, that just sounds like a good number.’”
109 Several other faculty participants agreed that developmental math students lack very basic skills. According to Robyn, “Students aren’t coming in with basic knowledge that they need to have and be aware of, such as multiplication facts and long division.”
Besides a deficiency in addition, subtraction, multiplication, and division skills, the participants pointed out that students also lack a basic understanding of numbers and are incapable of basic mental math. Katie explained, “They literally have to add numbers together using their fingers because they don’t understand; they don’t have a firm enough grasp on number sense. They just don’t know their basic fundamental mathematical facts.” Many of the participants pointed out that even in the lowest level class, when students are that deficient in basic skills, it is difficult for them to keep up with the class, and inevitably they fail or withdraw from the class. That is because it is difficult for a student to develop number sense and master the basic operations with addition, subtraction, multiplication, and division and also ascertain more advanced arithmetic skills such as fractions and decimals within the time constraints of an academic term.
Many of the faculty participants pointed out that the severe underpreparedness of incoming developmental mathematics students stems from the fact that an inordinate amount of incoming developmental math students are calculator dependent. In fact, some of the participants mentioned that many students begin using calculators as early as the second grade. When students enroll in developmental math classes at SCC, which do not allow calculator usage on exams, they struggle.
Several of the faculty participants argued that calculator dependency can hinder the maturity of basic number sense. Jenny stated, “They’re so used to plugging in numbers, there’s no logic about what they’re doing, why they’re doing it.” She added,
110 “Along with that, they’re not learning when an answer makes sense, when an answer doesn’t make sense; if they plug in a division problem the wrong way, they don’t understand why it’s wrong.” According to Ann, “I don’t think they really see the value in knowing this stuff, since calculators can do it for them.” Verne specified that “with the use of calculators kids don’t have to think anymore. They don’t have to know the basic facts because they have the calculator that does the thinking for them.”
During the interviews, some of the faculty participants reported that the math area has received external pressure from the SCC administration to allow students to use calculators throughout their developmental math classes and on all exams as this will increase success rates. However, many of these faculty members pointed out that such a practice would only hinder students later in their academic endeavor. Taylor, who has taught college level classes, stated “If students don’t have number sense, the most advanced calculator in the world won’t help them.” Taylor recalled “When I’ve taught a business math class, where they can use the calculators, it’s so obvious if a student doesn’t have number sense because they don’t even know how to enter a formula or what not on the calculator.”
The faculty participants also maintained that there is general misalignment in regard to student expectations between most high school mathematics curricula and in developmental math in post-secondary education. Some of the participants expressed frustration that in high school, students are simply required to memorize formulas and facts for the Ohio Graduation Tests (OGT). Dylan voiced his frustration: “They just want students to memorize formulas and facts. Students really don’t learn anything.” The overarching belief from the faculty participants was that students do not gain an in-depth
111 understanding of the mathematical concepts; therefore, shortly after taking the OGT, they forget everything.
Behaviors that thwart success.
When discussing reasons for students’ lack of success in developmental mathematics, the faculty participants expressed frustration with various student behaviors. More specifically, these are behaviors that faculty feel thwart student success and lead to failure in developmental mathematics. The most noted obstructive behavior that developmental math students exhibited was subpar attendance. In general, the faculty participants asserted that most of the students who miss several classes are generally unsuccessful. As a result of these absences, students develop gaps in their knowledge base, and because of the linear structure of developmental math, they struggle with advanced material since they do not have the necessary understanding of the pre- requisite material. For example, Larry recalled a former student in his DEV 108 class who missed the two classes in which he introduced basic linear equations. “By the time she came back, I was already doing advanced linear equations with fractions and decimals. She just got really frustrated because she still couldn’t understand one or two step equations. She just never recovered from that.”
The patterns of attendance issues vary. As mentioned above, there are those students who miss classes several times during the term. However, there are also students who simply stop attending class altogether at some point in the term. Blake recalled, “Every quarter I get students who attend class for maybe the first few weeks and just drop out. They don’t even officially withdraw from the class, so they just get an
‘F.’” Even more baffling to faculty are the students who are successfully passing the
112 course and then simply stop attending. Katie explained, “I’ve had students that make it through the first two units of a course and pass, and I had a good feeling they would pass the course, and then they just stopped coming.” Katie further speculated: “I assume they would have successfully completed the course, but it’s hard to predict.” There are also students who only attend the first or second class session, and then there are students who never attend a single class but do not withdraw. Sally shook her head when reflecting on that particular behavior: “That’s about the one thing I can predict every quarter. There will always be at least one student who will never come to class and not even withdraw.”
The faculty participants expressed irritation over paltry attendance. Several of the respondents believe that more students would pass if they merely came to class. These interviewees were frustrated because if a student ceases attending class or never attends class and does not withdraw within the first week of the term, it negatively impacts the faculty member’s overall success rates because non-attendance is counted as a non- success. Verne said it best: “They [the students] never show up to class, and it looks like it’s our fault.” Jerry reflected on a student who did not show up to class until the sixth week of one academic term: “This guy came in and asked if there was anything he could do to pass the class. I told him it was too late, and he needed to withdraw. On the way out he said, ‘What a sucky teacher!’” Jerry laughed, “How does he know I’m a sucky teacher? He’s never seen me teach!”
Some of the students who attend still display in-class behaviors that thwart their success. The faculty participants reported that many students exhibit chronic tardiness; that is, they consistently stroll into class 15 or 30 minutes late. Many students will also leave class for long periods of time to take a call on their cellular phone. It is also
113 common for developmental math students to put their heads on the desk and sleep during class. Dylan mentioned that he had a student spring quarter of 2012 who slept during every class. Taylor recalled: “I had one guy that would fall asleep and snore loudly. I would wake him up, and he would fall asleep again!” Even though these students technically attended class, they would still miss vital parts of the class thereby encumbering their success. Casey remarked that many developmental math students often sit at their desks during class not taking a single note. “They don’t think they need to take notes, so they don’t, and then they don’t pass.” Other faculty members observed that many unsuccessful developmental math students exhibit loner behaviors in class.
More specifically, these students do not engage with their peers or the instructor.
According to Jeff, “Some students will walk into class the first day and purposely walk to the farthest corner of the class to sit down; they don’t want to interact with anyone at all.”
Larry observed, “Students who don’t talk to any of their classmates or me and just sit in the back of the room are somehow not successful in the long run.”
The faculty participants maintained that many developmental math students simply lack work ethic and self-responsibility. Oftentimes, students who miss class or parts of class do not take advantage of faculty office hours or SCC’s tutoring center for extra help. Even the students who attend regularly and are struggling often do not take advantage of these services. The faculty participants also explained that students do not spend enough time reviewing their class notes or on their homework assignments.
Several participants argued that math is difficult for many students, and they need to spend the appropriate amount time on the material. As Jose said, “Students should be working on their math every day.” Quite a few of the participants cited that there are
114 several developmental math students that have the ability to pass; they simply do not put in the time and effort. Kelly attributes this lack of self-responsibility to the fact that many students have never had to pay for their own education in their K-12 years or at
SCC. Many students receive public grants or have their parents pay for their education.
“They don’t see any value in education and as a result they don’t feel that they need an education.” Kelly added that many students expect to be awarded something for giving nothing. She labeled this current group of students “the entitlement generation.”
Along with putting in the time and effort, several of the faculty participants articulated that organizational skills are imperative for succeeding in math. Many developmental math students seem to lack such skills. Blake elaborated, “It is quite common to see a student walk in with papers hanging out of a notebook, if they even have a notebook!” According to Sally, “Their organization when doing math is atrocious!
When I look at their tests and quizzes, there are numbers all over the place, upside down and sideways!” The participants remarked that students also lack structured study schedules. They simply do not understand how to organize their time efficiently. Again, many of the faculty participants believe that some of these students could be successful, but their haphazard organization obstructs their potential success.
A few of the faculty participants attributed low confidence levels to some of the students’ behaviors such as loner behavior, not putting forth maximum effort, and subpar attendance. Megan gave her thoughts: “I think that when some students come in they believe they’re going to fail. They didn’t get it when they were younger; they’re not going to get it now.” Other faculty participants articulated that some students will start
115 the term on a good note, but as the material becomes harder, they become frustrated and stop trying.
External issues.
The interviewees mentioned that developmental math students also contend with various external issues that encumber their success. “Some students have so much going on in their lives between working full-time, and their kids; they can’t put in the time even if they wanted to” stated Jenny. Faculty participants reported that the majority of their students work full-time and many of these students must care for small children. This is the same for both younger and older students. Oftentimes these external obligations prohibit students from attending class and putting forth the time and effort to successfully complete the course.
Developmental math students struggle with family and work obligations; however, those are only a few of the external issues that hinder student success. Some of the faculty participants pointed out that some developmental math students struggle with drug and alcohol problems. Jerry recalled: “I had one guy that tried to take my class three different times, but every time he stopped coming because he was an alcoholic. He wanted to do well, but he couldn’t kick the habit.” Other students have recently returned home from the war, and some have been released from prison. In both cases, students encounter adjustment and post-traumatic stress issues that inhibit them from putting the necessary time into succeeding. Sally elaborated, “I remember this one gentleman who had just returned from Iraq. He was very cordial but was listless in class and he would miss many classes. He later explained to me that he was having night terrors as a result of his experience in Iraq and he couldn’t sleep. He never finished the class.”
116 In this section, I described what the faculty participants conveyed as the major inhibitors to student success in developmental mathematics. In summary, the interviewees cited that severe underpreparedness, various behaviors, and external issues are the major reasons for lack of student success. In the next section, I discuss some of the general best practices that the participants employ to enhance student learning in developmental math.
General Best Practices
During the interviews, I inquired about best practices that the participants employ in their developmental math classes. I defined best practices for the participants as the methods, techniques, or strategies that have consistently shown positive results such as increased student success rates and student retention. It is worthy of note that these were practices that were effective on a consistent basis for the participants as opposed to practices that worked simply once or twice. I categorized the best practices in this section as “general best practices.” Such practices are not geared toward any specific math content; they are overall practices that instructors use in their developmental math classes. I found that there were five common general best practices: communication with students, the art of organization, collaborative learning, frequent low stake assessments, and technology supplements.
Communication with students.
Several of the faculty participants asserted that it is important for developmental math instructors to establish effective communication with their students. Blake articulated:
117 It’s not like Harvard where you lecture to 150 students and you don’t know or
care about who they are. As DEV instructors, we need to go the extra mile and
reach out to our students. Our students need that!
Based on responses from the participants, I arranged the practice of communication into two sub-categories: communicate with students regularly regarding their progress and general meaningful interaction.
Communicate with students regularly regarding their progress.
Quite a few of the faculty participants pointed out that one of the key mistakes made by novice developmental math instructors is treating their students like first-year university students rather than community college students in a developmental course.
Blake reflected on his first teaching experience in a developmental math course: “I would just lecture each day, give homework after each class and give tests on assigned days. I never talked to them about how they were doing. I figured they were in college so they knew!” Blake received a surprise at the end of the term:
There were students with overall percentage points that were 50 or 60 points
below passing that were shocked that they failed! Some hadn’t done homework;
others had missed exams. I knew then that I needed to establish better
communication with my students throughout the quarter.
Jenny discussed the mid-term review, a practice she uses half way through the term to alert students to their current academic standing in the class. During a designated class period, Jenny provides students with a sheet of paper that lists all of their grades
(tests, quizzes, and homework assignments). Using the class grading formula, students compute their overall average in the class. The students must translate their average into
118 a letter grade: A, B, C, D, or F. Jenny double checks each student’s calculations to ensure that they are accurate and checks “agree” or “disagree” on his or her paper.
After the students have computed their averages, they must answer a series of questions that Jenny has listed. These questions require students to reflect on their progress and overall commitment to the course. Jenny articulated that such questions include: “How many times have I been absent? How many times have I been late? Have I been using the college’s Tutoring and Learning Center? How many hours each week?”
Jenny first attempted the mid-term review because she grew tired of students failing and not even comprehending why they were failing.
Jenny noted that employing the mid-term review has made an impact on many students. “Every quarter I have students that are not passing at that time and then in the remaining weeks are able to turn things around.” Jenny further cited that these students tend to come to her office hours for extra help and also begin to demonstrate an improved overall effort and attitude in class.
Jose stressed the importance of consistent email communication. All instructors who teach distance learning must utilize the exact same computer software, syllabus, assignments, exams, and even daily schedule throughout the course. However, it is at the discretion of the instructor as to how little or often he or she communicates with students.
According to Jose, “It really becomes incumbent on the teacher to be aware of all students’ progress. If a student is falling behind or hasn’t even logged into class, the teacher needs to get in touch with that student.” Jose pointed out that this can be simply a gentle reminder such as “Hello, I see you are a little behind in class; is there anything I can do to help?” Jose argued that consistent email communication should not simply be
119 reserved for the students who are struggling. He also mentioned that instructors should send various uplifting messages when students are succeeding: “Hey way to go for being a little bit ahead of schedule. Keep up the good work and let me know if you have any questions!”
Jose advocates that all instructors who teach distance learning communicate with their students on a regular basis. He believes that most developmental math instructors could successfully implement this practice; however, they must be willing to communicate with students every day and that includes weekends. Jose also articulated that consistent communication can positively impact most developmental math students in distance learning courses: “I’ve noticed that the students that were behind in the class, instead of never hearing from them again, they actually become more engaged.” Jose further noted, “These students often send me an email thanking me for being concerned.”
Jose pointed out that as he has increased his communication with all students, his success rates have increased as well. Robyn, who also teaches developmental math distance learning regularly, communicates with her students on a regular basis. However, she warned that instructors must be consistent. “A lot of times we can be excellent communicators at the beginning of the quarter and then we get busy. Life happens.
Then, we lose students.” Robyn’s advice to instructors: “Keep staying in touch and keep touching base with your students throughout the quarter, not just at the beginning.”
Blake utilizes email reminders in his face-to-face classes; however, he asserted that email reminders about student absences and upcoming assignments are not enough.
Therefore, he often includes a riddle or joke in his communications. Students must then come to class to receive the answer or punch line. Blake mentioned that such riddles and
120 jokes are not necessarily math related; they simply get students to think. Blake relayed his favorite email riddle:
A man walks through a dessert and into a bar and sits down at the bar. The
bartender takes one look at him and instead of giving the man a drink, he grabs a
shotgun and fires two shots in the air. The man leaves feeling satisfied. Why?
Blake laughed: “He had the hiccups! The gun shots scared him and his hiccups were cured!” Blake explained how he discovered this practice: “I wasn’t getting anywhere with the plain old reminder emails. So I decided to spice them up with a joke or something.”
He maintained that since he has been using these email communications, his attendance has increased. Moreover, students come to class with a more positive and relaxed attitude. “They show up to class eager to get an answer to a riddle or joke. After I give the answer, we all laugh; the positive mood seems to linger.”
Of course persistent communication about student progress does not work for all students. In her face-to-face classes, Ann reminds students of their current academic standing throughout the term. However, she recalled a student who approached her before taking the final. He asked Ann how many points he needed to pass the course, and
Ann informed the student that he needed 220 points. This was unfortunate as the final exam was only worth 100 points. Basically, the student had missed several classes and assignments and failed some of the exams. Therefore, failure was imminent for this student. Ann had several conversations with this student throughout the term; she even informed him that he needed to withdraw to avoid receiving an “F.” However, this student simply did not acknowledge those conversations and was genuinely stunned that he was doomed to fail.
121 Communication regarding progress is not always about relaying information regarding grades or keeping after students regarding attendance. Jeff and Casey stressed the importance of communicating with students during class when they are learning or even reviewing material. Jeff explained, “I will sit with every student at some point during class to see if they’re getting something. I say things like, ‘Hey you’re getting this’ or ‘Good work but here’s what you could do differently.’” Casey has employed this strategy as well:
When I first started teaching DEV math, I would simply lecture and never really
touch base with students individually during class. I had really high attrition
rates. When I reach out to students like that, students appreciate it; I can see it in
their faces that they know someone cares. Now, I have students who stay and
pass who would have most likely withdrawn from the class because they were
frustrated.
Both Jeff and Casey pointed out that faculty members must be willing to reach out to students. Both participants also noted that this type of practice is the most successful in the lower level developmental math courses where there are the students with the lowest skill level.
