Running Head: COLLEGE ALGEBRA

College Algebra

Running head: COLLEGE ALGEBRA

College Algebra as a Transition Course: What Teachers and Students Should Know?

Linda Reichwein Zientek Department of Mathematics Blinn College

G. Donald Allen Department of Mathematics Texas A&M University College Station, TX 77843

Mel Griffin Department of Mathematics Texas A&M University College Station, TX 77843

Gloria White Charles A. Dana Center for Mathematics and Science Education

Paula Wilhite Department of Mathematics Northeast Texas Community College

Inquiries concerning this paper can be addressed to Linda Zientek, Blinn College, 902 College Avenue, Brenham, Texas 77833, [email protected], 979-830-4437 College Algebra 1

Abstract The success of our nation depends on the academic excellence of our students. With the increase in enrollment in dual-credit and developmental mathematics courses, the line between collegiate and secondary education is less apparent, and the two can no longer operate as separate entities. For the sake of the next generation, we must begin to understand disconnects and help provide a smoother transition for our students. Results from the present study suggest that (1) community college and university mathematics departments parallel each other on instructional modality, use of technology, and assessment methods with slight variations between institutions; (2) neither community colleges nor universities have moved far from the traditional classroom; and (3) the transition from community college to university is rather seamless in regards to teaching environment, but high school students emerging from non-traditional classrooms are faced with adjusting to the traditional class settings in higher education.

