The Effects of Reflex Math As a Response to Intervention Strategy
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THE EFFECTS OF REFLEX MATH AS A RESPONSE TO INTERVENTION STRATEGY TO IMPROVE MATH AUTOMATICITY AMONG MALE AND FEMALE AT-RISK MIDDLE SCHOOL STUDENTS by Daphne Moore Sarrell Liberty University A Dissertation Presented in Partial Fulfillment Of the Requirements for the Degree Doctor of Education Liberty University July, 2014 THE EFFECTS OF REFLEX MATH AS A RESPONSE TO INTERVENTION STRATEGY TO IMPROVE MATH AUTOMATICITY AMONG MALE AND FEMALE AT-RISK MIDDLE SCHOOL STUDENTS BY DAPHNE MOORE SARRELL A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Education Liberty University, Lynchburg, VA July, 2014 APPROVED BY: Gina Grogan, Ed.D., Committee Chair Dr. Vivian Jones, Ph.D., Committee Member Dr. Jeremy Williams, Ed.D., Committee Member Scott B. Watson, Ph.D., Associate Dean of Advanced Programs 2 THE EFFECTS OF REFLEX MATH AS A RESPONSE TO INTERVENTION STRATEGY TO IMPROVE MATH AUTOMATICITY AMONG MALE AND FEMALE AT- RISK MIDDLE SCHOOL STUDENTS ABSTRACT The search for evidence-based math interventions that are easy to use and impact academic achievement are in demand, and the impact that these interventions can have on students who struggle with math achievement is of concern. In this study, the effects of Reflex math computerized intervention to improve the automaticity of basic math facts among male and female middle school students identified as at-risk for academic failure in mathematics was examined according to differences in mean scores and based on gender. A quasi-experimental pretest-posttest nonequivalent control group design was used for the purposes of the study. Convenience sampling among students receiving or qualifying for response to intervention services for math was used to determine the study participants. The Basic Math Operations Task (BMOT) served as the pretest and posttest against which differences in mean scores were determined with analysis of covariance used to examine the differences. Results as well as assumptions, limitations, and recommendations for the future are included. Keywords, mathematics, achievement, interventions, at-risk, fluency, accuracy, automaticity, middle school, gender, Reflex math 3 Acknowledgements First and foremost I would like to thank God for allowing me the opportunity, ability, and fortitude to undertake such as challenge and then surrounding me with much needed family, friends, and colleagues who both encouraged and counseled me. To my husband Rick, thank you for understanding when I had to read, write, revise, and so on for what seemed an eternity. Thank you for buying me thousands of colored sticky notes, a new computer, and a heating pad for my neck. Without your support and encouragement this process would have been futile. To my wonderful children Bonnie Ann, Richard, Leland, and Jenna, who also attend college, thank you for being so supportive when I needed to work on my classwork and papers. You are my inspiration and my greatest achievement in life. To my mom and dad, Barbara and Charles Moore, thank you for instilling in me a lifelong yearning to learn and for modeling the importance of education. I appreciate that you always inquired about the process and celebrated my accomplishments. Mom, thank you for keeping me on your prayer list and moving me up to the top when needed. To my committee chair, Dr. Gina Grogan, thank you for your calm and reassuring support, and guidance. To my committee members, Dr. Vivian Jones and Dr. Jeremy Williams, thank you so very much for your patience when helping me with the statistics and for your eternal encouragement. Last but not least, I want to thank my friend and colleague Julie Hale. We began this process together and will finish it together. I am ever thankful for your encouragement, support, and friendship. 4 Table of Contents Acknowledgements………………………………………………………………….……4 List of Tables………………………………………………………………………..…….9 List of Figures……………………………………………………………………………10 List of Abbreviations………………………………………………………………..…....11 CHAPTER ONE: INTRODUCTION...…..…………………………….…………………12 Background ........................................................................................................... 13 Problem Statement ................................................................................................ 17 Purpose Statement ................................................................................................. 18 Significance of the Study ...................................................................................... 19 Research Questions……………..………………………………………..………20 Hypotheses ............................................................................................................ 