Pursuing Excellence in Mathematics Education: Essays in Honor of Jeremy Kilpatrick (Mathematics Education Library)

Chapters in this book recognize the more than forty years of sustained and distinguished lifetime achievement in mathematics education research and development of Jeremy Kilpatrick. Including contributions from a variety of skilled mathematics educators, this text honors Jeremy Kilpatrick, reflecting on his groundbreaking papers, book chapters, and books - many of which are now standard references in the literature - on mathematical problem solving, the history of mathematics education, mathematical ability and proficiency, curriculum change and its history, global perspectives on mathematics education, and mathematics assessment. Many chapters also offer substantial contributions of their own on important themes, including mathematical problem solving, mathematics curriculum, the role of theory in mathematics education, the democratization of mathematics, and international perspectives on the professional field of mathematics education.​ Contents 6 Introduction 8 Part I: Jeremy Kilpatrick: Colleague, Mentor and Collaborator 12 Chapter 1: Fifty Years and Counting: Working with Jeremy Kilpatrick 13 Introduction 13 The Person 14 Honors and Recognition 15 Doctoral Students 15 A Key Event 16 Family 17 The Leland Stanford Junior University 18 SMSG Headquarters and NLSMA 19 Mentors 21 Teachers College, Columbia University 22 University of Georgia 22 Regents’ Professorship 23 Transforming Mathematics Education 23 Analysis of Verbal Protocols 23 Editorship of JRME 23 Bridging the Disciplines 24 International Ambassador for Mathematics Education 24 Assessment 25 History of Mathematics Education 25 Moving Us Forward 25 Epilogue 26 Chapter 2: What’s Involved in the Work of Dissertation Advising? An Interview with Jeremy Kilpatrick and Some Personal Reflections 27 Introduction 27 Images of Dissertation Work 28 My Own Experience Writing a Dissertation Under Jeremy Kilpatrick 32 Jeremy Kilpatrick’s Acknowledged Style of Dissertation Advising 34 The Dissertation and Its Stakeholders 38 Four Stakeholders 39 Jeremy’s Reaction to the Four Stakeholders 44 Other Ways of Being a Dissertation Advisor 48 Another Dissertation Advising Style and a Personal Learning Note 54 Conclusion: Whither Dissertation Advising in Mathematics Education? 57 References 59 Chapter 3: Collaboration and Friendship with Jeremy Kilpatrick: Two Sides of Success and Challenge 61 Part II: Mathematical Problem Solving and Curriculum 63 Chapter 4: When Is a Problem? Contribution in Honour of Jeremy Kilpatrick 64 Introduction 64 ‘Problem’ as Problematic 65 Problems in the Curriculum 66 Experiential Approach 68 Circle Dissection 68 Comment 68 One Sum 69 Marbles 73 Comment 73 Reflections 74 References 77 Chapter 5: Problem Solving, Exercises, and Explorations in Mathematics Textbooks: A Historical Perspective 79 Introduction 79 A Framework to Analyze Mathematics Tasks 81 Mathematical Tasks in Algebra Textbooks of Different Periods 82 Augusto José da Cunha Cunha (1887): Elementos de Álgebra (Elements of Algebra) 83 Eduardo Ismael dos Santos Andrea (1924): Compêndio de Álgebra (Algebra Compendium) 84 J. Jorge G. Calado (1960, First Edition 1952): Compêndio de Álgebra (Compendium of Algebra) 85 António de Almeida Costa, Alfredo Osório dos Anjos, and António Augusto Lopes (1974): Compêndio de Matemática (Mathematics Compendium) 86 António de Almeida Costa, Alfredo Osório dos Anjos and António Augusto Lopes (1983): Matemática Jovem (Young Mathematics) 88 Maria Augusta F. Neves, Luís Guerreiro, and Armando Neves (2004): Matemática 9 (Mathematics 9) 89 Conclusion 91 References 91 Chapter 6: From Mathematical Problem Solving to Geocaching: A Journey Inspired by My Encounter with Jeremy Kilpatrick 93 Meeting Jeremy 93 Becoming a Doctoral Student 94 Where Technology Are Inviting Us 94 Mystery Caches and Mathematics 96 Theoretical Standpoint 97 Research on Geocaching 98 Smartphone 99 References 101 Chapter 7: Ruminations on the Generated Curriculum and Reform in Community College Mathematics: An Essay in Honor of Jeremy Kilpatrick 102 Part 1: Various Notions of Curriculum 104 Basic Mathematics: Converting Percents to Decimals 106 College Math: Mutually Exclusive Events 108 Trigonometry: Frequency and Phase Shift 110 Discussion 112 Coda 115 References 115 Part III: The Interaction of Theory, Practice and Politics in Mathematics Education 118 Chapter 8: Mathematics, Knowledge and Political Power 119 Introductory Remarks 119 Historical Accounts of Mathematics and Political Power 120 Mathematics as a Distinctive Tool for Problem-Solving in Social Practices and Means of Social Power 120 Mathematics as Theoretical System and a Base of a Universal Political Worldview 121 Mathematics as a Human Force for General Scientific and Social Development 122 Mathematics as Rationality and Common Sense 122 Social Needs for Mathematics Education 123 Professionalisation and Specialisation of Knowledge 123 (Mathematics) Education as a Public Task 124 Mathematics Education for All 125 Changing Mathematical Sciences and Its Applications by Information Technologies 126 Mathematical Literacy for Critical Citizenship in a Democratic Society 127 References 129 Chapter 9: Democratising Mathematics Education and the Role of Research 131 Why Choose Democratisation as a Theme for This Chapter? 