Submitted for publication. College Algebra 2

The success of our nation depends on the academic excellence of our students. With a national push to Close the Education Gaps between socio-economic groups, the reality that a large percentage of students are not academically ready to enter college mathematics classes has been brought to the forefront. On average, approximately 42% or more of community college students are initially enrolling in developmental mathematics courses (National Center for Educational Statistics, 2000). In Texas, where the present study was situated, 51% of community college students and 28% of university students entered developmental mathematics courses with some institutional rates as high as 80% (Texas Higher Education Coordinating Board, 1999a). Curriculum Movements The past decade has been replete with reform movements to improve teaching and learning in mathematics. In 1997, the Texas Higher Education Coordinating Board (THECB) adopted the exemplary objectives for the required core curriculum hours in mathematics. Written as a mandate to Texas institutions of higher education, the mathematics objective of the core curriculum was to create a quantitative literate graduate (THECB, 1999b). In 2000, the National Council of Teachers of Mathematics (NCTM) unveiled the Principles and Standards - an extension of NCTM’s original Standards - that helped bring about colossal changes in the classroom. These standards, accompanied with the advances and affordability of technology, aided in changing the delivery of instruction and methods of learning. The Committee on the Undergraduate Program in Mathematics (CUPM) of the Mathematics Association of America (MAA) sought to reconsider a mathematics curriculum developed in the 1950s that contained traditional topics and methodology of mathematics focusing on preparing students to enroll in calculus. The CUPM’s goal was to develop a curriculum encompassing relevant real-world applications that would build quantitative literacy and enhance the use of technology such as graphing calculators, spreadsheets, and computer algebra systems. The student population of the 50s differed markedly in background, maturity, and outlook from today’s student population. Therefore, the curriculum of the 50s was insufficient to help students of the 21st century reach their goals. In the 50s, only a mere 12% of students attempted college and most students attended as full-time students. Today, more than 66% of high school completers are attending college and many of these students attend as part-time students (United States Census Bureau, 2006). In addition, students are bringing with them a diverse array of mathematical abilities ranging from having mastered only basic mathematical skills to completing Advanced Placement mathematics courses (Mathematical Association of America’s Committee on Undergraduate Programs, 2004). College Ready Despite the efforts to improve mathematics teaching and learning, a large percentage of students are not college ready. In a report by Hart and Associates (2005), college mathematics instructors estimated that approximately half of their students were not ready for college-level work, and only 28% of college instructors believed that public high schools adequately prepared graduates to meet college expectations. Students participating in the Hart and Associates survey indicated had they known what they know now, they would have applied themselves more in high school (65% and 77%; college and workforce students, respectively). Hart and Associates found that students who had College Algebra 3 been challenged and who had faced high expectations were more likely to feel prepared in college. In order for high school graduates to be college ready, effective communication between students, parents, and higher education needs to begin before students enter high school and continue throughout the high school years. According to a report by the American Diploma Project (ADP; 2004), the majority of 8th graders (90%) and their parents (67%) considered college a necessity. Yet, academic inconsistencies within our system – among high schools, colleges, and universities - make college readiness difficult to determine and hinders our students’ ability to attain college readiness. Mathematics standards set by states rarely reflect real-world demands and standardized exams often reflect 8th and 9th grade skills rather than skills needed at the time students graduate (ADP, 2004; Callan, Finney, Kirst, Usdan & Venezia, 2006). In addition, very few states specify the particular mathematics courses students need to complete nor do they have “effective mechanisms for ensuring that the course content reflects the knowledge and skills required for success in college and work” (ADP, p. 7). Determining college readiness by transcript review is difficult because inequities exist between high schools. A grade in a course or a high school diploma does not establish college readiness. The ADP report states that “high school students earn grades that cannot be compared from school to school and often are based as much on effort as on the actual mastery of academic content” (p. 2). The ADP report concluded that No state can now claim that every student who earns a high school diploma is academically prepared for postsecondary education and work. The policy tools necessary to change this do in fact exist — but they are not being used effectively (p. 7). For this reason, colleges typically do not rely solely on transcript review to determine course placement and often rely on placement examinations. The ADP concluded that the array of placement exams that varied between college campuses and sometimes within a single college system becomes even more confusing for students and educators. Beginning in fall 2008, Texas will require a fourth year of mathematics for all students pursuing the recommended or distinguished graduation plan. Mechanisms established to increase the number of required mathematics courses is a positive move towards improving student success and college readiness (Neely, 2006). However, a fourth year of mathematics will not guarantee college readiness unless both the coursework and instruction are considered high quality. Both the quality of courses and teachers play key roles in student preparedness. According to a report by Callan et al. (2006), ”The quality and level of the coursework and instruction, and their level of alignment with postsecondary expectations, are the key elements of reform” (p. 7). In an Illinois statewide study, researchers found that both the quality of the course and the teacher were essential for college readiness with a possible exponential relationship existing between teacher quality indices and college readiness of students who completed trigonometry or other advanced mathematics courses. In the Illinois study, 52% of students who completed Calculus from a low quality teacher were classified as not college ready or the least ready compared to 6% of students who completed calculus from a high quality teacher (Presley & Gong, 2005). In addition to quality coursework and College Algebra 4 instruction, Callan et al. recommended that states provide financial incentives to support K-12 and post-secondary collaborations on improving college readiness. Purpose While Texas has a common course numbering system that eases the transfer of credits between institutions, the transition from secondary to higher education has not been as seamless. The purpose of this survey is (a) to investigate in detail the current status of College Algebra (Math 1314), (b) to determine what colleges expect from students, (c) to determine what students can expect when they enroll in College Algebra, and (d) to discover possible disconnects between high schools, community colleges, and universities. Method Participants The population consisted of about 145 mathematics department chairs from community colleges and universities in Texas that offered College Algebra. Forty-six departmental chairs or designees completed the survey. Thirty-three were community colleges (72%) and 13 were universities (28%). College Algebra College algebra was selected for the following reasons: 1. College Algebra has retained the status of having the highest enrollment of any credit-bearing course over the past 30 years – 173,000 nationally in 2000 (Lutzer et al., 2002); 2. Although not guaranteed, success in subsequent courses is inherently related to success in College Algebra; 3. Algebra at all levels has been identified as the gatekeeper to higher education (Moses, 2001); and 4. College Algebra is a core requirement and a prerequisite mathematics course for advanced mathematics required of most liberal arts and science, technology, engineering, and mathematics (STEM) majors. Instrumentation In an attempt to determine consistencies between institutions of higher education, the survey was developed by five educators who have K-20 experience. The survey was distributed at a statewide departmental meeting and also by email through statewide mathematics organizations. The survey requested information on students’ future mathematical intentions, departmental grade distributions, mathematics topics, instructional modality, prerequisite scores, technology, assessments, and liaisons. The present study depended on the departmental chair or designee’s ability to read their department’s teaching style. Topics considered important for students to understand were rated on a 3-point scale: (a) most important, (b) somewhat important, or (c) marginal or no importance. Instructional delivery and teaching methods were dummy coded as “1” = “method was used” and “0” = “method was not used”. Data Analysis Reporting recommendations of the APA Task Force on Statistical Inference were followed. P-values, descriptive statistics, and effect sizes were reported (Wilkinson & APA TFSI, 1999). Effect sizes aid in meta-analyses and in interpreting results (Thompson, 2000; 2006). While Cohen arbitrarily assigned effect size benchmarks, they College Algebra 5 should not be interpreted with the same rigidity as  is often chosen in statistical significance testing (Thompson, 2001). For the present study, effect sizes greater than .05 were considered noteworthy. Analyses Comparing higher education with K-12 research will help in identifying possible inconsistencies between high school, community colleges, and universities. Research on teaching and learning at the collegiate level has been relatively sparse. By investigating College Algebra, the present study sought to identify possible disconnects and similarities between community colleges, universities, and K-12 education by answering the following questions: 1. What are the future mathematical intentions of College Algebra students? 2. What are the departmental grade distributions of College Algebra? 3. What topics and prerequisites do mathematics departments believe are important for incoming College Algebra students? 4. What should College Algebra students expect in the classroom (i.e., instructional modality, technology, and assessment)? 5. Are liaisons being formed between K-12 and higher education? 1. Future Mathematical Intentions Departmental chairs identified the percent of students who were enrolling in College Algebra (a) as a terminal course, (b) as a prerequisite for other mathematics courses, (c) with plans to enroll in a calculus course, and (d) with plans to enroll in a statistics course. Figure 1 illustrates future mathematical intentions of College Algebra students. Analysis of variance (ANOVA) results indicated noteworthy differences between community college students and university students in enrollment in College Algebra as a terminal course (F(1, 38) = 4.49, p = .04, η2 = .11; M = 65.76, SD = 24.71; M = 46.25, SD = 29.33; community colleges and universities, respectively) and in enrollment in a subsequent statistics course (Welch-statistic(1, 11.70) = 3.94, p = .07, η2 = .18; M = 6.51, SD = 15.69; M = 22.95, SD = 24.44; community colleges and universities, respectively). The Welch statistic was provided because the homogeneity of variance assumption was not met. Community college students were more likely than university students to take College Algebra as a terminal course and less likely to enroll in statistics, at least at the community college institution. College Algebra 6