Faculty can communicate with students regarding their progress in other ways as well. Andrea explained how she uses partial credit to alert students to their development on a specific topic. However, this is more than simply awarding a student two points out of a possible five for a given math problem. When reviewing a student’s homework or quiz problem, Andrea points out the mistakes; however, she also brings to light what a student did right. For example, if a student solved a six step linear equation and made a
122 mistake on two of the steps, Andrea explains the mistakes to her student but also praises him or her for the steps performed correctly. By reviewing their work thoroughly,
Andrea is also able to establish common mistake patterns that students make.
Furthermore, she is able to help them cease those patterns.
Andrea noted that students become more engaged when she utilizes this kind of communication and encouragement. They put forth more effort to correct their mistakes, and since Andrea has employed this strategy, student grades on higher stake exams have improved. Andrea warned that this practice does not work for all students: “This works for most students except for the ones [students] that don’t care or hardly come to class.
It’s for the students who want to put forth the effort.” Andrea offered the following advice for faculty looking to implement this practice: “Be thorough; don’t just look at the answer, but really look at the steps. It will take a lot of time, but it’s worth it.”
General meaningful interaction.
Effective communication need not always center on informing students of their progress. Frankie and Daniela articulated that they encourage group discussions when introducing a new mathematical concept. Frankie explained, “After I introduce a concept, like solving proportions, we talk about it. I ask various students to explain the process and why they’re doing each step. We talk about the importance of various steps and potential mistakes.” Frankie added, “It gets the class involved. A lot of different people contribute.” Both Frankie and Daniela mentioned that the concept of a group discussion relaxes the students and they are more likely to participate. Daniela commented, “They don’t really feel like they’re on the spot because it’s a group discussion.”
123 Both Frankie and Daniela have noticed improvement in their students’ progress since they started utilizing these group discussions. Daniela specified, “When I grade their assignments, I can tell their work is more sufficient compared to before I did this.
These discussions are helping them go from point A to point B to point C in a math problem.” Frankie noted, “When I used to just lecture without interaction, students would look completely disinterested; many would start putting their heads down on the desk.
Now they’re interested in doing math, and I even see higher test grades!”
I asked Frankie and Daniela in separate interviews if group discussions would be a good fit for most developmental math students and instructors. Both pointed out that this works better when there are at least a few students who want to socialize and be interactive. Frankie elaborated, “When a few students start participating, it gets more people involved, and suddenly there is a group discussion.” However, Frankie warned,
“Sometimes there are classes where no one wants to talk to each other. No matter what I do; they won’t talk.” Both Frankie and Daniela mentioned that they have outgoing personalities, and that helps them to facilitate these group discussions. Daniela specified that some instructors may need to “come out of their shell” for this to work.
Interaction with students does not always have to focus strictly on math. Dylan explained how he breaks up his developmental math classes with an anecdote or joke:
“I’ll usually try to bring in an anecdote…something funny one of my kids did, and I usually try to make it funny.” Dylan does this to lighten the mood and most of all help students associate a positive emotion with math. For example, during one particular class, Dylan gave an anecdote about three of his fifth grade boys who were constantly in trouble. “That little break gives their [the students] minds a chance to get off the topic.
124 They’re refreshed. As soon as we get the chuckle, we’re on to something new.” Dylan mentioned that since he has been using this technique his retention rates have increased.
“Students are just having more fun and they are hanging around and actually learning!”
Robyn stressed the importance of connecting with students at the beginning of the term. She explained that on the first day of class she asks students to write their name on a card stock to display on their desks. This way Robyn can learn everyone’s name as soon as possible. Robyn also asks students about their individual majors and overall college goals. She also conferences with students individually and points out how math can help them with their future careers or how much math they may need to take to achieve their career goals. “I’ve found the more I engage with them, the more I connect, and the more I build rapport with these students, the more likely they are to keep coming to class and even pass.” Robyn added, “Even if they don’t make it through the course, they come back the next quarter and take me again.” Robyn pointed out that her academic background in education, which consists of a lot of interactive learning, and her outgoing personality has contributed to successfully implementing this technique. However, she was not comfortable with this technique when she started teaching at the community college level. “At the beginning I was a little shy. I was not confident being a college instructor because I’d never done that before. So I went through the motions without really engaging them.” However, as time passed, Robyn learned that the more she built rapport with the students, the more they trusted her. Of course Robyn warned that this practice will not work with every student: “Some students just don’t want to talk, and that’s fine.”
125 Megan discussed various ice-breaker activities that she employs on the first day.
She will have students talk and share information: their name, major, and personal interests. Megan has also facilitated games where each student introduces themselves to the class, and after each introduction, each student must recount the names of the students who have just introduced themselves. For example, if Henry is the sixth student to introduce himself, he must reiterate the names of the five prior students who introduced themselves.
Megan articulated that such ice-breaker activities help students to become more comfortable in class. “People start making connections with each other. They will realize that they have things in common like majors, interests or even the same type of dog.
Then, they start sitting next to each other in class.” Furthermore, Megan has observed that the students who make these connections tend to come to class regularly, which she asserted is the first step toward learning.
Andrea, however, has imposed one of the ice-breaker activities that Megan mentioned and did not find it to be a proper fit with developmental math students.
I’ve asked them to give their name and introduce everyone before them. I won’t
do that again. We have a lot of special needs students in DEV. To ask them to
stand up and introduce themselves or the person next to them and remember
names could be incredibly traumatic. They can’t remember names, and they get
really embarrassed. I could see it in their faces; I lost them on the first day.
The art of organization.
The participants noted that poor organizational habits often hinder the success of a developmental math student. Therefore, the importance of organization and structure
126 ascended as a best practice theme. However, it is not only important for students to develop organizational skills but also for the developmental math department or area to create structure.
The development of student organizational skills.
Quite a few of the faculty participants stressed that the organizational skills of developmental math students are not beyond reproach. According to Jerry, “DEV math students often fail because they don’t know what to study or even how to study. It’s really up to us to help them with their organizational skills so that they can prepare better and eventually succeed.” Several of the participants stressed the importance of providing detailed notes for students. The participants further emphasized this need by citing that developmental math students’ lack structure when solving or simplifying a math problem.
Larry clarified, “It’s not always that students don’t know how to do a problem; they are just so disorganized.” I asked Larry to provide an example. “Take this guy in my DEV
085 class who was trying to simplify expressions using the order of operations. He had numbers all over the place: upside down and sideways. He had numbers coming out of numbers!” Many of the faculty participants believe that such disorganization when working a math problem impedes student learning and student success. Larry further articulated: “They’re just not seeing how it all fits together when they make a mess out of the math problem. Math is about logic. How can you truly learn and understand math when you’re that disorganized?” Larry, Jerry, and Katie asserted that students must be able to rely on an algorithm, which is an effective step-by-step method for completing a math problem, for support when working a math problem. Larry elaborated, “During each class, we construct the steps to solving a specific math problem. I have students
127 work on problems during class, and I walk around to make sure that they are showing all of the steps.” I asked Larry if this is successful with most developmental math students:
Usually, they are resistant at first, but I keep after them to show all the steps. I’m
like a broken record, and the only way they get me to shut up is to show all their
steps. Eventually, most of them come around.
Larry maintained that by the end of the term the majority of the class is showing all the necessary steps in an organized fashion.
Jerry and Katie have been employing the same technique as Larry. “When a student begins to struggle with a problem, I ask ‘OK what is the first thing you do?’ If they can remember the first couple of steps, the rest comes easier for them” explained
Jerry. Katie described her approach: “I’ll introduce the step-by-step process and we follow that step-by-step process through problem, after problem, after problem.”
The participants pointed out that over the course of the term students begin to thank them for showing the steps so clearly and developing such coherent algorithms.
Larry’s students further commented that these algorithms provided a “safety net” when taking exams. Katie reflected on a comment she often hears from her students after they master the step-by-step approach, “‘Well if they would have just taught it to me that way in high school, I would have learned how to do it, and I wouldn’t need to be here [in a
DEV math class].’”
Jerry, Larry, and Katie emphasized that this technique of creating structure when working math problem does not work for all students. If students have missed many classes and have fallen far behind, structure is useless. The participants also mentioned that there are also those students who simply refuse to comply. These students will not
128 attempt or stay with a structured method and simply continue or fall back into their disorganized ways. Such students are generally not successful in the course.
I asked the participants to provide some advice to other developmental math faculty who wish to implement this practice. Jerry had an immediate response: “The double p’s: preparation and patience.” Jerry explained, and Larry’s comments were similar, that developmental math instructors must be well prepared for class. They must review each math problem that they are going to cover in class several times so that they can convey a solid algorithm. Jerry also stressed that developmental math instructors need patience because students will be initially resistant to such structure. “Just keep after them [the students] to adopt the method. Most of them will come around, and they will thank you later!” Katie emphasized that while it is important to be thorough, too much information can be an issue. She pointed out that when explaining a problem, many math textbooks simply utilize “too many words, too many conditions and too much clutter.
Students get way too confused because there is too much information.” Katie’s advice to other faculty: “Be as specific as possible without being overwhelming. Explanations are good, but keep it as minimalistic as possible because they need to go back and follow what you did.”
When working with students to create structure while working math problems, a couple of the instructors emphasized that in addition to showing students the step-by-step approach, it is important to allow students to practice on their own in class. When
Daniela first began teaching developmental math, she would work problems with her students as a group stressing the structure, but she began to notice an issue. “Some of the students were not keeping up because they weren’t as quick as other students. So they
129 were just writing down answers, but they didn’t know what they were writing down.”
Daniela explained her solution: “I make them work out a few problems on their own in class, and every 15 minutes, I’ll put three or four answers on the board with the answers explained. That way they get the practice.” Brenda accentuates the guided step-by-step approach to her classes as well, but she also believes that they develop even more organizational skills by working the problems themselves in class:
We’ll work a problem together in class, and then I will clear everything from the
board, but I will leave the problem itself. I tell them to take out a clean sheet of
paper. I will say, ‘I want you to do it again, and see if you can do it faster and
smoother then before.’
Brenda argued that through this drill and repetition, students develop structure and organization when working math problems.
Kelly discussed another tool that she created to help students with their organization and structure while also helping them to master the math concepts. The instrument originally consists of topics covered in a developmental math class with no further information (i.e. prime and composite numbers, multiplication of fractions, finding least common denominator.). Together, Kelly and her students examine each concept, and the students write down all the pertinent information. For example, when dividing fractions, this would include the steps involved and mistakes to avoid and any other information that helps students understand and remember the process. The instrument becomes a tool for students to use when studying, and it is easy to follow as all topics are clearly labeled. Kelly explained, “I do believe that all students do need that; it’s sort of a crutch for them to remember all the concepts because short-term learning
130 seems to be one of the difficulties they have.” Kelly also noted that such instruments are not uniform. In other words, each of the DEV 108 classes for spring quarter of 2012 did not follow the same protocol. Kelly may use different wording or even a different way of explaining a math concept for different classes. “It all depends on what they need; it can vary from class to class.”
Kelly relies on her many years of experience when developing this instrument with each class. She advised faculty who wish to implement this concept to be flexible and accessible to the various learning styles of students so that they can be open to different ways of explaining a concept, because again, the instruments that she develops are not uninform; they tend to the needs of an individual class. The indicators for Kelly that this strategy has enhanced student learning are in her student evaluations. She constantly receives comments such as “‘this was such an extreme help. It helped me learn the material and pass the class.’”
Other faculty participants highlighted the overall importance of providing developmental math students with detailed notes. Jenny articulated, “No matter how many times I repeat something and say ‘this is really important,’ the majority of time students will not write it down unless I write it down.” Casey has had a similar experience in the classroom. “When I first started, I just assumed students would take notes because this is college. I realized very quickly that they weren’t writing anything down. They weren’t retaining any information, and they would soon forget everything!”
Both Jenny and Casey stressed that it is important for the developmental math instructor to write everything on the board in a linear and organized fashion.
131 Jenny, Casey and Daniela emphasized the inclusion of algorithms when developing and providing notes, but the instructors also highlighted the extra detail in their notes. Jenny elaborated, “I’ll make a comment that you need to be careful here or watch out for that. I’ll asterisk specific examples that I know will be trouble on the forthcoming exams or the final.” Daniela added that detailed notes should include the chapter, the section, and the page number of the corresponding textbook so that students know where to get more information. Daniela explained that many students will take their work to SCC’s tutorial center for extra help. Including the aforementioned information will help the tutors locate the content in the textbook to better assist the students. Casey pointed out that bad penmanship is contagious. “I couldn’t figure out why my students were taking such sloppy notes until I realized my board work was atrocious. I practiced writing more neatly on the board, and I noticed a difference in their
[the students] notes as well.” Katie advised that when giving notes, it is imperative to create an environment where students feel comfortable asking questions. “Me walking them through it step-by-step is a start, but at some point in time they have to be able to walk through those steps on their own. They have to feel comfortable asking questions.”
Casey agreed: “Giving detailed notes doesn’t mean anything if the students are lost. As a teacher, you have to make sure they feel comfortable asking questions.” There have been some indicators that providing detailed notes has enhanced student learning. Both Jenny and Casey mentioned that on their evaluations, students consistently praise them for providing detailed notes and attribute this strategy to their success. Casey has also specified that since giving more detailed notes, students retain more information and consequently perform better on unit exams.
132 Providing detailed notes for developmental math students certainly develops their organizational skills; however, this strategy also requires organizational skills and flexibility from the instructor. The participants stressed that instructors should be prepared and develop an outline of their notes in advance. However, Casey articulated that it is impossible to prepare the entire day’s notes in advance. “It all depends on what the students need. Obviously if students are struggling with something, you need to elaborate as much as possible.”
Ann has developed a practice to ensure students are better prepared for their unit exams. She observed that when students complete their homework throughout a particular unit, they are more likely to pass the unit exam. Therefore, Ann requires all of her students to complete all homework assignments in a given unit before they can even attempt a unit exam. Students may take a test late (when they have completed such assignments); however, they receive a 10% penalty. Ann will refer to the syllabus and reiterate to her students throughout a unit: “All these things [homework assignments] have to be done and checked off before you can attempt the test.” She further stressed that this forces students to become more organized and it places responsibility on the student. Ann mentioned that the practice of requiring students to complete all homework assignments before a unit test can require some time to take effect, but it is mostly successful in the long run. “In the first unit, I always get a few who don’t do their homework. By the time we get to the last unit, it’s only one or two people who don’t
[complete their homework].” Ann then reiterated that most of the students who complete all homework assignments are successful on the unit exam.
133 Quite a few of the participants reported that many developmental math students are unsuccessful in the long run because they lack time management skills. Moreover, it is quite common for developmental math students to wait until the last minute to complete a hefty homework assignment or begin to prepare for a major exam. Verne explained, “Time management is huge, especially for those who have family, have another job, have this, have that, but they don’t see the value of doing a little bit each day and then get overwhelmed.” Therefore, Verne works with her students on developing learning calendars. For example, Verne gives her students five days to complete 40 math problems. However, she explains to her students that they can simply work eight to ten problems each night and helps them plan accordingly. Verne further emphasizes to the students that rather than almost two hours of work in one night, they only have to complete 20 minutes of work each night. “By showing them that you can break it down and do a little bit each day, they tend to be more successful. They aren’t as overwhelmed, and they understand it more.”
Verne maintained that learning calendars have been very successful with those students who buy into them. These students are successful in their homework assignments and perform better on unit exams. However, Verne pointed out that some students simply do not buy into learning calendars and still insist on waiting until the last minute to complete mammoth assignments. Verne advises faculty to be patient as word of mouth is very strong, and she will often hear her students say to each other, “‘this really worked for me; why don’t you try it?’” Consequently, more students may attempt learning calendars.
134 Departmental organization.
It is not enough for developmental math students or even their individual instructors to be organized. The department as a whole must be structured and organized.
A few of the adjunct faculty participants articulated that when beginning their teaching assignments at SCC, they were impressed with the uniformity and structure of the math area. Megan exclaimed, “At Sinclair, we are kind of set up to succeed with everything we’re given: the handouts, the tests, the quizzes.” As mentioned earlier, SCC has common final exams for all developmental math courses. In addition all adjunct faculty are required to give common departmental exams. Several of the adjunct faculty participants were grateful that they were given a syllabus with a course schedule that specifies which topic should be taught on what date. There are also several worksheets that adjunct faculty can use in the classroom as well. Each adjunct faculty member is also assigned a mentor. This mentor is a full-time developmental math instructor who serves as a contact person for the adjunct faculty member. The mentor supplies the adjunct faculty member with all of the required material at the beginning of the term
(textbook, syllabus, and exams) and works with this individual throughout the term.
