An Examination of the Factors and Characteristics that Contribute to the Success of Putnam Fellows Robert Alexander James Stroud, PhD University of Connecticut, 2015 The William Lowell Putnam Mathematical Competition is an intercollegiate mathematics competition for undergraduate college and university students in the United States and Canada and is regarded as the most prestigious and challenging mathematics competition in North America (Alexanderson, 2004; Grossman, 2002; Reznick, 1994; Schoenfeld, 1985). Students who earn the five highest scores on the examination are named Putnam Fellows and to date, despite the thousands of students who have taken the Putnam Examination, only 280 individuals have won the Putnam Competition. Clearly, based on their performance being named a Putnam Fellow is a remarkable achievement. In addition, Putnam Fellows go on to graduate school and have extraordinary careers in mathematics or mathematics- related fields. Therefore, understanding the factors and characteristics that contribute to their success is important for students interested in STEM-related fields. The participants were 25 males who attended eight different colleges and universities in North America at the time they were named Putnam Fellows and won the Putnam Competition four, three, or two times. An 18-item questionnaire, adapted form the Walberg Educational Productivity Model, was used as a framework to investigate the personal and the formal educational experiences as well as the role the affective domain played in their development as Putnam Fellows. Further, research (DeFranco, 1996; Schoenfeld, 1992) on the characteristics of expert problem solvers was used to understand those elements of the cognitive domain that contributed to their success. Data was collected through audio-recorded interviews conducted over the telephone or through Skype, and through written e-mail responses. The interview data was coded according to the coding category it represented and then sorted to identify existing themes and patterns for within-case and cross-case analyses. The results indicated that four subcategories of personal experiences, four subcategories of formal educational experiences, seven subcategories involving the affective domain, and three subcategories of the cognitive domain all played an important role in the development of Putnam Fellows. Future research should include a thorough examination of female Putnam winners as well as the problem- solving strategies used by Putnam Fellows. An Examination of the Factors and Characteristics that Contribute to the Success of Putnam Fellows Robert Alexander James Stroud BS, University of New Haven, 1990 MAT, Connecticut College, 1995 CAS, Sacred Heart University, 1999 A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy at the University of Connecticut 2015 Copyright by Robert Alexander James Stroud 2015 APPROVAL PAGE Doctor of Philosophy Dissertation An Examination of the Factors and Characteristics that Contribute to the Success of Putnam Fellows Presented by Robert Alexander James Stroud, BS, MAT, CAS Major Advisor ___________________________________________________________ Thomas C. DeFranco, Ph.D. Associate Advisor ___________________________________________________________ Stuart J. Sidney, Ph.D. Associate Advisor ____________________________________________________________ Hariharan Swaminathan, Ph.D. Associate Advisor ____________________________________________________________ Mary P. Truxaw, Ph.D. Associate Advisor ____________________________________________________________ Charles I. Vinsonhaler, Ph.D. University of Connecticut 2015 ii DEDICATION For my first teachers, Robert R. Stroud and Joan Ferguson Stroud with love and appreciation iii ACKNOWLEDGEMENTS And whatsoever ye do in word or deed, do all in the name of the Lord Jesus, “ sians 3:17 King James Version). giving thanks to God and the Father by him” (Colos First and foremost, I am thankful to my advisor, Dr. Thomas C. DeFranco, who has been my mentor throughout this journey, which first began with my favorite class EDCI 369, The Teaching and Learning of Mathematical Problem Solving. assion and enthusiasm for the teaching and learning of mathematicsDr. DeFranco’s has endless inspired p me throughout the years and I will forever be grateful for his wisdom and guidance. I would also like to thank the members of my advisory committee, Dr. Stuart J. Sidney, Dr. Hariharan Swaminathan, Dr. Mary P. Truxaw, and Dr. Charles I. Vinsonhaler, for their guidance and feedback on my research the past few years. Thank you also to Dr. Kimberly B. Sofronas for her advice and guidance, which contributed greatly to my work. I am also indebted to the participants of my dissertation study. Without the help of the Putnam Fellows, these studies would not have been possible. Finally, I would like to thank the two most important people in my life, my parents. Without the loving memory of my dad and the love and support of my mom, none of this would have been possible. Although my dad did not live to see me complete my doctorate, I know the Fire Chief would be proud. And thank you to my mom for giving me the two greatest gifts of all her love and her time. – iv TABLE OF CONTENTS Page LIST OF TABLES .................................................................................................................................. viii LIST OF FIGURES .................................................................................................................................... ix CHAPTER I: OVERVIEW OF THE STUDY Introduction .............................................................................................................................................. 1 Background of the Study ...................................................................................................................... 4 Research Questions ............................................................................................................................. 16 Methods and Procedures .................................................................................................................. 16 Participants .............................................................................................................................. 16 Data Collection ........................................................................................................................ 17 Data Analysis ........................................................................................................................... 18 Limitations.............................................................................................................................................. 19 CHAPTER II: REVIEW OF RELATED LITERATURE Introduction ........................................................................................................................................... 21 A History of the Putnam Competition .......................................................................................... 22 Mathematics Contests and Competitions ................................................................................... 31 Problem Solving ................................................................................................................................... 40 The Walberg Educational Productivity Model.......................................................................... 44 v CHAPTER III: METHODS AND PROCEDURES Participants ............................................................................................................................................ 50 Materials .................................................................................................................................................. 53 Procedures for Data Collection ....................................................................................................... 53 Procedures for Data Analysis .......................................................................................................... 55 Research Question 1 ............................................................................................................. 58 Research Question 2 ............................................................................................................. 58 Research Question 3 ............................................................................................................. 59 Research Question 4 ............................................................................................................. 60 CHAPTER IV: RESULTS Introduction ........................................................................................................................................... 61 Research Question 1 ........................................................................................................................... 62 Research Question 2 ........................................................................................................................... 70 Research Question 3 ........................................................................................................................... 82 Research Question 4 ......................................................................................................................... 101 CHAPTER V: DISCUSSION Overview of the Study .....................................................................................................................