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ANOVA results, with effect sizes close to zero, did not indicate noteworthy differences between community college and university on their students’ enrollment in College Algebra as a prerequisite for higher level mathematics courses (F(1, 39) = .591, p = .48, η2 = .02; M = 31.94, SD = 24.76; M = 38.75, SD = 28.35; community colleges and universities, respectively, η2 = .02) or on the percent of College Algebra students that later enrolled in calculus (F(1, 38) = 1.23, p = .27, η2 = .03; M = 9.31, SD = 7.60; M = 12.88, SD = 12.56; community colleges and universities, respectively, η2 = .03). These results indicated only a small percentage of College Algebra students intended to enter STEM fields. 2. Grade Distributions Student retention rates were defined as the percent of students who did not withdraw from the course. Completer success rates were defined as the percent of students, excluding withdrawals, who received a passing grade (i.e., A, B, or C). In the present sample, student retention rates were 72% with a 70% completer success rate. The homogeneity of variance assumption was met and effect sizes from analysis of variance (ANOVA) results indicated noteworthy differences between community colleges and universities on the distribution of C’s (F(1, 34) = 3.44, p = .07, η2 = .09; M = 27.88, SD = 7.48; M = 23.53, SD = 2.89; community colleges and universities, respectively), somewhat noteworthy differences on the distribution of A’s (η2 = .05), and no noteworthy differences on the distribution of B’s (η2 =.03), D’s (η2 <.01) or F’s (η2 <.01). Standard deviations suggested that universities were more dispersed on the percentage of students earning A’s (SD = .11) and community colleges were more dispersed on the percentage of students earning F’s (SD = .12). The dispersion of A’s at universities ranged from 8% to 40% and the dispersion of F’s at community colleges ranged from 6% to 53%. Variations in grade distributions illustrated in Figure 2 shows that universities were more disperse than community colleges on the percent distribution of A’s. While the dispersion of F’s for community colleges was sizeable, the range and standard deviations appeared to be influenced by outliers. As illustrated in Figure 2, removing the outliers gives a more accurate depiction of community college F rates and suggests rates comparable to universities.

Despite the existence of outliers in community college grades, no outliers existed when computing pass or failure (i.e., D’s or F’s) rates and no statistically significant differences existed between passing rates of universities (M = .68, SD = .13; Range = 53% to 88%) and community colleges (M = .70, SD = .12; Range = 44% to 85%). The one outlier community college that had 53% of their College Algebra students fail had College Algebra 7 only 2% of their students obtaining a D. Therefore, the percentage of students collectively not passing did not constitute a far reaching percent from the remaining community colleges in the present sample. 3. Succeeding in College Algebra Important Topics. Departmental chairs rated eight mathematics topics on their importance for incoming College Algebra students to know in order to be successful in College Algebra. Topics were rated on a three-point scale: (1) most important, (2) somewhat important, or (3) marginal or no importance. Cross-tab results indicated no statistically significant differences between universities and community colleges on what topics were deemed important. As presented in Table 1, 100% of mathematics departmental chairs identified algebraic manipulation as being most important. Fractions were considered the second most vital topic for students to know with just over 80% believing this was most important and the remaining indicating fractions were at least somewhat important. Identified as the least important topics for incoming students were (a) regression modeling, (b) trigonometry, and (c) group work. Cross-tab results indicated no statistically significant differences by topics considered important and the percentage of students who passed/failed, withdrew, or obtained an A, B, C, D, or F.

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Prerequisites. Departments reported prerequisite scores on five examinations: (a) ACCUPLACER, (b) ACT, (c) COMPASS, (d) SAT, and (e) the Texas Higher Education Assessment (THEA). Only eight schools reported prerequisite scores on all five placement examinations. As presented in Table 2, bivariate correlations indicated that prerequisite scores on THEA were related to prerequisite scores on ACT, COMPASS, and ACCUPLACER but not SAT. Effect sizes from ANOVA results indicated possibly noteworthy differences between community colleges and universities on ACT (F(1, 23) = 2.25, p = .147, η2 = .09) and SAT scores(F(1, 24) = 10.27, p = .004, η2 = .30) with squared effect sizes on the remaining exams less than .02. The predominant prerequisite score for THEA was 270 (M = 258.64, 17.63; M = 264.29, SD = 14.12; community colleges and universities, respectively), SAT was 500 (M = 514.00, 21.22; M = 476.25, SD = 39.26; community colleges and universities, respectively), and ACT was 19 to 21 (M = 20.75, 1.98; M = 19.67, SD = 1.11; community colleges and universities, respectively). Prerequisite scores on COMPASS ranged from 39 to 70 (M = 57.18, 14.50; M = 56.25, SD = 11.84; community colleges and universities, respectively) and prerequisite scores on ACCUPLACER ranging from 39 to 109 (M = 69.08, 16.58; M = 67.00, SD = 19.86; community colleges and universities, respectively) with a cluster of scores around 63 and 64.