Adjunct faculty who teach at one of the satellite campuses are generally assigned a mentor who is a full-time faculty member who teaches at the Dayton campus.
I asked the participants to identify the indicators that the organization and structure of the math area enhanced student learning and success. Blake gave his thoughts: “When I taught part-time at this other school, there was no structure. I had no mentor; I didn’t know what I was supposed to put on tests.” Blake described the end result of this: “It was horrible! Teachers would complain in the next class that students
135 did not learn anything in the last class. This is so much better. Now I know what I should be doing, and I do it.” Sally reflected on her experience:
It’s so scary to start a new teaching job, especially because as a part-timer, you
are out of the loop. Having everything prepared for me and also having someone
I could talk to really helped. I know that alone has made me a better teacher.
Collaborative learning.
Several of the participants cited various forms of collaborative learning activities as a best practice in their developmental math classes. More specifically, these various forms of group work and collaborative activities have enhanced student learning. There were two distinct approaches to collaborative learning that emerged from this study: general group work and guided inquiry.
General group work.
Brenda described a collaborative activity that she created. “It’s where students work in pairs or in threes, and they work through this packet that I’ve created.” In these groups, students must read two pages of information on math content and then complete about eight math problems together. About twice an academic term, Brenda dedicates about half a class to this activity. As the groups work, Brenda circulates throughout the classroom and touches base with each group. “I’m able to sit with them and ask questions such as ‘how did you guys do? How did that feel? Did everyone get it?’” Brenda articulated that throughout this activity students are communicating with each other and helping one another.
Brenda specified that this collaborative learning activity is not suitable for every topic in developmental math. Brenda utilizes this as a culminating or review activity for
136 topics such as fractions or decimals. The activity gives them to chance to review prior concepts. Brenda also mentioned that self-contained topics that are more primitive, such as exponents, are better suited to this activity as well. Topics that are too complex may cause confusion.
Brenda noted some signs that this activity enhances student learning. “I can see it on the test because the questions from this activity are the ones they get right on the test.”
Many of Brenda’s students also provide her with consistent positive feedback: “I’m always hearing comments like ‘I love it when we do this. Why can’t we learn like this all the time?’”
I asked Brenda to describe how she goes about assigning groups. “I pair a strong student with a weak student or two weak students.” Brenda further emphasized that the weaker students learn from the stronger students, and the stronger students become even stronger by explaining the content to others. For instructors interested in implementing this activity, Brenda had the following advice: “You have to build a sense of community and trust in your classroom; you also have to get to know your students very well to determine who will work well together.” Brenda also pointed out that she received the idea of the group-work concept by observing several of her peers. “I saw so many of my colleagues having students work together in class. The students seemed so engaged, so I thought I would give it a try.”
In her developmental math classes, Kelly employs what she refers to as pair-share activities. More specifically, Kelly will assign a math problem (or several math problems) and have students work with their neighbors to complete the problem. She does not assign students a partner; they must simply work with the person next to them in
137 class. Kelly gives her students the following instructions: “Every single one of you should be able to tell somebody else how to do this problem. Just start with step one and then step two and so forth.” Kelly emphasized that she has found that students learn the material better when they explain it to someone else rather than work problems quietly by themselves. “If they can teach it, they truly understand it.”
Kelly argued that pair-share activities enhance student learning. However, she warned that students may be initially resistant: “It frustrates them because they think the teacher is supposed to explain everything to them.” However, Kelly pointed that as time progresses students begin to embrace the pair-share activities and even start employing them outside of class. More specifically, students will sit in groups before and after class and explain various math problems to each other. Students even utilize the pair-share activities in their next math class as well. Kelly has observed that the students who embrace the pair-share activities also score higher on exams and are more successful in the class in general.
Other participants such as Robyn, Daniela, Jeff, Larry, and Jerry employ various group activities as well. Usually, these activities consist of students working together in small groups on a set of math problems related to a topic that the instructor has just introduced or reviewed. These instructors have also noted that group work can enhance student success. According to Jeff, “There is more interaction in class. The students truly seem to learn from each other. As the term goes on, more and more students start to join in the group work.” Daniela gave her thoughts: “If I put them in groups, I’ve noticed that the students who don’t ask me questions but need to ask questions are more likely to ask other students for help, and then they start to get it.” Unlike Brenda and Kelly,
138 Robyn, Daniela, Jeff, Larry, and Jerry do not always mandate group work in their classes.
Whether or not Daniela mandates group work depends on the class. “Overall, if they are an interactive class, I make them work in groups. But some classes just don’t work well in groups, so I don’t require it.” Daniela further articulated that when group work is optional, she stresses to the class that those who choose to work in groups must keep the noise level down so that those working individually are not disturbed. Robyn has assigned groups but has then changed that practice during the term: “I’ve had classes where they’re not good group workers. You’ve got to recognize that, and you’ve got to be flexible enough to change. So in the middle of the quarter, I just stop requiring the group work.” Larry shared his experience with group work:
There are times group work has been great, and the students really get into it, and
I can tell they’re learning a lot, but I learned not to require it [group work]
because when I did, I got a lot of whining. There are times when I assigned a
group, and they all sat silently and didn’t talk to each other. Other times, one
person did all the work; sometimes they would just argue; other times, they would
get distracted and talk about non-math stuff.
Guided inquiry.
Two of the faculty participants, Ann and Verne, reported that the practice of guided inquiry has helped to enhance their students’ learning. It was the participants who used the term “guided inquiry.” Both participants employed this practice in their previous teaching prior to their employment at SCC. In this practice, the instructor dedicates the first 10-15 minutes of class by providing a basic overview of the day’s content. More specifically, the instructor may explain the basics of simplifying expressions, solving
139 basic equations, or introduce geometry. Verne explained that following this introduction, the instructor gives the students a group assignment. “We give them real-life applications where they have to talk to each other and explain it to each other. Basically, they have math dialogue.” Verne then provided an example of such an application:
If we’re talking about geometry, one of their application problems might be that
they have to figure out how much fencing they need to go around the backyard to
put the dog in there. Or how much grass seed they would have to spread out there
in the yard.
The instructor circulates throughout the classroom and poses questions to the various groups to provoke critical thinking but does not provide any direct answers. At the end of the class, the instructor selects a group at random to present a different math problem to the class that covers the concepts that they learned that day. Students work in the same groups each time.
During the interviews, the participants briefly compared guided inquiry to pure inquiry. As a result, one question immediately crossed my mind: How is guided inquiry different from pure inquiry? Ann explained that in pure inquiry, the instructor does not give an introduction to the topic of the day. Students are given an assignment, and they must collaborate to uncover the basic elements of that topic. Ann elaborated, “Pure inquiry is not a fast process, and we have time constraints, so we give them the quick and dirty and then give them the application.”
As I spoke with the participants about guided inquiry, a second question emerged.
How is guided inquiry different from the general group work utilized by many other instructors? Verne explained:
140 Because you expect them to apply it and not just solve problems. And they have
to compare answers and discuss the problem. If I see members of a group just
sitting and working independently, I go over and say ‘If I wanted you to work
independently, I would have given you some kind of other work to do.’
Both Ann and Verne mentioned that while it can take some time, they eventually get the students talking to each other.
Ann and Verne highlighted several signs that guided inquiry enhances student learning. Both participants noted that their success rates have increased. Ann specified that her success rates have increased by ten percentage points since employing guided inquiry, and her overall retention and attendance has increased as well. “Students are staying until the last day of the quarter instead of just disappearing.” Also, students’ attitudes toward math have improved. “I have noticed that my attendance is up, my scores are better, and they come in talking about math” added Verne. Verne elaborated on the last part of that comment:
You hear them talking about math before class and after class and in the hallway.
I see those little groups from class elsewhere on campus working on math, so I
think because they are engaged so much more in class that it can’t help but be
successful.
It is noteworthy, however, that other faculty members have attempted guided inquiry and did not have success with this modality. However, these faculty members attributed this lack of success not to the practice itself but to their own pedagogical comfort level. Jose attempted the guided inquiry method and discussed his experience:
141 It just put me out of my comfort zone, which is a very dynamic, very humor-
based lecture style where students are very engaged. When I tried this [guided
inquiry], students weren’t doing as well. I was covering the same content, but I
was not covering it in a method that I was particularly competent in.
Jose further articulated that he had never received any prior training in inquiry-based instruction.
Jenny was another faculty member who did not find success with guided inquiry.
Both Jenny and her students struggled with this modality. “I had never been exposed to it, so I was really not comfortable with it. The students were angry that I wasn’t doing the traditional teaching.”
As much as Verne and Ann praise the guided inquiry method, both instructors recognized that this practice is not for all instructors. Ann asserted, “Instructors who aren’t comfortable with it, their nervousness and anxiety spreads to the students. So the students are nervous and anxious. So if you’re not comfortable with it, I don’t think you’re gonna be successful with it.”
Verne and Ann were full of advice for instructors who are interested in attempting guided inquiry. Both participants suggested observing another instructor who utilizes guided inquiry. However, Verne advised that interested faculty do more than observe.
“I’ve had faculty come in who have wanted to see this approach and they just want to sit in a corner and watch. Oh no, no, no, I tell them ‘join a group so you are immersed in it.’” Verne specified that this will give interested faculty a deeper understanding, and these instructors will be able to better judge if this practice is suitable for them. Ann also suggested that when novice faculty implement this practice, they should start small. In
142 other words, they should begin by using guided inquiry with only a few topics in class rather than every topic as novice instructors need to get the feel for how guided inquiry will work for them. Both participants attributed part of their success with guided inquiry to their multiple years of experience employing the practice. Therefore, they agreed that successful implementation of guided inquiry requires some training and experience.
Verne explained that part of guided inquiry is allowing students the freedom to utilize various methods of arriving at an answer, and the instructor must accept that there is more than one way to solve a math problem. Verne gave the following example:
If I asked you to go in the house, you might go in the front door; you might go in
the back door; you might go in the garage door; you might go in through the
window; you might go down the chimney, but you still end up in the house.
Therefore, Verne argued that instructors who employ guided inquiry must be flexible: “If you’re too much in control or like to be in control, this approach will not work for you.”
I asked Verne and Ann if most developmental math students could benefit from the guided inquiry approach. According to Ann, “I think it makes the students, especially the lower level students, more comfortable. They realize other people struggle with math too, and they don’t feel like they’re alone.” Verne acknowledged that this approach is not for all students:
I’ve had students for one reason or another, just can’t get the hang of group work.
It might be a learning disability; it might be an attention issue; it might be that
they’re so shy that they don’t know how to talk to people.
143 Frequent low stake assessments.
As in many post-secondary education classes, developmental math students are subject to high stake assessments such as cumulative final exams and unit exams. These assessments are high stake because much of the students’ final grades depend on the successful completion of such assessments. Sometimes there are lengthy intervals of time between these assessments since finals only occur once an academic term, and unit exams are generally at least two weeks apart (possibly more). Therefore, if developmental math instructors relied solely on high stake assessments, they would only be able to assess their students every couple of weeks at minimum. Taylor discussed his experience:
When I first started teaching, I just gave the unit exams and the final. That’s the
way it was when I was in college so why not? But when it came time for the unit
tests, they would fail miserably. They couldn’t seem to remember everything.
That’s when I realized I need to assess their progress more often.
Therefore, several of the participants stressed the importance of frequent low stake assessments throughout the academic term.
Jose asserted that regular or even daily quizzes are a best practice in developmental math. Such quizzes generally contain two questions that Jose administers which covers the material of the previous class. Jose provided an example of a class that met on Tuesdays and Thursdays, and on Tuesday, the class covered the laws of exponents. During class on the following Thursday, the students would take a quiz that would consist of two questions focusing on the laws of exponents. Jose specified that he dispenses 10 to 15 quizzes each academic term, and they count for about 10% of the
144 overall grade. According to Jose, “It’s a quick and dirty way to diagnose the state of the class’s understanding collectively, and I can zero in on individual problems because everybody gets the same quiz.” Jose explained what led him to implement these quizzes.
“I would spend all this time covering the material in class, and they [the students] would shake their heads ‘yes’ like they understood me. Then, when the next class started, it was like the lecture never existed. They didn’t remember anything.” Jose further articulated,
“Students need more frequent lower-stake assessments to make sure that they are getting it and not falling behind. I can’t assume that my great and powerful lecture is enough for students to succeed.”
What are the indicators that regular or daily quizzes enhance student learning?
Jose asserted that his students retain more information because they must prepare for a quiz each class. He also pointed out that on the unit exams, students perform better on the types of questions that they have seen on a quiz.
For the past two years, Frankie has utilized math journaling in all of his developmental math classes. Frankie explained the practice of math journaling. “At the end of each class, besides their regular math homework, I give students an assignment.
They have to write about one new concept that they learned and one new concept that they still struggle with.” Frankie added that he requires students to write in complete sentences and be as specific as possible about the content that they have mastered and the content with which they are struggling. “It helps them understand their accomplishments, but it’s also a way for them to tell me what they need help with. Then, we can nip those problems in the bud before they snowball.” Frankie added, “If the class in general is
145 struggling with something, we review it. If it’s individual students, I meet with them before or after class to help them.”
Frankie has noticed that this practice has enhanced his students’ learning. “Most of them do better on the unit tests. I think that’s because we catch potential mistakes early. The math journals help me to intervene, and I can help them.” Frankie has also observed that math journaling has helped students master new topics as well:
Before I used the journals, it was more of a struggle when I introduced a new
concept like factoring trinomials. Students struggled because they still didn’t
understand how to multiply terms or use the FOIL method, and you need to
understand that to factor. With math journaling, I can catch those issues early.
Now, more of them are able to follow along with new topics because they don’t
have as many gaps.
Frankie’s students are appreciative as well: “I get a lot of positive feedback on my evaluations. They [the students] really appreciate that I give them this opportunity to let me know they need help.” Frankie had the following advice for instructors interested in implementing math journaling:
It works for the students who take the class seriously. The ones who don’t care
will write, ‘I am fine with everything’ and they’re really not; they just don’t want
to do the assignment. Some don’t even do the assignment at all.
Taylor, like Frankie, wants to assess his students on a class by class basis.
Therefore, Taylor employs a practice that he calls, “the problems of the day.” Taylor elucidated, “At the end of each class, I reserve about 15 minutes for students to complete three to five problems. It’s pretty informal; I put the problems up on the board. Students
146 copy and complete them and turn them in.” I asked Taylor if these were quizzes or if they counted for a grade. “No, I just give them participation points for completing them.”
Taylor further articulated: “They are just problems similar to the ones we covered that day. It just gives me a way to see if the class as a whole is understanding the material and who needs more help.” Like Frankie, Taylor conferences with students before or after the following class. “I just touch base with the students who made mistakes. We go over what they did wrong, and hopefully they won’t make the same mistake on a test.”
Taylor has taught developmental math for several years, but he has only been administering the problems of the day for the last four. In that time, he noticed that the problems of the day have positively impacted his students’ learning. “They get a problem wrong, and we go over it. They’re happy they understand it, and a lot of time, they get that problem right on the unit exam or the final. They also seem more confident in class.” Taylor had the following advice for other instructors interested in putting the problems of the day into practice:
It’s pretty simple; just be organized and reserve about 10-15 minutes at the end of
each class. Pay attention to the kinds of problems they struggle with that day,
because those are the ones you’ll want to use, and just be willing to do a little
extra paperwork outside of class.
Similar to Frankie’s math journaling, Taylor pointed out that while the problems of the day help many students, they are ineffective for students who miss many classes or do not put forth the effort.
A few of the participants employ a practice that they entitled “correction reflections.” Students can correct some of their mistakes on exams or homework
147 assignments and receive partial credit; however, in addition to making these corrections, students must explain their mistakes coherently. When Blake and Taylor return their students’ exams, they allot them 20 minutes to correct a maximum of five incorrect problems. Students may use their notes, but they may not use calculators, converse with each other, or ask the instructor for assistance. In addition to simply providing the correct answer, students must show all of the steps and explain their original errors in one or two sentences. When students are finished, they turn in their work to their instructors.
For each problem that they get correct, they receive half credit toward the unit exam. For example, if an original exam question was worth four points, a student can receive two points toward the exam. The result can be an increase of a maximum of ten points on the exam. Ann employs a similar practice with homework assignments as she allows her students to redo all homework problems for half credit. I inquired as to how these participants became aware of such a practice, and all mentioned that they learned about it from their mentors or other developmental math colleagues.
