EVOLVING STUDENT PERCEPTIONS OF MATHEMATICAL IDENTITY: A CASE STUDY OF MINDSET SHIFT by Lori Ann MacKinder Clyatt A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Education in Curriculum and Instruction with Mathematics Education Emphasis MONTANA STATE UNIVERSITY Bozeman, Montana April 2017 ©COPYRIGHT by Lori Ann MacKinder Clyatt 2017 All Rights Reserved ii DEDICATION This dissertation is dedicated to my father, Wilbert (Toby) MacKinder, who shared his passion for education, mathematics, broadening perspectives, and the outdoors with me before he died in 1980. This dissertation is also dedicated to my mother, Genevieve (Cookie) MacKinder-Hayes, who impressed upon me the importance of childhood, learning and growing, and playfulness before she died in 2006. I hope I have made them both proud. iii ACKNOWLEDGEMENTS I would like to thank my husband, Todd Clyatt, for believing in me when I did not and for his encouragement, patience, and humor throughout this entire higher education journey. I would also like to thank Dr. William Ruff, my dissertation chairperson, for his continued support, inspiration, and patience. His heartfelt reassurance, insightful feedback, and gentle guidance during this process have been instrumental. I would also like to thank my dissertation committee: Dr. Beth Burroughs, Dr. David Henderson, and Dr. Fenqjen Luo. Their unique personalities, personal strengths, and broad perspectives have been influential in the direction and completion of this dissertation, as well as in the deepening of my own identity as an educator and researcher. To Dr. Kurt Laudicina, I could not have asked for a better friend to have as a guide on this journey with me. His invaluable wisdom, feedback, humor, and encouragement made writing a dissertation enjoyable. Thank you for keeping me laughing and on track. To my wise, adventurous, and beautiful daughters: Thank you for believing in me, encouraging me to go ever deeper, and challenging my own areas of fixed mindset. It’s your turn now and I believe in you! iv TABLE OF CONTENTS 1. INTRODUCTION .......................................................................................................... 1 Student Identity and Mathematics Education ................................................................. 1 Metacognition and Student Mindset ............................................................................... 4 Statement of Problem ..................................................................................................... 8 Studies in Mindset .......................................................................................................... 9 Purpose of Research ....................................................................................................... 9 Overview of Methodology ........................................................................................... 12 Theoretical Framework ................................................................................................ 13 Role of Researcher .............................................................................................. 14 Summary of Teaching Experience ............................................................. 14 My Philosophy as a Teacher ...................................................................... 15 Instructional Practices ................................................................................ 17 Limitations .................................................................................................................... 18 Definitions of Terms .................................................................................................... 19 Summary of Chapter One ............................................................................................. 21 2. REVIEW OF THE LITERATURE .............................................................................. 22 Student Achievement in Mathematics .......................................................................... 25 Family Background ............................................................................................. 26 Learning Environment Characteristics ................................................................ 27 Student Motivation and Emotion ........................................................................ 27 Self-Efficacy ............................................................................................... 27 Moods, Emotions, and Attitudes ................................................................ 28 Mastery Experiences .................................................................................. 30 History and Definition of Mindset ............................................................................... 31 Fixed Mindset ...................................................................................................... 32 Growth Mindset ................................................................................................... 34 Mindset and Mood ............................................................................................... 35 Mindset and Math Education .............................................................................. 36 Inequality .................................................................................................... 37 Speed in Learning ....................................................................................... 38 Practice ....................................................................................................... 38 Mistake-Making ......................................................................................... 38 Mathematical Mindset ......................................................................................... 39 False Growth Mindset ......................................................................................... 40 Defining the “Aha!” Moment ....................................................................................... 40 Metacognition ............................................................................................................... 42 Student-initiated Metacognition .......................................................................... 45 v TABLE OF CONTENTS – CONTINUED Attribution Theory ........................................................................................................ 45 Attribution Theory in Action ............................................................................... 47 Chapter Summation ...................................................................................................... 48 3. THE METHODOLOGY ............................................................................................... 51 Research Design ........................................................................................................... 52 Purposeful Selection and Context ................................................................................ 53 Participant Identification ..................................................................................... 53 Human Subject Consideration ............................................................................. 56 Creating the Space for Learners ................................................................................... 57 Instructional Methods .......................................................................................... 57 Evolution of Interest in the Research Topic ................................................................. 60 Procedures .................................................................................................................... 62 Data Collection .................................................................................................... 62 Data Sources ................................................................................................................. 64 Student Writings .................................................................................................. 64 Researcher Field Notes ........................................................................................ 66 Small Focus Group Interview .............................................................................. 66 Data Analysis Procedure .............................................................................................. 69 Data Analysis ...................................................................................................... 70 Coding ........................................................................................................ 73 Trustworthiness ................................................................................................... 75 Limitation of the Study ................................................................................................. 77 4. REVIEW OF FINDINGS ............................................................................................. 79 Description of Participants ........................................................................................... 80 Participant Identification ..................................................................................... 80 Attendance ........................................................................................................... 82 Emerging Self-perceptions of Mindset ........................................................................