SUPPORTING SECONDARY STUDENTS’ PERSEVERANCE FOR SOLVING CHALLENGING MATHEMATICS TASKS by Joseph DiNapoli A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Education Summer 2018 © 2018 Joseph DiNapoli All Rights Reserved SUPPORTING SECONDARY STUDENTS’ PERSEVERANCE FOR SOLVING CHALLENGING MATHEMATICS TASKS by Joseph DiNapoli Approved: ____________________________________________________________ Chrystalla Mouza, Ed.D. Interim Director of the School of Education Approved: ____________________________________________________________ Carol Vukelich, Ph.D. Dean of the College of Education and Human Development Approved: ____________________________________________________________ Douglas J. Doren, Ph.D. Interim Vice Provost for the Office of Graduate and Professional Education I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ Amanda Jansen, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ Alfinio Flores, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ James Hiebert, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ James A. Middleton, Ph.D. Member of dissertation committee ACKNOWLEDGEMENTS Realizing my dream of earning a Ph.D. in Mathematics Education would not have been possible without the support of two special groups of people: the wonderful community at the University of Delaware and my loving family. First and foremost, I would like to express my appreciation for my advisor, Dr. Amanda Jansen. Thank you for being the best possible mentor I could ever have imagined. Your constant encouragement and meaningful feedback helped shape my development in so many productive ways. Also, your tireless work ethic and unparalleled ambition have set such a strong example for the professor I hope to become. I want you to know that I regard the privileged decision to work under your tutelage to be the best decision of my professional life. Your positive influence will continue to guide me throughout my career in education. To my committee members, Drs. Jim Hiebert, Alfinio Flores, and Jim Middleton: thank you for your thoughtful engagement with my ideas throughout the dissertation process. Each of you provided a unique expertise from which I learned so much. Thank you for your time and energy in making me a better researcher. To the mathematics education faculty members at the University of Delaware: thank you for being such passionate and enthusiastic scholars. It is abundantly clear to me why the doctoral program at UD is one of the best in the country. You are all wonderful at your jobs. iv Thank you to the mathematics education doctoral students with which I have had the pleasure of working over my four years at UD. The sense of community amongst grad students is a prominent reason why this program is so terrific. I want to single out and thank Emily Miller and Alison Marzocchi for their mentorship and kindness; I owe so much of my success to you both. I also want to especially thank Tony Mixell and Siobahn Suppa for their empathy and friendship as we navigated the stages of the Ph.D. journey together. To my parents and sister: thank you for your unwavering support along every step of the way these past four years. It was your initial encouragement that gave me the confidence to pursue my Ph.D. dream, even if it meant leaving a teaching job I enjoyed. Your genuine interest in my journey has been so motivating to me. I would not be here without you. Last, but, most assuredly, not least, I would like to recognize my wife, Kendi, to whom this dissertation is dedicated. This achievement would not have been possible without your love and sacrifice. Everything I have accomplished and everything I will accomplish is because of your support. Thank you, Kendi. v TABLE OF CONTENTS LIST OF TABLES ............................................................................................................. ix LIST OF FIGURES .............................................................................................................x ABSTRACT ...................................................................................................................... xii Chapter 1 DISTINGUISHING BETWEEN GRIT, PERSISTENCE, AND PERSEVERANCE FOR LEARNING MATHEMATICS WITH UNDERSTANDING ...............................................................................................1 Grit ...........................................................................................................................5 Measures/Operationalization .............................................................................7 Associations between Grit and Learning ...........................................................9 Critiques of Grit Relative to Learning Mathematics with Understanding ......................................................................................11 Persistence..............................................................................................................15 Measures/Operationalization ...........................................................................17 Associations between Persistence and Learning ..............................................20 Critiques of Persistence Relative to Learning Mathematics with Understanding ......................................................................................24 Perseverance ..........................................................................................................28 Measures/Operationalization ...........................................................................31 Associations between Perseverance and Learning ..........................................37 Critiques of Perseverance Relative to Learning Mathematics with Understanding .......................................................................................43 Toward a Distinction between Constructs .............................................................46 Conclusion .............................................................................................................55 2 SUPPORTING SECONDARY STUDENTS’ PERSEVERANCE FOR SOLVING CHALLENGING MATHEMATICS TASKS ....................................56 vi Conceptual Framework: Perseverance in Problem-solving ...................................58 Supporting Student Perseverance with Mathematical Tasks .................................62 Scaffolding Perseverance via Mathematical Task Structure and Teacher Questioning ....................................................................................64 Considering Embedded Conceptualization Scaffolds for Perseverance Support ...................................................................................70 Next Steps in Perseverance Research ....................................................................75 Methods..................................................................................................................76 Participants and Context ..................................................................................77 Data Collection ................................................................................................79 Think-aloud Interviews ..............................................................................80 Mathematical Tasks .............................................................................80 Scaffold Conditions .............................................................................82 Video-reflection Interviews .......................................................................85 Exit Interviews ...........................................................................................86 Data Analysis ...................................................................................................87 Three-Phase Perseverance Framework ......................................................89 Coding Decisions .......................................................................................92 Reliability Procedures ................................................................................95 Results ....................................................................................................................95 Result 1: Higher Quality Perseverance on Scaffolded Tasks than on Non- Scaffolded Tasks, Especially during Additional Attempt............................96 James’s Perspective: A “Life-Preserver” amidst “Chaos” .......................101 James’s Experience with Cross Totals ...............................................102