All of the aforementioned participants have been quite pleased with the practice of correction reflections. Ann explained, “In the past when I graded their homework, and
I wrote down what they did wrong, they didn’t look at it. Now, I feel like they’re going back and finding their mistakes.” Taylor commented, “Students are less likely to make those mistakes again, and they’re really appreciative that they have a second chance.”
Blake relayed his thoughts: “It makes them really look for their mistakes, and I think they get a better understanding. Also, they take better notes in class because they know they will need them for the correction reflections.” The participants pointed out that correction reflections are effective for many students but not all. Taylor elaborated:
148 It really doesn’t work for the students who get 20s and 30s on their exams. They
are so far lost that a correction reflection won’t save them. It’s better for the
students who passed or failed by a close margin.
Blake shared his experience:
Some students will go home after a test and review their notes so that they are
ready for the correction reflection. Others either do not review or do not take
good notes or any notes and then don’t do any better on the correction reflection
than they did on the test.
Technology supplements.
A few of the participants reported that supplementing their classes with a technological component has enhanced student learning. More specifically, these instructors employ the tutorial program, Kahn Academy. Megan elaborated on this program.
Kahn Academy is an online tutorial program. It’s free. And the cool thing about
it is you can practice whatever math you want on it. And if you get stuck, if
you’re not sure how to do it, there’s a tutorial video that goes along with it. So
you can watch it over and over until you understand it.
The participants have shown Kahn Academy videos in class; however, they also email their classes Kahn Academy video links so that students can watch them outside of class. Jeff explained:
I just tell my class, ‘Here is a guy explaining something that I did today; look at
this.’ I figure that this person could either reinforce what I did or explain it a little
differently in a way that could help them.
149 Sally provided her thoughts: “I use it throughout the quarter, and I always email my students the links. I especially use it when we are covering difficult concepts like fractions.”
Kahn Academy has generated positive student feedback. Jeff commented, “The one time I forgot to email my class the link; I had students saying, ‘You didn’t send me the video!’” According to Larry, “The students love it! And I’ve noticed that the ones who use it a lot, get pretty good grades on exams.” Megan articulated, “Many of my students love it so much they recommend it [Kahn Academy] for their brothers, sisters, daughters, and sons.”
I asked the participants to explain why they feel their students have embraced
Kahn Academy and why it has enhanced their learning. “The videos are just a few minutes at the longest; it’s just really simple” explained Jeff. Jeff pointed out that he used to have his students watch the math videos that are available in SCC’s tutorial center, but they were simply too long. Blake had a similar experience: “Those videos in the tutoring center take three times as long to explain a concept as the Kahn Academy videos. Students always say how user-friendly they are. They’re just quick and to the point.”
There were some participants who have not had success with technological supplementation. Verne attempted to use the software program, MyMathLab as a supplement for students to use outside of class for extra practice:
We tried it as a supplement, and I don’t want to say that MyMathLab was a bad
software- I’m not saying that. I think … developmental students have very low
computer skills, and they weren’t comfortable working with the program.
150 Verne added that there were endless navigational issues: “The students were constantly asking, ‘How do I get in? How do I click on this? How do I find that?’ It just became a nightmare.” Another participant reflected on a comparable experience with MyMathLab as a supplement: “It was horrible! It’s just- you spend more time trying to figure out how to use MyMathLab than you spend doing the math.”
Throughout this section, I conveyed the general best practices that a group of developmental math instructors employ to improve student learning. Such practices included communicating with students regularly regarding their progress and general meaningful communication. The participants discussed the art of organization, which included the development of student organizational skills and departmental organization as an effective method. The interviewees acknowledged collaborative learning as a best practice as well. The two types of collaborative learning that the participants described were general group work and guided inquiry. The participants identified frequent low stake assessments as an effective strategy for enhancing student success as well. Lastly, the interviewees recognized that technology supplements can improve student learning in developmental math. In the next section, I will describe the content-specific best practices employed by a group of developmental math faculty.
Content-Specific Best Practices
In order to dive even deeper into the best practices in developmental math, I asked the participants to describe the content-specific best practices that they utilize. The practices discussed below relate to a specific content area in developmental math. Again, these were practices that were effective on a consistent basis. There were two overall categories of content-specific best practices that emerged from this study: The first
151 category was comprised of mnemonics and memorable wording and the second consisted of manipulatives, visuals, and real-life applications.
Mnemonics and memorable wording.
Several of the participants explained that developmental math students often struggle with the metric system. However, these struggles are related more to memorization. Jerry explained, “Once they remember how many spaces and in what direction to move the decimal, they’ve got it. They just have trouble remembering that kilometers comes before hectometers and that millimeters comes after centimeters and so forth.” Therefore, some of the participants employ various mnemonics to help students with their memorization. These mnemonics are not original; in fact some have been used in education for quite some time. However, the participants mentioned that they are new to the students, and more importantly, they help the students. Before any further explanation, it is worthy of note that the correct order of prefixes for the metric system is as follows: kilo, hecto, deka, (then either liter, meter, or gram) deci, centi, and milli.
Depending on the unit of measurement, the suffix would be liter (for volume), meter (for length), or gram (for weight).
The participants provided some examples of the mnemonics they use when discussing the metric system. When Megan covers the metric system with her classes, she has them remember, “kangaroos hop down mountains drinking chocolate milk.” The first letter in each word of the mnemonic mirrors the first letter in each word in the metric system prefixes in the correct order. When a student recites, “kangaroos hop…” they can already remember that kilo precedes hecto. Blake employs this as well and gave his thoughts. “Obviously ‘mountains’ is where the actual unit [meters, liters, or grams] is
152 inserted, and in this case it’s meters because mountains and meters start with an ‘m.’ So when covering the metric system, we always start with length [meters] to help them remember.” Kelly gave another example, “keep hungry ducks munching delicious corn meal.” Kelly added, “It’s so ridiculous, they remembered it!” Jerry described his mnemonic and the story behind it:
One time during class, people were really struggling with remembering the metric
system, and I had a student mention something he had learned in prison when
taking classes. Yes, this guy had been in prison. He said, ‘kill him dead don’t cut
me.’ Everyone started laughing, and they remembered it!
Megan and Larry use a common mnemonic to help students with long division.
Larry provided the reason for the mnemonic: “Students really struggle with long division.
They can’t remember the steps, and then they get really frustrated.” Megan explained the mnemonic: “dead monkeys smell bad. It will tell you divide, multiply, subtract, and bring down, which are the four steps for long division.” Both Megan and Larry explained that they had used this mnemonic in their previous teaching; therefore, they were curious to see if it would be effective with developmental math students.
Andrea shared a mnemonic that she uses when working with her students on solving equations. She provided the following linear equation as an example:
5(x 8) 6 3(x 4) 5. Andrea conveyed her mnemonic: “please cook very nice desserts.” Andrea elaborated, “For solving equations, students need to do the parentheses first, combine like terms, variables to one side, numbers to the other, divide what is in front of the coefficient.” Andrea laughed, “And I always remind them, dessert comes last.
So always divide last.”
153 Some of the faculty participants noted that students struggle with identifying the location of the decimal in a number when it is not apparent. More specifically, consider the number, 5,369. That is a whole number; therefore, it is not necessary to show the decimal. However, every number has a decimal, and it always follows the digit after the one’s place. Therefore, in the aforementioned number, the decimal would follow the “9.”
The participants explained that when the decimal is not shown, students often misplace the decimal, and this can lead to all sorts of errors, especially when the students must employ actual operations with decimals. Kelly shared her practice to help students remember the placement of a decimal. “I tell students that all people sit on their derrieres
[behinds], and all numbers sit on their decimals.”
Megan described that rounding numbers can be very difficult for the low level developmental math students. “Students forget that you round up when the number is five or higher. Even worse, they think when it’s lower than five you go down.” Megan explained her practice to help students:
I tell them ‘five or more, go one more; one to four go no more.’ This helps
students to remember that when asked to round a number, and the digit indicated
is five or higher, the digit increases by one. When the digit indicated is four or
less, the digit remains the same.
Sally does not only employ fancy wording, but she performs an accompanying dance:
Students are always struggling with converting decimals to percents and vice
versa. So I came up with a catch phrase and a dance. It’s called p to the right and
d to the left. The letter ‘p’ faces to the right, so students remember to move the
decimal to the right when converting to from a decimal to a percent. The letter
154 ‘d’ faces to the left, so students remember to move the decimal to the left when
converting from a percent to a decimal.
I asked Sally to explain the dance routine, and she exuberantly performed it for me:
I take two steps to the left and sing,‘d to the left.’ I take two steps to the right and
sing, ‘p to the right.’ Then, I make the class get up and do the dance. Not only
does it reinforce the direction of how to move the decimal, but they remember
how many steps to move.
I inquired as to how Sally discovered this routine. “I just made it up. It comes from just being my kooky self.”
I asked the participants to describe indicators that the practices of mnemonics and memorable wording are enhancing student learning, and the participants cited two signs.
Most of the participants reported that students list these mnemonics and phrases on their quizzes and tests to help them remember. Jerry noted, “I see ‘kill him dead don’t cut me’ on a lot of tests, and even better, they get it right!” Larry mentioned that he receives positive student feedback both on their evaluations and verbally. “Students will say,
‘Wow I’ve never heard of that; it really makes sense! Thank you.’” Megan pointed out that some students find mnemonics and memorable wording somewhat silly and childish.
Therefore, when employing such practices, Megan explains to her class:
‘If you want to use it, use it. If you don’t, that’s fine, whatever works for you.
But here’s one way to remember it.’ So I kind of leave it up to the students to
decide if they would like to use it or not.
155 Manipulatives, visuals, and real-life applications.
Mastering the laws of signed numbers, which involves adding, subtracting, multiplying, and dividing positive and negative numbers, can be difficult for many developmental math students. Therefore, Verne uses red and white poker chips to help students understand the basics of adding signed numbers:
White poker chips represent positive values while red poker chips represent
negative values. When adding signed values if all the poker chips are the same
color, the signs of the values are the same, and therefore the values can be added
together.
Verne then elaborated on implementing this practice:
I start by grabbing some white poker chips and ask them, ‘If I gave you three plus
nine, could you add? If I gave you one plus seven, could you add?’ I explain,
‘Well there’s a pattern here. The signs and numbers are all positive, so they’re all
white poker chips. Because the colors are all the same, you can add them
together, and the color doesn’t change, so the signed number doesn’t change.’
Verne explained how she transitions to negative numbers:
I take some red poker chips and ask, ‘If gave you negative two plus negative
eight, can you add those together?’ And if you add them together, they stay red,
right?’ So that gives them a visual, because they know what a poker chip looks
like, but it also gives them contextual knowledge because they see it being put
together in a pile.
Verne has noticed that this practice has laid the groundwork for a solid foundation in the students’ understanding of signed numbers and since using this practice, her
156 students perform better on exams. However, Verne has noticed other subtle indicators that this practice is effective:
In class, I can see the light bulb go on in their heads; their heads nod; they smile;
their posture gets a little straighter, and I even get an occasional fist pump. And
when they walk out of class saying, ‘I get it; I get it’ to each other, that makes it
all worthwhile.
A few of the faculty participants remarked that basic graph paper has served as both an effective manipulative and visual for developmental math students. Robyn explained how she utilizes graph paper to help students with decimal place value:
I give them each a piece of graph paper, and we put a decimal point in the middle,
and then we draw a line. Then, we talk about the mirror effect of the ten’s place
and the tenth’s place and the hundred’s place and the hundredth’s place. This also
helps me point out that there is no one’s place to the right of the decimal. This
helps because I show them that every place value in decimals has a mirror, but the
one’s place. I’ve done activities where I will say, ‘put a six in the one’s place; put
a one in the ten’s place; put a five in the hundreds place, and so forth, and now
read me the number you have written.’ It helps students to see the numbers clearly
and also clearly read what they wrote.
The use of graph paper can help with students’ organizational skills as well.
Andrea has her students work addition, subtraction, multiplication, and division problems using graph paper. “When they put in the numbers, each digit has to be by itself in a box on the graph paper. That way they can see everything clearly.” Casey uses graph paper for the purpose of organization as well. “When they [the students] make mistakes, it’s
157 usually because they are so disorganized and sloppy. But the graph paper helps them line everything up, and they’re more likely to get the problem right.” However, Casey pointed out that getting students to utilize the graph paper correctly can be challenging.
Students still want to put numbers all over the place. I have to go around the
room during each class and work with students on putting each digit in its own
box so that everything lines up nicely. I’d say most of them come around, but
some never do.
The participants specified that the use of graph paper is very effective for the lower level developmental math students. According to Andrea, “It really builds a solid foundation for students. If they can get in the habit of good organization now, it will help them later.” Casey explained:
I will use the graph paper for my DEV 084 students, and then I notice, the ones
(the students) that I have for DEV 085 and even DEV 108, they have really good
organizational skills. They are neat and they line numbers up nicely. That’s how
I know this works because it becomes a habit for them.
Ann described how she applies the concepts of estimation and number sense to real-life situations:
On the second day of class, I send them out in groups of three around campus to
do estimating projects. And they have to do three things: estimate how many
books are in the library, estimate how many people are being served in the
cafeteria in an hour, and in the cafeteria how many quarters would be in a stack
ten feet tall. They have 45 minutes to visit the two locations. They have to devise
a method for their estimation, and then give the estimate, and then come back to
158 class and present their method of estimation. Then, we talk about how much
longer this would take if we couldn’t have a method of estimation, and how it’s
used to make educated guesses and how they can use it to anticipate their answers
on word problems, things like that. And I think it gives them a truer sense of why
we have estimation.
Ann has observed that this activity on estimation allows many of her students to feel more at ease in class. “They’re more apt to raise their hands, answer questions, because they get off on a more comfortable foot; they realize, ‘wow this isn’t so hard.’”
Ann further articulated that many of the students also begin to develop basic estimation skills, which leads to further success with operations with basic numbers.
Ann employs this practice with her lowest level developmental math course.
Because this can be a complex activity for lower level students, Ann had some advice for instructors interested in implementing this practice. “Go with them the first time. Don’t just send them out to complete this activity. Until you get to know students and what they’re going to do, go with them the first time.”
Some of the participants will embed real-life applications when covering various topics in their classes. Taylor described his strategy when discussing the order of operations of basic numerical expressions:
Students always mixed up the correct order of operations so I tell them a story.
One time at the gym, there was this guy who was 5’9”, and he wanted to know the
correct weight for his height. He asked the trainers, and each of them had a
different answer. One said he should weigh 180 pounds; another said his weight
should be 1,007 pounds, and yet another was sure his ideal weight should be 45
159 pounds. As the students laugh, I explain that if you don’t use order of operations
correctly, you get can some crazy answers, which could lead to some dangerous
results. After all, if this guy took one of the trainers seriously, he could wind up
gaining 800 pounds!
Taylor noted the signs that this practice enhances student learning. “I can see this creates a spark; I can see it in their body language. Their attitude changes and they start taking order of operations more seriously. That attitude change is always the beginning of success.”
Katie elucidated on a real-life application that she draws on when covering
estimation:
I ask them: ‘How many of you walk through the grocery store with your
calculator calculating every single individual purchase that your make while
you’re walking through the store so you have an exact total? Or how many of you
just kind of walk through the store and kind of keep a running estimate in your
head?’
Katie pointed out that at this point, the students identify with the latter question. She then continues her application:
I tell them that I have three kids, so when Christmas shopping, I try to keep a
good balance between the three kids, so I don’t spend more money on one kid
than another. So I keep a bit of an estimate going on while shopping. I explain
that we estimate so much when we shop.
Daniela specified that when a decimal in not visible in a given number, a student will most likely make the mistake of placing the decimal to the far left instead of the far
160 right: .28 instead of 28. Daniela relates this concept to money. “I say, ‘Why would you put a decimal in front of $28.00 to devalue it to $0.28?’ They’re like ‘Oh, I never thought about it that way.’”
Jenny and Kelly embed real-life applications when covering combining like terms in algebraic expressions. Jenny provided the following expression as an example:
4x 5x.
I tell them that the ‘x’ stands for inches. So if we add four inches and five inches,
we get nine inches. The answer is 9 x. Then, they can see that the coefficient
changes, but the variable does not change.