INSERT TABLE 2 ABOUT HERE College Algebra 8

4. Experiences in the Classroom Instructional Modality. Department chairs identified the traditional lecture method as the predominant instructional modality for College Algebra professors. On average, community college professors lectured approximately 91% of instruction time and university professors lectured approximately 94% of instruction time. The occasional institution served as an outlier institution where lecturing occurred only about 70% of class time. Twenty percent of community college departments lectured around 80% of the time. Eight percent of university departments and 3% of community college departments integrated group work into the course with another 12% of community college departments integrating online components into their teaching. Technology. Our study focused on teaching with technology. Figure 3 illustrates instructional delivery methods by institutions in our study. For providing instruction, these institutions most often used overhead and calculator projectors. Community colleges (82%) were slightly more likely to have used overhead projectors in their classrooms than universities (58%). Only 38% of community colleges and 25% of university mathematics departments utilized computer labs for College Algebra courses. The use of calculator projectors indicated that mathematics professors were incorporating technology in their teaching (76% of community colleges and 58% of universities). Multiple regressions indicated that the percentage of passing grades did not depend on whether or not departments used calculator projectors or computer labs (F (2, 33) = .45, p = .642, R2 =.03).

Assessment Methods. The NCTM Principles (2000) emphasized the need for various forms of assessments. In the present study, departmental chairs were asked about a full gamut of assessment methods, which were dummy coded as “1” = “Used” and “0” = “Not Used”. As illustrated in Figure 4, traditional exams were the predominant assessment method (100% of universities and 97% of community colleges) with 60% using multiple-choice answers on at least one examination and/or quiz. The one community college that did not choose traditional tests marked that their exams were multiple-choice. Community colleges (52%) were more likely than universities (29%) to assess students with technology and collaborative group work. Approximately 39% of community colleges and about 1% of universities administered projects as a part of their assessment measures. A small percent used other assignments typically in the form of homework (12% and 17%; community colleges and universities, respectively) and direct observations and/or essays (3% and 8%; community colleges and universities, respectively).

