Exploring Best Practices in Developmental Mathematics
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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 ii 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. iv 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. v 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. vi 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 vii 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 viii 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 ix 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 x Mandatory advisement…………………………...………………..189 A certain degree of uniformity…………………………………….190 Acceleration: a best