Jenny further articulated: “Let’s say we have 7x 3y. I tell them ‘x’ is feet and ‘y’ is inches. So if we add, all we get is 7 feet and 3 inches, which is just 7x 3y. Since the variables are different, we can’t combine.” Kelly provided more insight:
Students always have trouble with expressions like 4x3 5x2 9x. They think
they can combine because there are all x’s. So I tell them, ‘ x 3 stands for apple
sauce; x 2 stands for apple pie, and x stands for apples. They’re all similar, but
they are not exactly the same, so we can’t combine them.’
The participants stressed that the use of real-life applications enhance student success. Both Jenny and Kelly have observed that students often write examples of applications used in class on their test papers to help them remember, and moreover, their answers are correct. According to Kelly, “It’s a good application and a good mental visual, and I find they don’t mess expressions up as much.” Katie has also observed that this strategy has helped students. “They are able to relate this to their lives and often they
161 say, ‘I get it’ and I can see that they get it on their quizzes and tests.” Katie also believes that using such real-life applications could work for most developmental math students:
We’re talking about people who are, at least in some respect, adults. They pay
their own bills; they drive their own car or they have to pay for public
transportation. Whatever the case is, they, like all people, have to spend money
every day.
Katie had some advice, however, for instructors interested in implementing this practice:
You have to find a way to make it relevant to something they already know a lot
about. You’ve got to take time to get to know your students. If you can relate it
to something they know, it will stick.
Brenda stressed that in addition to providing the step-by-step process for students, it is also imperative to offer an in-depth and detailed explanation of the underlying concept of the specific topic. Brenda pointed out that this is necessary when working with fractions as they are a continuous area of difficulty for students. “The students have to understand why they are doing what they are doing, and I think a lot of teachers gloss over that.” Brenda elaborated:
Fractions tell us a story. If the denominators don’t match, you can’t add them
because you’re not speaking the same language. So it takes me a long time to
explain that. I use a lot of pictures and examples to help them understand why we
can’t add two fractions with unlike denominators. If they truly understand
fractions, they will have more confidence in working with them.
Brenda maintained that students who are open to her explanations of fractions often grasp the step-by-step concepts and are more successful with fractions in general.
162 The students who do not pay attention or are not in attendance are not as successful. “It all comes down to motivation and dedication. Those are qualities we can never, as teachers, control over another human being.” Brenda provided the following advice:
“Take the time to really explain fractions; just explaining the steps is not enough.”
Jeff, Blake, and Dylan stressed the importance of using visuals in the classroom, especially when explaining geometry. “You got to be visual; you can’t just stand there and lecture. You have to let them see it. If they don’t see it, they’re not going to understand it” asserted Dylan. Dylan further articulated that when covering geometry, he brings various examples of rectangles, squares, triangles, and circles to class so that students can truly grasp the concept of such shapes and figures. Jeff described a common difficulty that students face when studying geometry: “They can never grasp the concept of what is an inch, a square inch, and a cubic inch.” Therefore, Jeff will demonstrate the difference between one, two, and three dimensional objects. For the one dimensional figure, he will bring in a yard stick to show how it is measured foot by foot. For the other two dimensions, he will design an object out of paper to show the difference between two and three dimensional figures. Blake uses himself in his visuals:
When I explain perimeter, I run around my desk, which is a rectangle by the way.
As I run and pant, I yell, ‘I’m covering the perimeter of this desk!’ Then, I stop
and sit on top of the desk, and I say, ‘I’m sitting on the area of this desk. If this
desk had no area, I’d fall on my butt!’
The participants reported that the visuals help students with their understanding of geometry. Blake recalled:
163 One time I was grading a test, and there was a question about perimeter. Next to
the question, the student had drawn a picture of a desk and me running around the
desk. Then, next to question on area, he had me sitting on the desk. He got both
problems right, and it felt good.
The participants advised all developmental math teachers to be creative and use some sort of visual when explaining geometry.
This section was comprised of the content-specific best practices employed by a group of developmental math instructors. First the interviewees described their employment of mnemonics and memorable wording and how this strategy enhances student learning. Thereafter, the participants discussed their use of manipulatives, visuals, and real-life applications and how this practice can be effective. Next, I will discuss the practice of acceleration in developmental math, which I addressed with the interviewees.
Accelerated Instruction
As I discussed in Chapter Two, many developmental math programs across the country have implemented some sort of accelerated instruction. This has become a national initiative as schools are facing external pressure from state and federal legislators to remediate students at a quicker pace. As I explained in Chapter Three, SCC employs two types of acceleration: the math academy and the boot camps. Therefore, I decided to address this issue with the participants. Of the 20 participants, twelve have experience in teaching in either or both of the accelerated modalities. However, since all of the participants work with and understand developmental math students, I asked each of the
20 participants to give their input on acceleration.
164 Acceleration: a good fit.
Several of the participants remarked that accelerated instruction could be a good fit for those developmental math students who enter SCC with a solid background in developmental math content but simply possess gaps within the content. Daniela commented, “It works for those students who need it as a refresher and have number sense. They just have some gaps that need to be filled.” Andrea conveyed her experience:
It’s great because if they already know how to do this stuff, they can just move on
to the material they need help with. In my face-to-face classes, I get those
students who are bored because they already know most of this stuff. It’s too bad
they weren’t in the math academy.
Jose, Jenny, and Brenda pointed out that accelerated instruction is suitable for high ability developmental math students. Jose specified that a student’s score on the placement test is a good indicator as to whether acceleration is appropriate for that student. Students who score on the high end of the placement exam for a specific course would be better candidates for accelerated instruction.
The participants also reported that acceleration is a good fit for students who are willing to complete the work. Brenda explained, “I’ve noticed that it is the motivated and dedicated students that simply need a refresher that are the most successful.” Jeff gave his thoughts on students who are successful in accelerated instruction: “I think it’s how they approach their educational process. They need to have good study skills; they need to prepare, and they need to do the work.” Daniela has had a similar experience as well:
165 I had one student who tested into my DEV 085 class, and she was really nervous,
but she put that extra effort into taking notes, understanding the notes that she was
taking, reading the textbook, completing the exercise problems and making sure
everything was correct before she turned anything in. And, wow! She completed
both DEV 085 and DEV 108 in the same quarter.
Acceleration: a poor fit.
Participants stressed that accelerated courses require motivation, a solid worth ethic, and the ability to work and learn independently. Therefore, all of the participants pointed out that accelerated instruction is a poor fit for students who possess paltry attendance habits, have difficulty working independently, and possess poor organizational skills. The participants also argued that accelerated instruction is not for the academically borderline or lower level developmental math students who cannot keep up in class. Robyn articulated:
Some students really need that extra support. In a lab, you can ask questions and
ask for advice, but it’s not the same as getting guided instruction from a teacher.
Those students who need that extra support should really not be in accelerated
instruction.
Jerry gave his thoughts: “Some DEV math students are so disorganized. They don’t know how to structure their time. An accelerated class is the worst setting for them. It gives them too much freedom. They need a structured and traditional class.” Verne explained:
166 For those students who just need a real quick refresher, it’s fine. But for those
students who never got it to begin with; you’re trying to make them run before
they know how to walk, and that’s not fair to them.
Brenda articulated that “placing an ill-prepared or low level student in an accelerated class is like trying to fit a circle where a square should be.”
Other participants emphasized that students must have competent computer skills when taking an accelerated course that is primarily computer based. Daniela explained,
“There are some students who just don’t like to work on computers and are immediately turned off by the math lab.” Jose described the computer skills of some of the students who enroll in the math academy:
The problem is people are coming into these sections not even knowing, really,
how to competently use a mouse, and then we have to put them on this very
sophisticated software. It’s important to realize that there’s a huge learning curve
with this software.
Dylan, Kelly, and Verne expressed trepidation over the lack of communication between the developmental math student and the instructor in a computer-based course.
Kelly specified:
Even if the computer talks to them, it’s not really talking to them. They have to
have that rhetoric back and forth with the instructor to be able to sort everything
out and have it all make sense to them. The computer can’t do this with a student.
Dylan gave his thoughts: “I think students need to connect with their instructor. They need to be praised for their work. Having some damn computer simply say ’good job’ when they answer a question is not enough.” Verne added, “They [the students] need eye
167 contact; they need that assurance that ‘you can do this. Just step back, breathe, you’ll be fine.’ They need that from their instructors.”
Acceleration: the bottom line.
All 20 of the participants conveyed one uniform belief: Accelerated instruction is an ideal fit for a small group of developmental math students. Students who fall into this group include those with solid number sense, good time management and organizational skills, motivation and dedication toward their academics, and previous experience with the developmental math content. Also, if the accelerated course is software-based, students must be comfortable working with computers. All of the participants also believed that this aforementioned group of students makes up less than 20% of the developmental math student population at SCC. The other students belong in a traditional face-to-face class.
All of the participants asserted that developmental math students must be screened prior to enrolling in an accelerated course to judge whether accelerated instruction is indeed suitable for them. Several interviewees pointed out that incoming placement scores are certainly a valid indicator for the proper fit. However, a few of the instructors pointed out that there are other factors to take into consideration. Katie explained:
When I’ve talked with some students about accelerated classes, they’ve said, ‘I
just don’t feel comfortable with that. I don’t want to do this on my own or on the
computer.’ A lot of time these are older students and they just want face-to-face
instruction.
168 Sally added, “I’ve had students that probably had the ability for an accelerated class; they just don’t feel comfortable with that format. If that’s the case, it’s not fair to force it on them.” Jose mentioned that many students who enroll in the math academy are completely unaware of the format for the class.
They have the expectation that they’re gonna be taught like in a traditional class.
There’s no lecture in the math academy, and that makes a lot of students
uncomfortable. Students like to be taught in certain formats, so you have to
respect their individual learning style.
Ann pointed out that currently there is no mandatory advising for students at SCC. “If we had mandatory advising for any student who tests into DEV, they [the students] could sit down and talk with someone about their major and their needs.” Ann and several other participants also asserted that mandatory advising could assist developmental math students in enrolling in the modality (acceleration or face-to-face instruction) that better meets their individual needs.
Jose and Ann emphasized that instructor comfort level is just as important as student comfort level when considering acceleration. Ann reflected on her experience when teaching a computer-based course.
I didn’t feel comfortable in that setting because I’m an active person in the
classroom, and I like my classroom to be interactive, me and them. And I felt like
I was just sitting there watching them do work. I don’t think I did as good a job
as I would have, had I been comfortable with it.
Jose commented, “Teaching in the computer lab works for some, but some just don’t like to teach in that format. Management has to respect the teacher’s teaching style.”
169 In this section, I described the participants’ views and experiences with acceleration in developmental math. Depending on the student, acceleration can be a proper or poor fit. In the next section, I will describe the institutional improvements that faculty feel are necessary to enhance student success in developmental math.
Improving Institutions to Enhance Student Learning in Developmental Math
As the interview concluded, I asked each participant to describe how SCC or community colleges in general could better enhance student success in developmental math. Several of the interviewees pointed out that successful implementation of these practices may require external help from the college’s administration. Furthermore, the successful enactment of such practices could enhance the application of instructor best practices and augment student learning.
Sharing of best practices.
Several of the participants remarked that they would like to learn more about various best practices that their developmental math colleagues employ. The participants stressed that they often learn about various methods that are effective from their colleagues; therefore, they would prefer more opportunities for open communication regarding best practices so that everyone can learn from each other.
Jenny provided an example of sharing best practices: “We could have a meeting where everybody can discuss one thing they do in a class that they feel works and helps the students.” Jeff articulated, “I wish I could hear more about what’s going on and get some more ideas about what works for students.” Some of the participants pointed out that being an adjunct instructor can be isolating since there may be little to no communication with other faculty members. Robyn commented:
170 I just think it would be good to hear what other people are doing specifically in
our content. Maybe we could have some training on best practices that have
worked in DEV math. That would help because when I was an adjunct, I never
really got to talk to the full-time faculty.
Frankie added:
I’ve learned a lot from some of my colleagues, but as a part-timer, I just don’t get
to talk to my colleagues that much. I would love it if we could have some kind of
idea sharing session on a regular basis.
Katie also mentioned that through the sharing of ideas, instructors could get to know each other’s teaching style:
Teachers, especially adjuncts, don’t always know each other’s style. I like to
recommend certain teachers to students because I know their teaching style
matches the student’s learning style. So it would help if we could all share our
ideas and styles.
Less administrative interference.
A few of the faculty participants expressed concern over losing their pedagogical freedom and their input not being considered in curricular decisions. As mentioned in
Chapter Three, SCC has received various grants and has taken on several initiatives to increase student learning. While the participants applauded SCC’s proactive approach to improving student success in developmental math, some have become concerned that there has been too much administrative interference, thereby limiting their effectiveness in employing best practices.
171 A few of the interviewees have become concerned that SCC administrators have attempted to mandate various teaching styles. The participants cited that in 2008, as part of the Achieving the Dream initiative, all full-time faculty teaching the DEV 108 course were required to employ either one of two instructional modalities: guided inquiry or computer-based instruction. Basically, some of the SCC administrators noted that both of these aforementioned modalities had been successful at other institutions. Therefore, in an attempt to increase student success, full-time faculty teaching DEV 108 were required to choose and implement either one of the two modalities. Consequently, their pedagogical freedom was removed as all instructors had to follow the same format when teaching. One interviewee gave his thoughts:
There is a problem with extrapolating a teaching style to the whole department. If
the faculty member is not comfortable with it, it will most likely fail. So you
can’t mandate someone’s teaching style because it’s a very personal thing. In
some cases, it’s something that the faculty member developed over many years.
This lasted two academic quarters, and since then, faculty have been able to resume utilizing personal teaching methods. However, while there has not been an official mandate from the administration, some of the participants have also reported that they have felt pressure from administration to teach some of the accelerated sections in the math academy. One participant articulated:
I feel pressure to teach in that math academy. I haven’t yet, but I will probably
have to at some point to keep my job. After all, I’m an adjunct. My contract is
renewed each term, so they could easily fire me if they want to. I taught in that
type of environment before at another school, and it doesn’t work for me; I’m not
172 comfortable with it. I get my best results when I’m up at the board interacting
with the students. So why can’t I just do that? Leave me alone, and let me teach!
Two of the participants expressed concern over administrative involvement in the boot camps. One interviewee explained:
When I first heard of the idea [boot camps] at a conference, I thought it could
work for us, but it would be specifically for students who were on the cusp of
placing into a certain math class. It would be for those high end students, who
really could complete a DEV math course in a week and then move on. So we
determined the placement cut off scores, and I worked with registration, and for a
while it worked. We got two or three hundred students a quarter who were on
that high end.
Another interviewee added, “We had huge success rates because those students were a perfect fit for the boot camps.” However, both participants maintained that this is no longer the case as one of them clarified:
Now it’s open to all students. Also, if a student fails a class, they can take a boot
camp. It’s important to acknowledge that a student who fails a class probably
doesn’t have an understanding, so we’re probably not doing them a favor by
letting them take an accelerated course.
The interviewee speculated why this has happened:
One of the things the administration has been doing lately is pushing everyone
through. They want students to get through DEV math. Acceleration isn’t for
everyone because the students are gonna get the rush job, and they’re gonna miss
a lot.
173 The other participant expressed frustration:
And we find that out a lot around here. When you design something, they [the
administration] tweak it, ramp it up, do all kinds of mutations to it, and it’s no
longer what it was intended to do, and that becomes frustrating.
Early intervention.
Several of the participants mentioned that students often enter their developmental math classes severely underprepared in many ways. As a result, there is little that the individual developmental math instructor can do to help, and the students ultimately too often fail. Therefore, the participants suggested various ways that an institution could provide early intervention for students to assist them in becoming more equipped for even their developmental classes.
Jenny suggested a mandatory entrance course:
They really need, especially a DEV student, an orientation course, a study skills
course, a reality course. They need to know what it takes to succeed in college.
We could also have a half-day seminar where we bring in previous students who
have successfully passed their developmental courses and talk about, ‘This is
what I needed to do to succeed.’ Incoming DEV students could also be paired up
with these students for mentoring throughout the quarter as well.
Quite a few of the participants asserted that there has to be better alignment between high schools and post-secondary institutions. Ann specified:
There needs to be more ties with the high schools. There is such a disconnect
between what they require on the state test and what we have on our Accuplacer.
We need more alignment of the curriculum between the two.
174 Other participants, such as Sally, argued that community colleges and high schools should collaborate to identify and help potential developmental math students.
We need to help some of those DEV math students before they take our classes.
We need to work with the high schools to find out which students would test into
a DEV math course and then help them with their basic skills. That way they are
more prepared.
