The Influence of Individual Differences in Math Anxiety on Learning Novel Mathematics Content by Amira Farid Abdelmoteleb Ibrahim A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Combined Program in Education and Psychology) in the University of Michigan 2018 Doctoral Committee: Professor Priti Shah, Chair Professor Thomas Carr, Michigan State University Professor Kai S. Cortina Professor Kevin F. Miller Amira F.A. Ibrahim [email protected] ORCID iD: 0000-0002-7371-8940 © Amira F.A. Ibrahim 2018 DEDICATION This dissertation is dedicated to my parents, Farid Ibrahim and Laila Elhalawani for instilling in me my desire for learning and growth. ii ACKNOWLEDGEMENTS There are many individuals, whom without their support, this work would not be possible. First, I would like to thank my chair Professor Priti Shah for all her support and the resources she made available to me to make this work possible. I would also like to thank the rest of my committee Professors Thomas Carr, Kai Cortina, and Kevin Miller for all their valuable feedback and support. I would not have been able to complete this work without the moral support of my wonderful friends in Ann Arbor that helped me keep going. Last but not least, thank you to my wonderful partner, Bryan Pinto, who has encouraged me on this journey from the start. iii TABLE OF CONTENTS DEDICATION ................................................................................................................................ ii ACKNOWLEDGEMENTS ........................................................................................................... iii LIST OF TABLES ........................................................................................................................ vii LIST OF FIGURES ....................................................................................................................... ix LIST OF APPENDICES ................................................................................................................ xi ABSTRACT .................................................................................................................................. xii CHAPTER I .................................................................................................................................... 1 Introduction ................................................................................................................................. 1 Math Anxiety: Its Known Correlates .......................................................................................... 4 Math Anxiety and Math Performance/Achievement ............................................................... 5 Neural correlates of math anxiety .......................................................................................... 11 Math Anxiety and Math Attitudes ......................................................................................... 13 Development of Math Anxiety .............................................................................................. 16 Math Anxiety: How it Works .................................................................................................... 20 Processing Efficiency Theory ................................................................................................ 20 Attentional Control Theory ................................................................................................... 26 Summary and Dissertation Aims .............................................................................................. 30 CHAPTER II ................................................................................................................................. 33 Math Anxiety, Math Skills, and Learning ................................................................................. 33 Math Learning and Basic Cognitive Processes ..................................................................... 34 The Current Studies ............................................................................................................... 39 Study 1 Methods........................................................................................................................ 40 iv Participants ............................................................................................................................ 40 Design .................................................................................................................................... 42 Materials ................................................................................................................................ 42 Procedure ............................................................................................................................... 46 Study 1 Results .......................................................................................................................... 47 Group Differences and Descriptives...................................................................................... 47 Base Number Conversion Learning ...................................................................................... 48 Learning and Memory Confidence ........................................................................................ 52 Exploratory Analyses ............................................................................................................ 55 Study 1 Discussion .................................................................................................................... 57 Study 2 Methods........................................................................................................................ 59 Participants ............................................................................................................................ 59 Design, Materials, and Procedures ........................................................................................ 60 Study 2 Results .......................................................................................................................... 62 Group Differences and Descriptives...................................................................................... 62 Base Number Conversion Learning ...................................................................................... 63 Learning and Memory Confidence ........................................................................................ 67 Study 1 and 2 Combined Analyses ........................................................................................ 69 Study 2 Discussion .................................................................................................................... 70 General Discussion .................................................................................................................... 71 Math Anxiety and Learning ................................................................................................... 72 Study Strategies and Learning Outcomes .............................................................................. 73 Confidence in Learning and Memory .................................................................................... 75 Conclusion ............................................................................................................................. 76 CHAPTER III ............................................................................................................................... 78 Math Anxiety, Math Skill, and Study Strategies Part II ........................................................... 78 Methods ..................................................................................................................................... 80 Participants ............................................................................................................................ 80 Design .................................................................................................................................... 81 Materials ................................................................................................................................ 81 Procedures ............................................................................................................................. 84 Results ....................................................................................................................................... 84 v Group Differences and Descriptives...................................................................................... 84 Overall Effects ....................................................................................................................... 86 Worked Example Versus Active Problem Solving ............................................................... 91 Worked Example Versus Faded Examples ........................................................................... 96 Active Problem Solving Versus Example Only .................................................................... 98 Worked Example Versus Example Only ............................................................................. 102 General Discussion .................................................................................................................. 104 Replication of Study 1 Findings .........................................................................................