INSERT FIGURE 4 ABOUT HERE College Algebra 9

Sixteen percent of the mathematics departments had common exams and 56% had common finals. Community colleges (61%) were slightly more likely to administer common finals than universities (42%). ANOVA results indicated no statistically significant differences in grade distributions between schools that did or did not administer common exams or finals with effect sizes close to zero. 6. Liaisons Forty-three percent of higher education institutions in the present sample identified liaisons between their institution and area high schools. The extent of involvement varied. Some mathematics departments indicated they met once a year or they met to discuss dual-credit enrollment. Only a few mathematics departments met to discuss curriculum items. Two mathematics departments indicated substantial interaction. One university indicated they were working on a city-wide initiative to address high school and College Algebra curriculum, and one community college visited with high school counselors and teachers, distributed brochures, and arranged on-campus activities for high school students. Discussion The future of our society depends upon the academic success of our students. In essence, we begin preparing students for college the minute they walk into our schools; yet, many high school graduates are unprepared to embark on the journey into higher education. Educators must begin to investigate why the journey has been so difficult and how best to prepare students to proceed. Without sacrificing academic rigor, barriers should be removed that preclude students from excelling, and students should be equipped with the skills necessary to achieve their goals. The present study sought to provide information about the aspirations and goals of College Algebra students, plausible disconnects between high school and higher education, and a glimpse of what was occurring in College Algebra classrooms. College Algebra Students The typical College Algebra student did not enter STEM-based fields nor did they subsequently enroll in statistics or calculus. Figure 1 illustrates the future mathematical intentions of College Algebra students. In the present study, College Algebra was the terminal course for the majority of community college students and for a high percentage of university students. Community college results would naturally be influenced (1) by transfer students who enrolled in mathematics courses at the university and (2) by students who completed technical or vocational degrees. Therefore, in isolation, the community college results may not be an accurate depiction of students’ final mathematical intentions. However, these results coupled with the university results indicated that College Algebra was a terminating course for many students. The College Algebra curriculum was traditionally designed to prepare students enrolling in Calculus. Results from the present study, which were supported by findings from the CBMS study, suggested that College Algebra’s primary purpose has changed and that only a small percentage of College Algebra students are subsequently enrolling in Calculus (Lutzer et al., 2002). Important Topics University and community colleges were consistent in their beliefs about what topics were considered important for incoming College Algebra students to know, but these topics were more aligned with the traditional curriculum than the NCTM standards- College Algebra 10 based curriculum. These results identified a possible disconnect between the curriculum of secondary and higher education. As presented in Table 1, mathematics departments believed students who entered College Algebra should be proficient with algebraic manipulation, fractions, and problem solving. Knowledge of trigonometric functions, regression for modeling, group work, and graphing calculators were considered the least important skills for incoming students. These results suggest that the NCTM constructivist curriculums’ primary focus on problem solving with a de-emphasis on algebraic manipulation may be leaving the very children they hope to help without the skills they need to succeed. Arranging problems where solutions require both problem solving skills and algebraic manipulation in balance may well serve students better when then enter the collegiate environment and may help promote future success. What Students Should Expect The incoming College Algebra student should expect to spend the majority of class time in a traditional lecture taking notes from an overhead project or laptop computer. They should also expect that assessments will be traditional examinations and quizzes that are contingent on algebraic manipulation and problem solving. However, professors will often use graphing calculators to help teach concepts. A very small percentage of students will be afforded time to work in groups, on projects, or in computer labs. Compared to university students, community college students will be more likely to be assessed on projects – some of which contain technology and collaborative efforts. Grade Distributions. With the exception of a few outliers, grade distributions of community colleges were fairly consistent. Universities varied on the percent of A’s earned by students in College Algebra. The distribution of A’s at community colleges ranged from 7% to 25% compared to 6% to 40% at universities. Community colleges and universities were aligned on pass rates with the trade-off being an increased distribution of C’s at the community colleges. The higher distribution of A’s at some universities may be related to stringent admission requirements that created a classroom whose students were more homogenous with regard to academic backgrounds than community colleges or universities with open door policies and more diverse levels of learners. Instructional Modality and Delivery Methods. University and community college teachers were consistent in their delivery of instruction. These results, which were gathered six years after the 2000 CBMS survey, corroborated earlier findings by CBMS that the “predominant instructional modality continued to be the standard lecture method” (Lutzer et al., 2002, p. 126). All university departments indicated their professors lectured over 90% of the time and at least 50% or more lectured 100% of the time. While community college professors lectured slightly less on average (91% of the time) than university professors (94% of the time), lecturing was still the predominant teaching modality. In the present sample, there was the occasional community college mathematics department who spent 20% to 30% of class time not lecturing, but these were the exception and not the norm. A small percentage of university (8%) and community college (3%) departments integrated group work into their teaching, and a small percent (12%) of community college mathematics departments also taught College Algebra online. While some of these were hybrid with the traditional courses, the percent of online courses was slightly higher than the 2000 CBMS results of 7% (Lutzer et al.). College Algebra 11