131 Democratisation and Mathematics Education: Some Preliminary Thoughts 132 Mathematics Curricula 134 Mathematics Learners and Learning 136 Teaching and Teachers of Mathematics 138 Democratising Mathematics Education and the Teaching of Values 139 References 141 Chapter 10: On the Diversity and Multiplicity of Theories in Mathematics Education 143 Preamble 143 Introduction 144 The Search for a Theory of Mathematics Education 144 What We Expect from a Theory? 146 Peirce’s Pragmaticism 147 Social Constructivism 148 Theories in Mathematics Education, Reconsidered 149 References 152 Chapter 11: Toward a Profession of Mathematics Education: Guidance from Jeremy Kilpatrick’s Words and Deeds 155 Professionals and Professions 156 Jeremy Kilpatrick: The Professional Mathematics Educator 157 Toward a Profession of Mathematics Education: Lessons from Jeremy Kilpatrick 161 References 164 Jeremy Kilpatrick 166 Bio Sketch (in His Own Words) 166 Jeremy Kilpatrick: Summary of Professional Background and Accomplishments 168 Education and Professional Experience 168 Education 168 Professional Experience 168 Visiting Appointments 168 Selected Professional Awards/Recognitions 169 Examples of Professional Service 169 American Educational Research Association 169 American Statistical Association 170 College Board 170 International Commission on Mathematical Instruction (ICMI) 170 Mathematical Association of America 170 National Council of Teachers of Mathematics 170 National Academy of Education 170 National Assessment of Educational Progress 171 National Research Council 171 National Science Foundation 171 Office of Education Research and Innovation 171 Organisation for Economic Cooperation and Development (OECD) 171 Selected Editorial Service 171 Chief Editor 171 Editorial Board Member 172 Selected Publications 172 Sole Author 172 Co-author 177 Editor or Co-editor 180 Biographical Sketches of Contributors 182 Index 185 Front Matter....Pages i-x Front Matter....Pages 1-1 Fifty Years and Counting: Working with Jeremy Kilpatrick....Pages 3-16 What’s Involved in the Work of Dissertation Advising? An Interview with Jeremy Kilpatrick and Some Personal Reflections....Pages 17-50 Collaboration and Friendship with Jeremy Kilpatrick: Two Sides of Success and Challenge....Pages 51-52 Front Matter....Pages 53-53 When Is a Problem? Contribution in Honour of Jeremy Kilpatrick....Pages 55-69 Problem Solving, Exercises, and Explorations in Mathematics Textbooks: A Historical Perspective....Pages 71-84 From Mathematical Problem Solving to Geocaching: A Journey Inspired by My Encounter with Jeremy Kilpatrick....Pages 85-93 Ruminations on the Generated Curriculum and Reform in Community College Mathematics: An Essay in Honor of Jeremy Kilpatrick....Pages 95-110 Front Matter....Pages 111-111 Mathematics, Knowledge and Political Power....Pages 113-124 Democratising Mathematics Education and the Role of Research....Pages 125-136 On the Diversity and Multiplicity of Theories in Mathematics Education....Pages 137-148 Toward a Profession of Mathematics Education: Guidance from Jeremy Kilpatrick’s Words and Deeds....Pages 149-159 Back Matter....Pages 161-185 Chapters in this book recognize the more than forty years of sustained and distinguished lifetime achievement in mathematics education research and development of Jeremy Kilpatrick. Including contributions from a variety of skilled mathematics educators, this text honors Jeremy Kilpatrick, reflecting on his groundbreaking papers, book chapters,℗land books - many of which are now standard references in the literature - on mathematical problem solving, the history of mathematics education, mathematical ability and proficiency, curriculum change and its history, global perspectives on mathematics education, and mathematics assessment. Many chapters also offer substantial contributions of their own on important themes, including mathematical problem solving, mathematics curriculum, the role of theory in mathematics education, the democratization of mathematics, and international perspectives on the professional field of mathematics education