Some of the participants also mentioned that SCC has attempted to connect with local high schools through the years, but for unknown reasons, these connections have either ceased or were never fully developed. Currently, SCC is attempting to work with certain local high schools to align curricula; however, this initiative is still very much in the inaugural stages.
Chapter Summary
In this chapter, I presented the findings from my data collection (face-to-face interviews and pre-interview questionnaires) from 20 developmental math faculty at
SCC. I began this chapter by conveying the main reasons for student non-success in developmental math: severe underpreparedness, behaviors that thwart success, and external issues. Severe student underpreparedness consists of extremely low arithmetic skills, which the participants linked to calculator dependency and misalignment in student expectations between K-12 and post-secondary institutions. Behaviors that thwart success entail paltry attendance and overall low motivation. External issues involve the students’ difficulty in balancing school, employment, and family obligations and as a result, students cannot devote the time necessary to their studies.
175 I reported the general best practices discussed by developmental math faculty informants to enhance student learning. The first practice was effective communication with students. More specifically, this involves faculty communicating with their students on a regular basis regarding their progress. It also involves general meaningful communication that establishes a rapport with students. Another general best practice is the art of organization, which consists of faculty assisting students in developing their organizational skills when studying math. This practice also includes overall structure and consistency among faculty within a department. Several of the faculty participants also employ collaborative learning, which includes general group work and guided inquiry, a more specific form of collaborative learning. Quite a few of the participants identified frequent low stake assessments as a best practice. Rather than relying on infrequent high stakes assessments such as unit exams and a cumulative final, this practice involves frequent assessments such as daily or regular quizzes, math journaling, the problems of the day, and correction reflections. The final general best practice involved the use of technological supplementation to traditional instruction.
After general best practices, I described content-specific best practices. These practices focus specifically on assisting students with certain content within a developmental math course. Several of the faculty participants employ the use of mnemonics and memorable wording. Other content-specific best practices utilize manipulatives, visuals, and real-life applications.
Because of the national emphasis on accelerated instruction in developmental math, I discussed the experiences and viewpoints from the faculty participants on this topic. The participants reported that accelerated instruction is an ideal fit for
176 developmental math students who possess solid number sense, high motivation and dedication, and efficient time management and organizational skills. However, the participants also expressed concern that acceleration is simply not appropriate for all developmental math students or even all developmental math instructors.
Lastly, I explained approaches that the faculty participants believe that post- secondary institutions could take to enhance student success in developmental math.
Some of the participants expressed the need for increased internal communication regarding best practices. More specifically, faculty should share best practice ideas with each other on a regular basis. A few of the participants articulated that administrative interference is obstructing student success. Administrators are mandating certain teaching styles, which places faculty members outside of their comfort zone. Finally, several of the participants pointed out that earlier intervention is needed for incoming students as this could help students enter postsecondary education with more basic skills.
177 CHAPTER V
DISCUSSION OF FINDINGS
Introduction
In this qualitative study my purpose was to gain a thorough understanding of the best practices employed by a group of developmental mathematics instructors at an urban community college through conducting interviews and collecting written documentation from participants. In the previous chapter, I identified and described these practices. I also explained how this group of developmental mathematics instructors employed such practices. Participants identified the following techniques as best practices: communication with students, the art of organization, collaborative learning, frequent low stake assessments, supplementation with technology, mnemonics and memorable wording, and manipulatives, visuals and real-life applications.
In this chapter, I discuss conclusions and implications of the findings and my recommendations based on these conclusions and implications. In constructing these conclusions, implications and recommendations, I considered all of the information presented in the previous chapter, which included the factors that instructors believe inhibit student success in developmental math, the general and content-specific best practices that this group of developmental math instructors employ, the current topic of accelerated instruction in developmental math, and the various ways that these instructors feel that institutions, in general, could help students succeed in developmental math.
178 Finally, I discuss some ideas for future research with regard to best practices in developmental math.
Conclusions, Implications, and Recommendations
Communication with students.
The findings from this study suggest that developmental math instructors should not assume that all students are cognizant of their current academic standing. It is quite common for these students to be failing a class and be completely unaware that they are failing. Therefore, developmental math instructors should make an effort to regularly communicate with their students regarding their academic standing and overall progress.
Instructors may employ the mid-term review where students determine their academic standing by computing their current grades and evaluating their own progress.
Developmental math faculty may also use frequent email communications to remind students of assignments, deadlines, and exams. Additionally, instructors can reach out to students via email who have missed classes or are struggling with the content. This study’s findings implied that email communication is a best practice for distance learning in developmental math. In distance learning, courses are generally uniform; however, instructors control the amount of communication they have with their students. While this may vary on individual personality or comfort level, instructors should consider adding something extra to their email communications. This could be a joke or riddle or something else that can grab their students’ attention and can consequently make class more enticing.
Overall, the findings from this study indicate that communication regarding academic progress can enhance student learning. Developmental math students are
179 generally appreciative of their instructors taking time to reach out to them. Most of all, when students become aware of their lack of progress, many of them will make an effort to improve. Such efforts include attending class more regularly, seeking extra help outside of class, and simply working harder to improve.
Developmental math instructors should also make an effort to establish rapport with their students. Again, the specific practices that instructors may wish to implement may vary on their individual personalities or comfort levels. However, there are many effective practices that faculty members may choose from to establish a rapport with their students: facilitating group discussions related to math content, touching base with and encouraging individual students during class, conferencing with students about their individual goals, and basically making an effort to get to know students. The participants in this study stressed that instructors should strive to create an environment where students feel comfortable asking questions and addressing struggles. This aligns with the beliefs of Hall and Ponton (2005) who asserted that developmental mathematics educators are responsible for establishing an atmosphere where students can ask questions and be pro-active in their struggles. Establishing a rapport with students can simply help them feel more at ease in class. They also begin to believe that someone cares about their success. Consequently, many of these students will attend class regularly, which is an all important step in their learning and overall success.
It is noteworthy, however, that the results from this study suggest that communication with developmental math students has some limitations. There are simply some students who will not respond to any kind of communication regarding their academic progress. There are also some students who may feel embarrassed about
180 speaking in front of the class. In summary, if an instructor attempts to make a connection or establish a rapport with a group of students, there will most likely be a subset of students who will be unresponsive.
The importance of student and instructor organization.
The participants in this study reported that incoming developmental math students often lack very basic organizational skills. More specifically, when working a math problem, their organizational skills are haphazard. They are sometimes sloppy and refuse to or simply do not know how to work a problem in an organized, linear fashion.
Therefore, in this study, the art of organization was defined as a best practice for developmental math students. To start, developmental math instructors should encourage all students to take notes in class. This recommendation aligns with the findings of Eades and Moore (2007) who advocated that faculty steer their students toward quality note- taking. When providing class notes, instructors should provide a structured step-by-step approach to completing a math problem. Clearly, there may be more than one way to work a certain math problem, and that may be dependent on the individual student’s learning style or comfort level. Instructors can always work with individual students who wish to adopt a different way of working a math problem. However, to be successful, it is imperative that developmental math students are able to rely on some sort of solid algorithm when completing a math problem. This conclusion coincides with Vasquez’s
(2003b) recommendation of the Algorithm Instructional Technique (AIT), which involves a step-by-step process for students when calculating every math problem.
In this study, several participants reported success using a combination of guided and in-class practice when teaching the structured step-by-step process of various math
181 problems. When providing class notes, instructors should model clearly and completely the necessary steps to working a problem. However, instructors should also devote time each class to allow students to practice by assigning various problems for students to complete in class. Students could work individually or in small groups. This will give students the chance to practice, and it will give the instructors an opportunity to circulate throughout the classroom to further help students adopt the structured approach. Some students will be resistant to adopting a more structured approach and abandoning their disorganized habits. However, instructors should be persistent as better organization and a more structured approach will likely help students to be successful.
When providing notes for developmental math students, the participants in this study emphasized being prepared, detailed, and flexible. It is important for instructors to prepare their class notes in advance and to also practice the problems they intend to cover in class so that they can clearly convey a structured process to their students. Instructors should also include extra detail by noting specific parts of a problem where students may struggle or need to be extra careful. Including the chapter, section, and page number of an accompanying textbook if applicable will be beneficial to students as well. However, the findings from this study also suggest that it is essential for instructors to remain flexible. A uniform set of class notes may not be suitable for all developmental math classes and students. For example, one class may require more explanation in solving linear equations than another class. Another class may need as much explanation but with different wording or even different examples. Instructors must organize their class notes in a way that provides such flexibility. The tool that Kelly utilizes (described in
Chapter Four) is an example of such a practice.
182 Frequent low stake assessments coupled with student outreach.
In this study, the participants reported that implementing frequent low stake assessments enhanced student learning. Furthermore, the identification and description of frequent low stake assessments as a best practice in this dissertation has added to the knowledge base of developmental math. Boylan (2002) suggested that developmental math instructors employ frequent assessment; however, this dissertation has detailed various forms of frequent low stake assessments. Rather than relying on high stake exams such as unit tests and a cumulative final to assess student learning, several of the participants implemented lower stake assessment practices on a regular basis and conveyed that such assessments helped students to retain more information and enjoy better success on higher stake assessments. Such practices included regular or daily quizzes, the problems of the day, math journaling, and test and homework correction reflections.
Developmental math instructors should not rely solely on high stake assessments to evaluate their students’ progress. In this study, the findings infer that while instructors may implement various best practices when explaining content, it is probable that developmental math students will not retain information on a long-term basis. As the participants noted, students have difficulty with memorization. Also, many developmental math students do not review their class notes as frequently as they should.
Therefore, developmental math instructors should make an attempt to assess their students’ progress on a class-by-class basis. Again, regular quizzes, the problems of the day, and math journaling are all effective ways for instructors to identify content areas in which individual students or even an entire class may be struggling.
183 It is notable that it was not only the participants’ execution of various frequent low stake assessments that enhanced student learning. Several of the participants pointed out that after administering these assessments, they would often conference with their students. More specifically, they would meet with their students individually or as an entire group to address mistakes or errors that the students displayed on these assessments. In summary, developmental math instructors should employ a combination of employing frequent low stake assessments and also touching base with the students to help them understand their mistakes.
As Boylan (2011) pointed out, math is linear; if students do not understand content covered in Tuesday’s class, they will most likely not understand the content covered in Thursday’s class. The findings from this study parallel that theory.
Employing these assessments on a regular basis will help instructors to touch base with students and assist them before their struggles snowball into unmanageable issues.
Instructors should consider implementing some sort of correction reflection for exams or homework assignments. As indicated in this study, developmental math students will often ignore their mistakes unless they receive some sort of encouragement or incentive to correct them. When students work to correct these mistakes, they are less likely to make them in the future. Again, these frequent assessments are low stake in that they do not severely impact a student’s overall grade. The fact that they are low stake can take pressure off of the students which can help them focus on mastering the material.
The muddy waters of collaborative learning.
In this study, several of the participants reported that various types of collaborative learning such as general group work and guided inquiry enhanced student
184 learning. The findings from this study imply that employing collaborative learning allows students to feel less embarrassed and less isolated about their struggles in mathematics. This aligns with the conclusions of Woodard (2004), Phoenix (1990/1991), and Phelps and Evans (2006). These authors also found that various group activities minimized the amount of isolation and awkwardness that students felt regarding their math skills. This study’s results, which align precisely with the findings of Woodard
(2004), also suggest that some students who are embarrassed about pursuing help from their instructor will seek help and learn from their peers through collaborative learning activities.
The findings from this study further suggest that collaborative learning can encourage students to become more engaged in math. As students make connections with their peers, the participants noted that they form study groups that meet outside of class. Establishing connections with peers has also increased student retention. In summary, the more engaged students are in their math and the more they attend class, the better chance they have of learning.
However, the findings from this study infer that collaborative learning is not effective for all students. Some of the participants stressed that collaborative learning is not a proper fit for certain students or even particular instructors. There may be some students who are overly shy or socially awkward, and this may hinder their success in group work. There could be groups of students who simply do not work well together for various reasons. One member may allow another to do all of the work; the participants may drift off into unrelated conversation; some members may simply not get along with each other.
185 The bottom line is that while collaborative learning can enhance student learning, instructors must take some considerations into account before implementing this practice.
Some of the participants in this study mandated group work in their classes while others made it optional. Whether an instructor should or should not mandate group work is dependent upon his or her individual comfort level and experience. Some instructors are comfortable mandating group work and even assigning the groups and attain positive results. However, developmental math instructors who are tentative about employing group work should study the dynamics of a certain group of students to determine if they are indeed “good group workers.” Instructors also need to consider which students would work well together and which ones would not.
Most of all, instructors must also examine their own level of comfort and feelings when considering the implementation of collaborative learning activities. For example, some instructors might be more comfortable utilizing pair share activities, which are quick and less formal, as opposed to group activities that are more structured and could monopolize large parts of a given class. Some collaborative learning activities may also require some training and experience. Both of the participants in this study who did not find success with guided inquiry noted that they did not have prior training or experience.
Even participants who successfully employ guided inquiry suggested that faculty who are interested gain some experience before application. In summary, collaborative learning activities are a best practice when the dynamic of a certain group of students is suitable and the individual instructor has a high comfort level for such activities. Therefore, collaborative learning activities should not be implemented extemporaneously.
186 Instructors must consider their own comfort level, the dynamics of a given group of students, and whether prior training is necessary.
Appropriate technology supplements.
Quite a few of the participants reported that supplementing their classes with the
Kahn Academy software has enhanced their students’ learning. However, it is important to examine why this software is effective. Some of the participants compared the Kahn
Academy videos to the videos available in SCC’s Tutoring and Learning Center. The participants reported that Kahn Academy software is easy to navigate and consists of videos that are only a few minutes in length but cover a specific math topic thoroughly whereas SCC’s videos are laborious. However, a couple of the participants reported experiencing difficulty with using another computer software program, MyMathLab
(MML), as a supplement. This coincides with the findings of Jacobson (2006) who reported that students become frustrated with the meticulous nature of computer software.
However, in this study, the participants stated that when utilizing MML, students found the software more than meticulous; they had so many navigational issues that they could not even get to point of actually using the software.
Based on the findings from this study, we should not conclude that Kahn
Academy ought to be the primary supplemental software program utilized by developmental math instructors, nor should we conclude that MML should be banned from developmental math. However, we can conclude that when implementing technology as a supplement, instructors must be careful, especially if students will primarily access this software outside of class with little guidance from the instructor.
Students should be able to practice their math without getting lost in the system.
187 Instructors should not assume that simply because a software program is successful in a computer-based or a distance learning class that it will be successful as a supplement.
After all, in distance learning course modalities, students may have stronger computer skills, and in a computer-based course, the instructor can devote sufficient time to helping the students adjust to the software. Therefore, when implementing technology as a supplement, instructors should choose software programs that are easy for students to navigate. Such programs should be thorough but also quick and to the point and free of extraneous detail.
Go the extra mile with creativity.
In this study, quite a few of the participants stressed that an instructor cannot treat developmental math students at a community college as though they are university students. Developmental math students often enter community college underprepared and also lack organizational skills as well as self-efficacy in their math ability.
Therefore, simply teaching and explaining the material is not enough. Developmental math instructors must be willing to travel the extra mile and get creative to help their students succeed.
The participants in this study described various ways in which they implement creativity into their teaching. When covering various topics in developmental math several instructors utilized various mnemonics and memorable wording when covering topics such as the metric system, decimals, long division, and rounding numbers. Several of the participants also discussed the importance of providing in-depth explanations and relating the content to real-life situations. This recommendation aligns with the findings of Galbraith and Jones (2006), who stressed that instructors should relate developmental
188 math content to real-life situations to make the subject matter more meaningful to students. A few of the participants also stressed the importance of utilizing visuals when explaining geometry. The participants pointed out that employing all of the aforementioned strategies has helped students to retain and even understand the material better. While memorization is important, it is imperative that instructors employ creative ways to truly help students understand the material. This way students can connect ideas and not rely solely on memorization, which was a concern expressed by some of the participants as well as Stigler et al. (2010).
The bottom line is that developmental math instructors must go the extra mile and use some creativity with their teaching. In summary, instructors must find a way to be succinct but also provide enough in-depth explanation and ingenuity when working with developmental math students.
Policy implications.
The findings from this study suggest various policy implications with regard to best practices in developmental math. More specifically, organizational leaders within an institution share a responsibility with faculty when implementing best practices in developmental math.