21 Identification of Variables .................................................................................... 22 Definitions............................................................................................................. 22 Assumptions and Limitations ............................................................................... 24 CHAPTER TWO: REVIEW OF THE LITERATURE ................................................... 26 Theoretical Framework………………………………………...……….………..26 Cognitive Learning Theory…………………………………...…….……27 Cognitive Load Theory…………………………………………….…….29 Instructional Hierarchy Theory…………………………………....……..31 Operant Conditioning and Reward Token Economy………….…………32 Related Literature………………………………………………………………..33 History of Mathematics Education in the United States..……….……….33 5 Legislation.……………………………………………….………….…..34 Response to Intervention (RtI)…………………………………………...37 Math Fact Recall………………………………………………….……...42 Educational Technology.………………………………………..……….47 Math Differences Based on Gender..………………………………….…54 Summary…………………………………………………………………………56 CHAPTER THREE: METHODOLOGY…………...........................................................59 Design ................................................................................................................... 59 Research Questions ............................................................................................... 59 Null Hypotheses……………………………...…………………………………..60 Participants ............................................................................................................ 61 Setting ................................................................................................................... 62 Instrumentation ..................................................................................................... 63 Procedures ............................................................................................................. 64 Data Analysis ........................................................................................................ 66 CHAPTER FOUR: FINDINGS …………………………………………………………68 Demographics……………………...…………………………………………….68 Testing the Hypothesis…………………………...………………………………69 Results……………………………...………………...…………………………..70 Hypothesis One…………………………………………………………..70 Hypothesis Two………………………………………………………….75 Hypothesis Three……………………………..………………………….80 Summary of the Results……….………………………..…………………..……85 6 CHAPTER FIVE: DISCUSSION…………………….………………………….………87 Overview………………………………………..……..…………………..……..87 Background of the Study…………..……………………………..……...87 Problem Statement………………….…………………………..………..89 Purpose of the Study…………………….…………………..…………...89 Summary of Results……………………………………………..…….…………90 Research Question One…………………………………………………..90 Research Question Two………………………………………………….90 Research Question Three………………………………………………...91 Discussion of the Results……………………………………….…………..……92 Research Question One…………………………………………………..92 Research Question Two………………………………………………….94 Research Question Three………………………………………………...94 Implications………………………………………………………..….………….95 Limitations………………………………………………………..……………...97 Recommendations for Future Research.……………………………………..…. 97 Conclusion……………………….………………………………….…………...98 REFERENCES………………………………………………………………………….100 APPENDIX A: PERMISSION TO CONDUCT RESEARCH………………………..121 APPENDIX B: TEACHER INTRODUCTION TO STUDY………………………..…124 APPENDIX C: PARENTAL CONSENT...….…………………………………….…..125 APPENDIX D: STUDENT ASSENT….……………………………………………....127 APPENDIX E: TEACHER TRAINING GUIDELINES FOR REFLEX MATH……..128 7 APPENDIX F: PRETEST/POSTTEST ADMINISRATION GUIDELINES……….....130 APPENDIX G: BASIC MATH FACTS PROBE SAMPLE………………………..….132 APPENDIX H: BASIC MATH FACTS PROBE FOR PRETEST………………..……133 APPENDIX I: BASIC MATH FACTS PROBE FOR POSTTEST………………..…...134 APPENDIX J: INSTITUTIONAL REVIEW BOARD APPROVAL……….…….……135 APPENDIX K: GEORGIA RTI GRAPHIC PERMISSION……………….……………136 APPENDIX L: PERMISSION TO USE BMOT…………………………………………137 8 List of Tables Table 4.1: Descriptive Statistics of BMOT Pretest Scores by Intervention Method…....63 Table 4.2: Descriptive Statistics of BMOT Posttest Scores by Intervention Method.......63 Table 4.3: Descriptive Statistics of BMOT Pretest Scores by Intervention Method Among Males…………………………………………………………………….…..…………...68 Table 4.4: Descriptive Statistics of BMOT Posttest Scores by Intervention Method Among Males………………………………………………………………………...…….……..68 Table 4.5: Descriptive Statistics of BMOT Pretest Scores by Intervention Method Among Females………………………………...……………………………………….………..72 Table 4.6: Descriptive Statistics of BMOT Posttest Scores by Intervention Method Among Females……………………………………………………………………..……………73 9 List of Figures Figure 1: Georgia Department of Education Pyramid of Intervention………………….28 Figure 2: Histogram of pretest scores by method………………………………….…....60