Technology in Teaching The large percent of professors teaching by means of overhead projectors and laptops supported the traditional classroom lecture. However, as illustrated in Figure 3, the use of calculator projectors indicated graphing calculators were being utilized in classroom teaching. In the present sample, 58% of university departments and 76% of community college departments taught with a calculator projector, which was comparable to the 2000 CBMS national sample of CC teachers (74%) (Lutzer et al., 2002). These results indicated that the majority of students, particularly in the community college setting, received part of their learning employing multiple representations by learning concepts graphically, numerically, verbally, and symbolically. Assessments Major Exams and Quizzes. In the present sample, the majority of teachers in higher education assessed their students in the traditional method of major exams and quizzes. As illustrated in Figure 4, approximately half of the departments also used multiple-choice responses on at least one exam. Approximately 8% of university mathematics departments identified that direct observations were used to assess students. The one community college not identifying with traditional exams and quizzes indicated their exams were multiple-choice. Slightly more community colleges administered common finals than universities, but the majority of institutions did not administer common exams. These results suggested that professors in higher education have some autonomy and control over their classrooms. Research has identified that high school mathematics and science teachers who left teaching were often dissatisfied with the lack of autonomy and control they experienced in their classroom (National Science Board, 2006). These results then imply that retention of mathematics and science professors in higher education may be higher than teachers in secondary schools. The use of common finals by approximately half of the institutions suggested institutions had some form of curriculum accountability. Projects and Collaborative Work. The modest effort by professors to assess with group work (25% and 52%; universities and community colleges, respectively) along with community college instructors assessments with technology & collaborative projects (39%) suggested that instructors in higher education were aligned with secondary educators and the recommendations by the American Mathematical Association of Two- Year Colleges (AMATYC) Crossroads in Mathematics (2006). While these numbers indicated a modest attempt by some universities to move beyond traditional methods, they also indicated that the majority of universities are continuing to rely primarily on traditional assessments. The AMATYC Crossroads in Mathematics recommends that mathematics faculty “provide learning activities, including projects and apprenticeships that promote independent thinking” (p. 4). The use of (1) technology and collaborative group work and (2) projects for assessing students suggested instructors, especially community college instructors, were moving beyond the limitation of traditional exams and understanding the benefits of collaborative reasoning to solve a problem. Working in groups has been advocated by MAA as a method (1) to improve problem solving skills beyond skill acquisition, (2) a way to build classroom camaraderie, and (3) a method to introduce multiple problem solving methods (Kasube & McCallum, 2005). The lack of extensive use of group work and projects by university departments College Algebra 12 may possibly be a reflection of the structure of higher education rather than differences in philosophy. University professors often have classrooms in excess of a 100 students compared to community college classrooms of less than 30 (Lutzer et al., 2002). Even two large university classes would exceed the number of students taught in five community college classes. Large class sizes accompanied with obligations to research and publish limits the time university professors can devote to preparing and grading student projects. Grading over a hundred projects per class would entail unfeasible time constraints. This thought is reflected by the strikingly small percent of university departments that indicated students were assessed with (a) projects (1%) and (b) technology and collaborative work group-projects (25%) compared to community college professors (39% and 52%; projects and technology and collaborative group-projects, respectively). Despite these differences, the small percent of university professors utilizing group work in their teaching suggested that some university faculty acknowledged the value added when students discuss and solve problems collaboratively. Prerequisites Community colleges and universities were using placement examinations. Therefore, students entering College Algebra should expect some form of placement criteria beyond high school grades or terminal high school mathematics course. The use of some form of placement exams by all institutions in the present study suggested that departments did not believe high school courses or grades were sufficient indicators of college readiness. Our results were consistent with the 2000 CMBS study, which found that “Virtually all two-year colleges with mathematics programs had diagnostic or placement testing” (Lutzer et al., 2002, p. 126). Placement criteria such as the Texas’ 10% rule along with standardized exams completed while in high school further complicates accurate placement of students in mathematics courses. The top 10 percent rule guarantees that Texas students who are in the top 10 percent of their class have automatic admission to any public Texas university (THECB, 2006a). Neither standardized exams nor the 10 percent rule encourages student enrollment in advanced mathematics courses. In Texas, educators are emphasizing to students and parents the need for more advanced mathematics for college-bound students. In Texas, House Bill 1 “requires four years of mathematics and science in the recommended and distinguished high school programs, beginning with students entering Grade 9 in school year 2007-2008” (Neeley, 2006, p. 1). The importance of completing a mathematics course their senior year is not a new concept. According to Bidwell and Clason (1970/2002), the 1899 Report of Committee on College-Entrance Requirements stated When a student who is preparing for college does not intend to offer advanced algebra, he should defer some or all of the mathematics at the eleventh grade until the last year of his school course, or be given opportunity for mathematical reviews in that year. (p. 194) Requiring four-years of mathematics is a move forward in preparing students to be college ready. Unfortunately, guaranteeing a fourth course does not guarantee college readiness. The quality of the course and teacher play an essential role in student preparedness (Presley & Gong, 2005). First generation college students – who often enter community colleges - rely upon the advice of counselors to determine what courses best College Algebra 13 prepare them for college. Requiring more mathematics reinforces the message that more rigorous mathematics correlates with college readiness. Because of inconsistencies among courses, prerequisite requirements consisting of placement examinations will probably continue to prevail in higher education. Community colleges and universities were consistent on their prerequisite placement examination scores on three of the five reported exams. Community colleges tended to set more stringent requirements on SAT scores. While a cluster of institutions set College Algebra SAT prerequisite scores at 500, one university set the score as low as 400 and 3 of the 18 community colleges using SAT scores set them as high as 550. In the present sample, 44% of community colleges set SAT prerequisite scores higher than 500 compared to 0% of universities. Universities tended to set more stringent THEA scores but a smaller percent tended to use them as a prerequisite requirement. The minimum passing score of 230 was set by the THECB (2006b) with a recommended score of 270 for College Algebra. In the present study, THEA scores ranged from 230 to 270 with the majority of schools (72%) setting 270 as their College Algebra benchmark and 6% setting their benchmark at 250. Only one university set the THEA score below 270 compared to 39% of community colleges with 32% (n = 9) of these schools setting the score as low as 230. The one university who set the THEA score at 230 was the same university who set the SAT score at 400. Table 2 shows the relationship between departmental benchmark scores. According to the standards established by ACT, Inc. (2006), some universities who set College Algebra prerequisite scores below 19 and the majority of community colleges who set ACT scores at 19 were setting benchmarks for students to enter with minimal proficiency in solving equations, graphing, and number concepts. ACT scores ranging from 20 – 23 appear to correspond better with the topics identified as important by the present sample by departmental chairs than the common value of 19 often used by institutions as an indicator for skills sufficient for College Algebra. Liaisons The fact that approximately half of schools in higher education had liaisons with local high schools suggests that institutions in higher education are realizing the value added of increased communication, but the degree of this involvement varied. Some school liaisons were limited to administrators, whereas others involved dual-credit courses. One university indicated a city-wide committee had been established to discuss curricula items, and one community college indicated they had formulated on-campus activities for high school students. The latter two examples seemed to be the exception. While communication between secondary and higher education appeared to exist, the present results indicated communication appeared to be inconsequential on areas of curriculum and relating more to dual credit or administrative concerns outside of the department. Conclusion In order to smooth the transition into the collegiate environment, we must begin to compare teaching modality and curriculum among institutions of higher education. While the present study was limited to community colleges and universities and was dependent upon departmental chairs understanding of their professors, these results gave us a glimpse into what was transpiring in College Algebra classrooms. Results from the present study suggested that (1) community college and university mathematics College Algebra 14 departments paralleled each other on instructional modality, use of technology, and assessment methods with slight variations between institutions, and that (2) neither community colleges nor universities have moved far from the traditional classroom. These results indicated that instructional modality was remarkably similar across institutions of higher education with the traditional methods prevailing. Unfortunately, the students who struggle in mathematics will probably be the students who will have more difficulty transitioning from a constructivist curriculum to the traditional classroom settings in the collegiate environment. The present study found the following consistencies: 1. College Algebra students were typically not entering STEM fields; 2. University and community colleges were consistent in their beliefs about what topics students should know with algebraic manipulation and fractions topping their list; 3. University and community college teachers predominant instructional method was traditional lecture, but graphing calculators were incorporated in teaching in learning with variations between institutions; 4. Professors in higher education typically assessed students in traditional methods of exams and quizzes; and 5. High school courses and grades were not enough to predict students’ college readiness. The consistency of traditional lectures across institutions suggests that underlying factors besides teaching modality impact student performance in College Algebra. Future studies should investigate direct linkages between teacher grade distributions and teacher attitudes in the collegiate environment. Despite the limitations of studying across departments, the results of the present study gave us an insight into what was occurring in the College Algebra classroom and showed consistencies and inconsistencies across institutions of higher education. While conceptually based state assessments and accountability measures helped facilitate reformations in K-12 classrooms, the transition away from traditional methods has been much slower in higher education. While some will contend that K-12 educators moved too quickly and maybe went too far in the reform movement, others will contend students’ failures are due to disconnects between K-12 and higher education in teaching methods, assessments, and expectations. We must continue to empirically investigate what is occurring in college classrooms and the expectations of higher education. With the increase in enrollment in dual-credit and developmental mathematics courses, the line between collegiate and secondary education is less apparent, and the two can no longer operate as separate entities. For the sake of the next generation and in an effort to fulfill the vision set forth by NCTM, AMATYC, and MAA where all students excel to their highest potential, we must improve communication between institutions and obtain a better sense of disconnects occurring across the P-16 spectrum. College Algebra 15