Mandatory advisement.
Several of the participants articulated that certain practices such as acceleration and collaborative learning are not suitable for all students. In fact, improper placement could impact students’ success in a course. Therefore, institutions should consider implementing mandatory advising for students. More specifically, students should be required to meet with a college advisor before registering for classes in a given academic
189 term. Advisors can evaluate the students’ performance on their placement exams and their performance in developmental math. The advisors can also talk with the students about their learning styles and individual needs. This way developmental math students are channeled toward the modality (traditional or accelerated instruction) that best meets their individual needs.
A certain degree of uniformity.
This study’s results suggest that developmental math departments and areas can benefit from a certain degree of uniformity and structure as several of the adjunct faculty participants asserted that the overall organization and structure of the math area at SCC made it easier for them to help their students. This included faculty administering the same unit exams and cumulative final. Adjunct faculty are also provided with a course syllabus, a daily schedule, and are paired up with a mentor. This ensures that all faculty are covering the required material and sets the stage for student learning. Pedagogical freedom should be encouraged in developmental math; however, developmental math departments and areas should take the time to ensure that all faculty are administering some sort of common assessments (exams) and are using common instruments (syllabi and course outlines). This will guarantee that students are gaining the necessary skills before progressing to another course. However, administrators and other officials should allow faculty to work together to design these documents. The study’s findings suggest that developmental math faculty are the true experts in their field, and therefore, faculty should have the utmost say regarding policy and academic content within a developmental math department or area.
190
Acceleration: a best practice but not a universal quick fix.
Developmental math programs have certainly faced increased scrutiny. Roueche and Waiwaiole (2009) noted the high cost of developmental education at community colleges, which is a major issue as state schools have faced decreased state funding over the last decade (Alexander, 2006, American Council of Higher Education, 2004; Hebel,
2010). This has led state legislators to question and criticize the low student success rates in developmental math and place pressure on the institutions to increase success rates
(Arendale, 2003; Bahr, 2008). Studies have also shown that students who complete their developmental math courses and reach college-level courses at a quicker pace are more likely to achieve an associates or bachelor’s degree (Edgecombe, 2011). In addition, the more developmental math courses that a student must take, the less likely he or she is to complete the entire developmental course sequence (Bailey et al., 2010). These issues have led to increased pressure on institutions to accelerate their students through their developmental math requirements at a quicker pace.
Based on findings from other institutions, acceleration in developmental mathematics has proven to be a best practice. Cleveland State Community College and
The Community College of Denver have reported that employing accelerated instruction has increased student success rates in developmental math. Findings from this dissertation study certainly support the notion that accelerated instruction in developmental math is a best practice. However, these findings also imply that accelerated instruction is a best practice for developmental math students with very specific characteristics. The participants in this study stressed that accelerated instruction
191 is a proper fit for students who already possess strong number sense and are somewhat academically advanced in developmental math content. Based on the incoming placement exam, these are the “high end” students. These students are also independent learners with solid organizational skills who are highly motivated and dedicated to their studies. If the accelerated coursework takes place in a computer lab, such students should be competent with computer software. A few of the participants advocated accelerated coursework as suitable for students who are comfortable with the modality itself. In other words, some students are not comfortable with computer-based instruction and simply require face-to-face or traditional instruction.
In this study, several of the participants pointed out that acceleration is simply not fitting for some developmental math students. More specifically, acceleration is a poor fit for students who lack organizational skills and miss class frequently. Acceleration is also inappropriate for students who lack number sense and struggle with basic mathematics.
Administrators and faculty should proceed with caution when implementing an accelerated modality into a developmental math program. As Boylan (2002) recommended, developmental students should be properly screened before being placed into accelerated coursework. A student’s placement score could be a valid indicator of whether he or she is candidate for accelerated instruction, but she/he should also meet with an advisor to further discuss whether accelerated instruction is suitable. Most of all, students should be made fully aware of the type of course (accelerated or traditional) for which they are registering. All of these aforementioned actions could lead to better placement for students.
192 Many institutions are facing or will face political pressure from state legislators or other external stakeholders to implement accelerated instruction in their developmental math programs on a large scale. Some institutions may feel pressured to convert the majority or all of their developmental math classes into some sort of accelerated instruction. If this happens, administrators and faculty must examine the skill level of incoming developmental math students. If many of these incoming students lack basic math skills as well as time management and organizational skills, institutions should consider putting some early intervention programs into place. More specifically, students could take basic courses that cover basic mathematics and even college survival skills such as time management, organization and computer skills (if the accelerated instruction is computer-based) upon entering college.
If acceleration is to be implemented on a large scale, faculty and administrators should also take a proactive approach in connecting with local high schools to better prepare incoming students. The initiatives within El Paso Community College (EPCC) serve as a good example. EPCC uses the Accuplacer exam to evaluate the mathematical ability of students from the area high schools. Students who place into a developmental math course can participate in a tutorial program while they are still in high school to assist them in becoming more college ready (Killough, 2009). These programs have allowed students to become more academically prepared (Miller, 2011). Therefore, community college officials should consider connecting with their local high schools and establishing various tutorial programs to help high school students become more college ready. Again, the findings from this study imply that accelerated instruction is a best
193 practice for a specific group of students. Therefore, institutions must ensure that only that specific group of students is enrolling in accelerated instruction.
The findings from this study also raise some other issues regarding accelerated instruction. A few of the participants expressed concern that accelerated instruction in a lab setting severely lessens the lines of communication between the student and the instructor. Furthermore, the participants were concerned that this lack of communication can hinder student learning as the instructor is an essential resource to the developmental math student. For instance, a computer cannot provide the kind of detailed instruction and overall reassurance and confidence building that an instructor can. This concern supports Boylan’s (2002) assertion that developmental math instructors provide social reinforcement for their students. Another participant conveyed concern that through accelerated instruction, students may develop gaps in their math knowledge base. Since students are moving through the course material at a quicker pace, they may not receive instruction that is as thorough as traditional instruction. Clearly, further research is needed on accelerated instruction in developmental math. For example, future research should examine whether developmental math students’ instruction is as comprehensive as their peers’ in a traditional class.
The importance of respecting instructor comfort level and input.
The findings from this study yielded several best practices in developmental math such as effective communication, organization, frequent low stake assessments, and the use of manipulatives, visuals, and real-life applications. Such practices are strategies that most development instructors should be able to successfully implement. For each overall practice, instructors may choose how to employ the practice based on their own comfort
194 level. For example, when employing effective communication regarding progress, instructors could choose to implement either the mid-term review or communicate via email or both. When implementing frequent low stake assessments, instructors could elect to employ the problems of the day, math journaling, regular quizzes, correction reflections or all of these strategies.
The findings from this study also suggest that practices such as the various forms of collaborative learning and accelerated instruction are simply not a proper fit for certain instructors. In fact, a few of the faculty participants voiced the importance of instructor comfort level with regard to implementing a practice into a developmental math class. In many cases, an instructor must be comfortable with a practice upon implementation for the practice to be successful. A best practice for one instructor may simply not be a best practice for another.
Public post-secondary institutions such as community colleges are being held more accountable for their success rates. Consequently, community college administrators may feel the need to take various measures to increase success rates in departments with traditionally low success rates such as developmental math. Such measures may include mandating that some or all developmental math instructors employ a certain practice in their classes. The participants in this study pointed out that when it comes to the attention of certain administrators that particular practices such as computer- based instruction and guided inquiry have been successful in another institution, their first instinct has been to mandate the implementation of that practice. There are situations where there must be a proper fit between the practice and the instructor, and administrators must recognize and respect the comfort level of developmental math
195 instructors. The findings from this study imply that if an instructor is not comfortable with a practice, it may hinder her/his implementation which could thwart student learning. In summary, while structure and uniformity is important, the findings from this study indicate that pedagogical flexibility is equally important. Instructor comfort level is very important with regard to the implementations of best practices. Therefore, administrators and other officials should refrain from requiring all developmental math instructors to adopt and implement a specific practice and allow these instructors the freedom to teach to the needs of their students. Instructors can employ common exams, a mutual textbook, communal course outlines and schedules but also enjoy the freedom to execute methods such as various forms of collaborative learning, communication, frequent low stake assessments, and technology supplements.
This research has addressed several best practices that contrast with traditional lecture-based instruction. These practices are new to many developmental math instructors; therefore, the implementation of such practices would require a change in instructional approach. In the literature review, I examined the use of supplemental instruction, learning communities, distance learning, acceleration and compression, computer-based instruction, and collaborative learning in various developmental math programs across the country. In the findings, I described how various developmental math instructors utilize forms of collaborative learning, acceleration, and technology in the classroom. It is quite possible that an administrator or developmental math faculty member may become aware of one these practices and wish to implement the practice on a departmental level, where a sizable percentage or even all of the instructors in the department would employ the practice.
196 However, administrators or faculty members should exercise extreme caution when implementing a practice on a large scale that contrasts with traditional teaching and may be new to many faculty members. Again, faculty comfort level must be considered.
Also, the person or persons who are considering implementation must make an attempt to understand whether such a practice would be fitting for the instructors and students of that developmental math program. After all, simply because a practice is successful in one developmental math program at one institution does not imply that it will be successful in a different institution.
If an administrator or faculty member is interested in implementing a practice on a large scale that may be novel to faculty members, he or she may want to take the time to talk with the faculty members. During these discussions, the administrator or faculty member could identify the comfort level of the group of instructors with the practice.
The administrator or faculty member should also determine whether or not the group of instructors feels that the practice would enhance student learning. If there is a great deal of resistance or if the group of faculty members believes that the practice will not be a proper fit for the students or the department, such a practice should not be executed.
Moreover, it is important to listen to the faculty. In this study, a couple of the participants expressed frustration that administrators do not listen to their input. Again, developmental math instructors are the true experts in the discipline of developmental math and can recognize the practices that are necessary to help them.
Professional development.
The findings from this study indicate that developmental math instructors should establish meaningful communication with their students, but they should also institute
197 active communication with each other. More specifically, in order for developmental math instructors to learn and grow professionally, they must share their best practices with each other. Some of the participants pointed out that they had learned about various best practices from their colleagues; others stressed that they wanted more opportunities to communicate with their associates about best practices. Certainly, there are national and state-wide opportunities for such professional development. For example, the
National Association of Developmental Education (NADE) holds an annual conference in which developmental instructors can share various best practices. Individual states also hold similar conferences as well. For example, in Ohio, there is the Ohio
Association of Developmental Education (OADE), where developmental instructors from various Ohio post-secondary institutions can congregate to share best practices.
However, such events occur on a sporadic basis and may require travel, which can be time consuming and expensive for faculty.
Developmental math departments should consider implementing internal and local professional development workshops that allow sharing of best practices. During these workshops, developmental math instructors could describe one or even a few best practices that they employ in their classes to enhance student learning. Such workshops could be especially beneficial to novice developmental math faculty. As Breneman and
Haarlow (1998) mentioned, most of the training for developmental math instructors tends to be in-service not pre-service. Therefore, this kind of sharing of ideas could be valuable professional development to neophyte developmental math instructors. Adjunct faculty would also benefit greatly as this group of instructors often does not share regular interaction with full-time or permanent faculty. Continuing to educate adjunct
198 developmental math faculty on best practices will be imperative because as AMATYC
(2006) mentioned, the use of adjunct faculty in developmental math has increased.
Developmental math departments and areas could also team up with their counterparts from local community colleges. More specifically, a developmental math department from one community college could work with the developmental math department from a community college 20 or 30 miles away and run a day long workshop on best practices.
This would bring even more ideas into the mix, and it would not require long travel.
The limitations of best practices.
As I discussed in Chapter One, lack of student success in developmental math is a national issue. Attewell, Lavin, Domina, and Levey (2006) reported that only 30% of all students pass all of the developmental math courses in which they enroll. Bahr (2008),
Depree (1998), and Wheland et al (2003) stressed that developmental math instructors must seek practices to help their students succeed. Therefore, the purpose of this study was to gain an in-depth understanding of the best practices utilized by a group of developmental mathematics instructors at an urban community college
The findings from this study have yielded several best practices to enhance student learning in developmental math. The participants reported that some of these practices can overcome some of the major obstacles to student success in developmental math. This study’s findings imply that communicating with students can increase student attendance, modify negative attitudes, and increase student confidence. Employing various mnemonics and memorable wording can help underprepared students master basic concepts such as long division, rounding whole numbers, and decimals. Aiding students with developing organizational skills and habits can reverse some of the
199 negative habits that the participants asserted inhibit student success. Also, utilizing various forms of collaborative learning can help students to feel more comfortable in class and move away from the loner behavior that a couple of the participants in this study and researchers such as Smith et al. (1996) and Merseth (2011) have attributed to non-success.
It is also noteworthy, however, that best practices have certain limits and cannot help every student. The participants in this study stressed that even when employing various practices, there are still students who display behaviors that thwart success such as paltry attendance and a poor attitude toward their studies. Lack of basic number skills can limit students’ success. There are also students who struggle with external issues such as work and family obligations as well as students who grapple with drug and alcohol dependency. Such external issues may make it impossible for even a dedicated student to succeed. The findings from this study illustrate that various student behaviors and external issues that students face limit the effectiveness of any best practice.
Again, the participants in this study asserted that many incoming developmental math students lack vital arithmetic skills and overall number sense. Earlier, I suggested that institutions that are considering implementing accelerated instruction on a large scale launch some sort of early intervention program upon entrance and also make better connections with their local high schools. If institutions find that many incoming developmental math students lack these basic skills, they should develop intervention programs to prepare students even for traditional developmental math instruction. Also, many of the participants in this study mentioned that incoming developmental math students are calculator dependent, and this dependency impedes their success in a non-
200 calculator developmental math class. This aligns with the beliefs of Hopkins (1977), who asserted that the use of the calculator may allow students to become more careless and pay less attention to detail. Therefore, when working with local high schools, developmental math instructors should work with high school teachers on various ways to enhance student learning of basic number sense and arithmetic skills. More specifically, high school teachers could still utilize the calculator in their classes; however, they would also implement various strategies into their instruction that would help students retain basic skills.
Even when instructors employ best practices, some students still display various behaviors and cope with issues that impede their success. Such issues and behaviors include being severely underprepared for developmental math, paltry attendance, and contending with external issues such as family obligations or even drug and alcohol dependency. If students are not successful in their classes because of the aforementioned issues despite their instructors employing best practices, administrators cannot hold developmental instructors accountable for such lack of success. Therefore, administrators must take these factors into account when evaluating a developmental math program. In Chapter Three, I discussed how Sinclair Community College considers success rates in developmental math that are 70% or higher to be “excellent” and success rates that are 60% or higher to be “good.” Therefore, institutions must examine their own developmental math students and set standards accordingly. If there is a consistently large amount of students who enter severely underprepared, display paltry attendance, and are contending with external issues, college officials must realize that despite employing the very best practices, not all students will succeed. However, when
201 implementing such standards, college officials should also consider state and external funding. For instance, are the standards in developmental math reasonable based on the specific student population and high enough to obtain sufficient external funding? As student success rates improve, institutions can certainly increase these standards as well.
Reactions from the Researcher
As a professor of developmental math at SCC, I was an insider to the study. I have also taught developmental math full-time since September of 2003. Therefore, I was aware of and familiar with many of the practices that my interviewees described.
However, conducting this study was also a learning experience as some of my findings were novel to me.
Before conducting this study, I was aware of many of the practices that my participants described such as the mid-term review, email reminders, various forms of collaborative learning, and the development of organizational skills. However, I was unaware of the depth and detail included in these practices. For example, in past department meetings and even casual conversations, Jenny referenced the mid-term review. However, after our interview, I was surprised and impressed with the amount of detail involved in implementing this practice and with the student feedback. In earlier conversations, I also recall Brenda describing her collaborative learning activity. Again,
I was unaware of the details of this activity. In summary, I was impressed with the amount of detail and effort that my colleagues put into their practices.
Some of the ways that the interviewees implemented best practices were completely new to me. The employment of math journaling was a novel concept and one that I wish to attempt with my students. I was cognizant of the importance of
202 organizational skills for the developmental math student; in fact, I stress this with my own students. Conversely, the use of graph paper as a tool for organization was new to me. In fact, I am looking forward to trying this practice with my own students. I was also unfamiliar with some of the uses of mnemonics and memorable wording. For example, I was unaware of Sally’s “p to the left, d to the right” song and dance. Since I am not much of a singer, and I have two left feet, I will most likely not try that with my students; however, I will recommend it to other colleagues. I found Kelly’s comparison of “all numbers sit on their decimals” to “all people sit on their derrieres” quite humorous, and I will certainly use that with my students. The interviewees’ use of manipulatives and visuals was quite innovative. Verne’s use of poker chips when explaining signed numbers and Blake running around his desk were very creative as well.