References ACT, Inc. (2006). College readiness standards. Retrieved October 24, 2006 from http://www.act.org/standard/planact/math/index.html American Diploma Project [ADP]. (2004). Ready or not: Creating a high school diploma that counts. Washington, DC: Achieve, Inc. Retrieved November 11, 2006, from www.achieve.org/files/ADPreport_7.pdf American Mathematical Association of Two-Year Colleges (AMATYC). 2006. Crossroads in Mathematics Executive Summary. Author. Retrieved October 12, 2006 from http://www.amatyc.org/Old/Crossroads/CrsrdsXS.pdf Bidwell, J. K., & Clason, R. G. (Eds.). (1970/2002). Readings in the history of mathematics education. Reston, VA: National Council of Teachers of Mathematics. Callan, P., Finney, J., Kirst, M., Usdan, M., & Venezia, A. (2006). Claiming common ground: State policymaking for improving college readiness and success. Washington, DC: National Center for Public Policy and Higher Education. Retrieved November 11, 2006, from http://www.highereducation.org/reports/common_ground/index.shtml Frick, R. W. (1996). The appropriate use of null hypothesis testing. Psychological Methods, 1, p. 379-390. Hart Research Associates / Public Opinion Strategies. (2005, February). Rising to the challenge: Are high school graduates prepared for college and work? A study of recent high school graduates, college instructors, and employers (Conducted for Achieve, Inc.). Washington, DC: Author. Retrieved November 11, 2006 from www.achieve.org/files/pollreport.pdf Kasube, H., & McCallum, W. (2005). Mathematics: Crafty curriculum mathematics project. In Curriculum foundations project: Voices of the partner disciplines (pp. 109-113). Retrieved December 2, 2006 from http://www.maa.org/cupm/crafty/Chapt12.pdf Lutzer, D. J., Maxwell, J. W., & Rodi, S. B. (2002). Statistical abstract of undergraduate programs in the mathematical sciences in the United States. Providence, RI: American Mathematical Society. Retrieved October 13, 2006 from http://www.ams.org/ams/copyright.html Mathematical Association of America’s Committee on Undergraduate Programs (CUPM). (2004). Undergraduate programs and courses in the mathematical sciences: CUPM curriculum guide 2004. Retrieved December 2, 2006 from http://www.maa.org/cupm/curr_guide.html Moses, R. P. (2001). Algebra and activism: Removing the shackles of low expectations – A conversation with Robert P. Moses. Educational Leadership, 59(2), 6-11. National Center for Education Statistics. (2000). Remedial education at degree-granting postsecondary institutions in fall 2000. Retrieved June 15, 2006 from http://nces.ed.gov/pubs2004/2004010.pdf National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author. National Science Board. (2006). Science and engineering indicators 2006. Retrieved May 16, 2006 from http://www.nsf.gov/statistics/seind06/ca/cas3.htm College Algebra 16

Neely, S. J. (2006, September). Proposed Amendments to 19 TAC Chapter 74, Curriculum Requirements, Subchapter A, Required Curriculum, and Subchapter F, Graduation Requirements, Beginning with School Year 2007-2008 (First Reading and Filing Authorization). Retrieved October 23, 2006 from http://www.tea.state.tx.us/sboe/schedule/0906/whole/item/7_rule_ch74_ltrprop_i. html Presley, J.B., & Gong, Y. (2005). The demographics and academics of college readiness in Illinois. (IERC 2005-3). Edwardsville, IL: Illinois Education Research Council. Retrieved October 14, 2006 from http://ierc.siue.edu/documents/College %20Readiness%20-%202005-3.pdf Texas Higher Education Coordinating Board [THECB] (1999a). The effectiveness of developmental education at Texas public higher education institutions. Retrieved June 15, 2006, from http://www.thecb.state.tx.us/reports/pdf/0177.pdf Texas Higher Education Coordinating Board [THECB] (1999b). Core curriculum: Assumptions and defining characteristics (Rev. 1999). Retrieved December 3, 2006, from http://www.thecb.state.tx.us/AAR/UndergraduateEd/fos_assumpdef.cfm Texas Higher Education Coordinating Board [THECB] (2006a). CollegeForTexas.Com: Top 10 percent rule for admissions. Retrieved November 28, 2006, from http://www.collegefortexans.com/additional/top10rule.cfm Texas Higher Education Coordinating Board [THECB] (2006b). Developmental education – Frequently asked questions. Retrieved June 15, 2006, from http://www.thecb.state.tx.us/OS/SuccessInitiatives/DevEd/faq.cfm#Q17 Thompson, B. (2000). A suggested revision to the forthcoming 5th edition of the APA Publication Manual. Retrieved June 25, 2005 from http://www.coe.tamu.edu/~bthompson/apaeffec.htm Thompson, B. (2001). Significance, effect sizes, stepwise methods, and other issues: Strong arguments move the field. The Journal of Experimental Education, 70(1), 80-93. Thompson, B. (2006). Foundations of behavioral statistics: An insight-based approach. New York: Guilford. United States Census Bureau. (2006). The 2007 statistical abstract: The national data book. Retrieved December 22, 2006 from http://www.census.gov/compendia/statab/ Wilkinson, L., & APA Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594-604. College Algebra 17

Variations by Schools on Future Mathematics Intentions of M1314 Students

Take M1314 as a 100 Terminal Math Course Take M1314 as a Prerequisite for Other Mathematics Courses Math 1314 Students that Go on to Enroll in 80 Calculus M1314 Students that Go on to Enroll in a Statistics Course

26 60 t n e c r e P 40

26 20 12

12 12 26 26 0

University Community College School

Figure 1. Variations in Mathematical Intentions of College Algebra Students. Note. Stars and circles represent outliers. Boxed numbers are the number of institutions responding. College Algebra 18

Grade Distributions for College Algebra by School Type

60 A B C 50 D F

40 t n e

c 30 r e

P 25 11 25 20 11 25 11 25 11 11 10 25

University Community College School

Figure 2. Grade Distributions for College Algebra by School. Note. Stars and circles represent outliers. Boxed numbers are the number of institutions responding. College Algebra 19

Technology Used in Teaching College Algebra (Math 1314)

Overhead 100 Laptop Calculator Projector Data projector Computer Lab 80

60 n a e M

40 82 76

20 39 36 33 25 25 18

0 University Community College School

Figure 3. Technology Used in College Algebra Classrooms. Note. Boxed numbers are the number of institutions responding. College Algebra 20

Assessment Methods of College Algebra University and Community College Professors

100 Test & Quizzes Multiple-choice Tests or Oral Questioning

80 After Observation Short-answer Questions t n

e 60 Technology c r Collaborative- e P 100 group Projects

n 97 a

e Projects

58 61 55 52

20 42 39

0 0 University Community College School

Figure 4. Assessment Methods of College Algebra University and Community College Professors. College Algebra 21

Table 1 Topics Indicated by Departmental Chairs as Important for Incoming College Algebra Students ______Percent by University Percent by Community College ______Most Somewhat Marginal or Most Somewhat Marginal or Topics Important Important No Importance Important Important No Importance ______

Algebraic Manipulation 100 0 0 100 0 0 Problem Solving 67 25 8 84 16 0 Fractions 83 17 0 84 16 0 Logarithmic/ Exponential 18 55 27 16 68 16 Trigonometry 0 36 64 3 13 84 Regression Modeling 9 9 82 3 20 77 Graphing Calculator 18 55 27 6 47 47 Group Work 9 27 64 0 48 52 ______College Algebra 22

Table 2 Correlations Between Prerequisite Scores and Departmental Grade Distributions ______Placement Exams SAT THEA COMPASS ACCUPLACER ______ACT .373 .506* .459 .821**

SAT .470* .680** .206

THEA .846** .520*

COMPASS COMPASS .453 ______Note. * indicates statistically significant at the .05 level. Effect sizes greater than .4 are italicized and considered noteworthy.