As a veteran developmental mathematics instructor, I found it enlightening to learn about new practices.
Several of the participants described practices that I employ with my students.
When explaining math concepts, I utilize a step-by-step process, and I also work with my students to rely on algorithms. I have used correction reflections with my students from time to time as this is a common practice in our area. More specifically, my use of correction reflections has been similar to the way that Blake and Taylor implemented this method. Like Taylor, I also employ the problems of the day. However, I have used different terminology such as the “wrap up problems” or “the end of class assignment.”
However, Taylor’s interview forced me to reflect on how I employ this activity. Taylor, along with the other participants who utilize various frequent low stake assessments, stressed that it is important for the instructor to touch base with the students on a regular
203 basis to discuss results from these assessments. I do not always do this. Therefore, I will make an attempt to touch base more with my students regarding their progress when employing frequent low stake assessments.
Entering this study, I did not know what to expect when addressing the topic of acceleration; I simply wanted to address the topic and therefore entered each interview with one lead question. However, I was pleasantly surprised that my participants provided rich data regarding acceleration that will certainly add to the knowledge base of development math.
Since I had experience with several of the best practices that my participants described, I struggled when I coded the data to separate my own feelings from the actual findings. However, as I described in Chapter Three, engaging in reflexivity and maintaining my journal allowed me to reveal my biases and work to ensure that my findings were not skewed by such biases and indeed grounded in the data. Each time a participant described a practice, I would write about my own feelings regarding this practice. Being able to visibly view my own feelings versus the raw data allowed me to separate the two. Participating in peer debriefing also helped to ensure that I achieved this as well. In summary, because I was an insider biases were inevitable; however, my goal was to ensure that the findings from this study reflected the data that I gathered.
Ideas for Future Research
The findings from this qualitative study imply that employing frequent low stake assessments in developmental math can enhance student learning. However, this concept should be studied further since it is not addressed in the knowledge base of developmental math. Researchers should consider conducting group comparison studies
204 between developmental math classes that utilize frequent low stake assessments along with high stake assessments and classes that rely solely on high stake assessments. Also, in the classes that use frequent low stake assessments, instructors would need to use the results of such assessments to communicate with the students regularly regarding their results. A study should be conducted to determine if there is a significant difference between the two groups and if developmental math students who are exposed to frequent low stake assessments perform significantly better than developmental math students who are only exposed to high stake assessments.
The results from this study suggest that instructor comfort level should be an important consideration when employing best practices in developmental math. For some practices to be effective, the instructor must be highly comfortable with executing the practice. Therefore, if we are to continue to implement best practices in developmental math, it is imperative that we understand more about the relationship of instructor comfort level and student success. Consequently, researchers should consider conducting correlational studies that measure the relationship between instructor comfort level and overall student success when employing various best practices in developmental math such as collaborative learning and accelerated instruction and student success.
In this study, the findings inferred that if developmental math instructors employ technology as a supplement in their classes, such technological supplements should contain the following characteristics: user-friendliness and simplicity yet a thorough enough explanation. There is very little in the literature of developmental mathematics with regard to technological supplementation, especially various types of suitable
205 computer software. Therefore, researchers should contemplate performing qualitative studies that seek to understand more about developmental math students’ experiences with computer software programs. Furthermore, researchers could use these studies to identify and describe various types of computer software that would be suitable for developmental math students. Such studies could provide an in-depth description of these software programs and how they can be effectively employed in developmental math classes as a supplement.
Acceleration continues to be a prevalent topic in developmental math.
Furthermore, state legislators and other external stakeholders will continue to pressure institutions to employ methods that will traffic students through their developmental math requirements at a quicker rate. However, the findings from this study imply that accelerated instruction in developmental math is a best practice for a very specific group of students. The participants in this study also expressed concern that accelerated instruction could actually hinder student learning if not employed properly. Therefore, more research must be conducted on the practice of accelerated instruction in developmental math. Researchers should oversee qualitative studies that examine the experiences of both developmental math students and instructors who have been involved with various types of accelerated instruction. In Chapter Two, I mentioned that some institutions have witnessed an increase in student success rates since implementing accelerated instruction. However, more research should be conducted to compare the student success rates from classes that utilize accelerated instruction with those that use traditional instruction.
206
Chapter Summary
In this chapter, I provided several, conclusions, implications, and recommendations based on the findings presented in Chapter Four. These conclusions, implications, and recommendations included suggestions for faculty regarding best practices as well as ideas for administrators and other officials with regard to the implementation of policy in a developmental math department or in an institution.
Faculty should consider employing various types of communication to connect with their students. Additionally, developmental math instructors should consider working with students to develop their organizational skills. Developmental math instructors should contemplate employing frequent low stake assessments in their classes rather than relying solely on high stake assessments to measure students’ progress. The findings from this study imply that collaborative learning can enhance student learning; however, it is essential that instructors attempt to understand if a particular form of collaborative learning is appropriate for a certain group of students. Instructors ought to evaluate their own comfort level with regard to the use of collaborative learning. Instructors may also want to consider employing some sort of technological supplementation into their developmental math classes. However, such supplementation should be straightforward yet thorough and user-friendly. Lastly, developmental math instructors may need to go the extra mile with creativity during instruction. Rather than simply teaching and explaining the material, instructors ought to think about using mnemonics, memorable wording, manipulatives, visuals and real-life application to help students understand and retain information.
207 As for policy implementation, institutions should employ mandatory advisement so that students’ individuals learning needs are being met. Faculty within a developmental math department or area should strive to create some sort of uniformity within departments or areas to make the transition easier for incoming instructors. This will also help to ensure that students master the required material. The findings from this study suggest that accelerated instruction is a best practice for a very particular group of developmental math students. Such students have strong organizational skills and are dedicated to their studies. These students also possess solid number sense and while they have gaps, they are somewhat competent in understanding developmental math content.
Therefore, institutions should exercise extreme caution before implementing accelerated instruction in developmental math on a large scale.
Professional development is also imperative for developmental math faculty.
Instructors should communicate with each other about practices that work and practices that do not. This can be done through local workshops and seminars. This is especially important for inexperienced or novice faculty.
Based on the findings from this study, there are other considerations that faculty and administrators must take into account with regard to employing best practices in developmental math. Instructors should be comfortable with the practice that they are using. There are also practices that work for certain students and not others. Therefore, administrators should not mandate that an entire department or area utilize a particular practice. Best practices in developmental math also come with limitations. Despite proper execution of a practice, some students will simply not respond.
208 This study on best practices in developmental math also introduced some ideas for future research. Researchers should conduct more studies regarding the use of frequent low stake assessments in developmental math, instructor comfort level with regard to employing a particular practice, the use of technological supplementation in developmental math, and the execution of acceleration in developmental math.
Concluding Comments
Developmental math continues to be a pressing issue in higher education.
Students continue to place into developmental math at a high rate. Furthermore, many institutions are struggling with helping students succeed. This dissertation provides several best practices that developmental math instructors can employ to enhance student learning. Do the findings from this study imply that if every developmental math instructor employed every one of these practices for every class that every developmental math student will succeed? The answer is no. The truth is that there are no universal answers to the challenges of developmental math. Some practices could be successfully used by most instructors and could work for most developmental math students. Other practices are suitable for only a certain group of instructors and a particular group of students. Some students may not respond to any practice. We must identify the practice or practices that will work for the group of students that we are trying to help at a given time. There is a good chance that some of those practices will change from year to year and from class to class.
It is also imperative that we continue to understand how to employ best practices and not to simply implement them. For example, there is a good possibility that developmental math instructors across the country have employed practices such as
209 frequent low stake assessments and collaborative learning and have not found success.
Therefore, our continued focus in developmental math should not simply be to identify best practices but to explore how to implement them and why they are successful or unsuccessful.
In summary, it is incumbent on all developmental math instructors to do our very best and to go the extra mile to help our students succeed. Together, we can make developmental math more of an entryway to higher education and furthermore help more students realize their college dreams.
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235 APPENDIX A
INVITATION TO INTERVIEW
Dear Colleague,
Thank you for responding to my previous questionnaire. Again, I am completing my doctorate in Educational Leadership at the University of Dayton, and I want to describe strategies and practices that developmental mathematics faculty are using in their classes that are working! This is your chance to share all the great stuff you are doing to improve student learning! My goal is to add to the knowledge base of developmental mathematics and provide best practice options for other developmental mathematics faculty and leaders. Therefore, I am inviting you to participate in an interview so that I can bring some of those great practices to light. This study has received the approval of Sinclair Community College’s and the University of Dayton’s
Institutional Review Board.
The interview process will consist of two parts. First, you will be emailed five written pre-interview questions. These questions will be part of our forthcoming face-to- face interview. The purpose of this activity is to simply get you thinking. In the same communication, I will also attach a brief faculty demographics questionnaire. Then, we will have a face-to-face interview, which will be scheduled at your convenience. The
236 face-to-face interview will consist of seven general questions with some follow-up questions. It will take anywhere from about 40 to 60 minutes. Please also note that as a full-time faculty member, I do not consider my position in any way superior to anyone else in the math area. In other words, I am not an administrator looking to collect data. I am a DEV math instructor looking to highlight best practices from my colleagues.
After all of the interviews, I will analyze all the information and present it in my dissertation. To add depth to my findings, I will use some exact quotes from our interviews. Please be aware that my dissertation will be available to the public.
Therefore, I will protect your confidentiality by assigning you a pseudonym during the interview. I will also keep all information that may reveal your identity locked safely in a drawer in my office or home at all times. I would also like to touch base with you again once I construct my findings. Basically, I will ask if you agree with my findings based on your responses during our interview. Your input will be an important part of this project, and I want you to be involved throughout the process. If you are interested in participating in an interview please reply to this communication, and we will work out the details.
Sincerely,
Brian Cafarella
237 APPENDIX B
INITIAL SELF-REPORT QUESTIONNAIRE
Dear Colleague,
As many of you know, I am completing my doctorate in Educational Leadership at the
University of Dayton. I have reached the dissertation phase of my doctorate, and the topic for my dissertation is exploring and describing best practices in developmental mathematics. Basically, I want to identify and describe strategies, methods, and techniques that developmental mathematics faculty are using in their classes that are working! In a few weeks, I will be contacting some of you for interviews, and you will be asked to share all the great stuff you are doing to improve student learning! To help me get started, I would like to collect some information from you. Please note that your responses to the below questions are confidential and will only be used to determine if you are eligible to continue in the interview process.
1) How many developmental mathematics classes have you taught since the
beginning of fall term in September of 2010? Please include the fall of 2010 and
the spring of 2012 in your answer. ____
2) Please calculate the overall average of your student success rates using each of
your classes for all academic terms starting with and including the fall of 2010
and ending with and including the spring of 2012. For the purpose of excluding
238 outlier classes, you may omit the class section with the lowest success rate from this calculation. Please check the percentage category in which your average falls.
Student Success Rates of 70% or higher____
Student Success Rates Between 60%-69%____
Student Success Rates Between 55%-59%____
Student Success Rates Between 50-54%____
Student Success Rates below 50%____
Thanks!
Brian
239 APPENDIX C
PRE-INTERVIEW QUESTIONS
Thank you so much for taking time out of your busy schedule to work with me.
Again, the purpose of this study is to identify best practices in developmental mathematics. More specifically, I wish to highlight the great work that so many of you are doing. These are a few of the questions that I would like you to answer. In fact, I will ask each question during our face-to-face interview. I just want you to start thinking about some of these issues in advance. Attached is also a demographics questionnaire. Please complete that as well before our interview.
There are no right or wrong answers. I will collect these responses from you when we meet.
1) Currently, the country is struggling with success rates in developmental
mathematics classes as so many students are simply not passing their
developmental math requirements. Based on your opinion, why are so many
students struggling in developmental mathematics courses?
2) Best practices are methods, techniques, or strategies that have consistently
shown positive results such as increased student success rates and student
retention. Please describe a best practice that you have utilized in a
developmental math class that has increased student learning.
240 3) How can you be sure that this practice increased student learning?
4) Please describe any other best practices or strategies that you have utilized in a
developmental math class that has increased student learning.
5) Please describe a content-specific best practice that you have utilized that
increased student learning. More specifically, this is a practice that you use or
have used to help students with developmental math content. For example, this
practice could help students with fractions, decimals, or linear equations.
241 APPENDIX D
FACULTY DEMOGRAPHICS FORM
Please answer the following and submit to me at the time of our interview. Write N/A if the question does not apply to you.
Date: ___/___/12
Name/pseudonym______Age____
Campus Phone Number______Preferred Email
Address______
Sex______Race______
Title at Sinclair Community College:______
How many years have you been teaching overall? This includes Sinclair and any other teaching positions. ______
Specifically, how many years have you been teaching math at Sinclair? ______
Please list all of the degrees that you hold (i.e. bachelor’s, master’s, doctorate) and your major/minor for each degree.
______
______
______
______
______
242 APPENDIX E
FACE-TO-FACE INTERVIEW QUESTIONS
1) Question: Currently, the country is struggling with success rates in
developmental mathematics classes as so many students are simply not
passing their developmental math requirements. Based on your opinion, why
are so many students struggling in developmental mathematics courses?
Follow-up: Please give me an example of a student who did not pass your
developmental math class.
2) Question: Best practices are methods, techniques, or strategies that have
consistently shown positive results such as increased student success rates and
student retention. Please describe a best practice that you have utilized in a
developmental math class that has increased student learning.
Follow-up: How can you be sure that this practice increased student learning?
Follow-up: How did you come to discover this best practice or strategy?
Follow-up: Do you feel that most developmental mathematics instructors
could successfully implement this practice or strategy?
Follow-up: Could this practice or strategy work for most developmental
mathematics students?
Follow-up: Are there certain students for which this practice or strategy
would be better suited?
243 Follow-up: Are their certain developmental mathematics students who would
not benefit from this practice or strategy?
Follow-up (if needed): Let’s say you were mentoring another faculty member
who was about to employ this practice. How would an instructor go about
using this practice to enhance student learning?
3) Question: Please describe any other best practices or strategies that you have
utilized in a developmental math class that has increased student learning.
Follow-up: How do you know that these practices increased student learning?
Follow-up: How did you come to discover these best practices or strategies?
Follow-up: Do you feel that most developmental mathematics instructors
could successfully implement these practices or strategies?
Follow-up: Could these practices or strategies work for most developmental
mathematics students?
Follow-up: Are there certain students in which these practices or strategies
would be better suited?
Follow-up: Are their certain developmental mathematics students who would
not benefit from these practices or strategies?
Follow-up: Please describe a content-specific best practice that you have
utilized that increased student learning. More specifically, this is a practice
that you use or have used to help students with developmental math content.
For example, this practice could help students with fractions, decimals, or
linear equations.
244 Follow-up (if needed): Let’s say you were mentoring another faculty member
who was about to employ this practice. How would an instructor go about
using this practice to enhance student learning?
4) Question: Please describe any strategies or practices that you have attempted
in your developmental math classes that did not work out that well.
Follow-up: What were the indicators that this strategy was not working out
well?
5) Question: Many schools, including Sinclair, are attempting to help students
complete their developmental math requirements by offering accelerated and
compressed course (if needed, I will provide the definitions of the two
aforementioned terms). As an educator, how do you feel about that?
6) Question: In your opinion, and based on your experience, please describe
how Sinclair and community colleges in general could do a better job of
increasing student success in developmental mathematics?
7) Question: Is there anything else that you would like to add about best
practices in developmental mathematics?
245 APPENDIX F
INVITATION FOR MEMBER CHECKING
Dear (actual name was inserted),
Thank you so much for taking the time out of your schedule to participate in the interview process. Thanks to your enlightening responses, I have constructed some tentative findings for my study. Again, the conclusions from this dissertation will add to the conversation on best practices in developmental mathematics, and you are a major part of that! Therefore, I would like to share my findings with you. After all, accuracy is important. My findings are attached to this communication. Please email me with your feedback as to whether or not you believe that my findings are grounded in your responses. I would ask that you reply by July 31, 2012. If I do not hear from you, I will assume that you are satisfied with my findings and do not have any feedback.
Thanks!
Brian
246