Researching the History of Mathematics Education : An International Overview

This book offers insights into the history of mathematics education, covering both the current state of the art of research and the methodology of the field. History of mathematics education is treated in the book as a part of social history. This book grew out of the presentations delivered at the International Congress on Mathematics Education in Hamburg. Modern development and growing internationalization of mathematics education made it clear that many urgent questions benefit from a historical approach. The chapters present viewpoints from the following countries: Belgium, Brazil, Cambodia, China, Cyprus, Germany, Iceland, Italy, the Netherlands, Russia,Spain and Sweden. Each chapter represents significant directions of historical studies. The book is a valuable source for every historian of mathematics education and those interested in mathematics education and its development. Contents 6 Editors and Contributors 8 The Hamburg Score (In Lieu of an Introduction) 10 References 16 1 Influences from the 1959 Royaumont Seminar. Proposals on Arithmetic and Algebra Teaching at Lower-Secondary Level in Iceland 17 Abstract 17 1 Introduction 17 2 The Royaumont Seminar 18 3 Literature Review 20 4 The Nordic Committee for Modernizing Mathematics Teaching 22 5 Iceland’s Educational Policy 23 6 The Development of the New Math in Retrospect 25 7 Research Question and Research Method 26 8 Analysis of Textbooks 27 9 Results 28 9.1 Introduction of Set-Theoretical Concepts and Logic, and Their Connection to Topics in Applied Mathematics 32 9.2 Structure of the Number Field 32 9.3 The Study of Numbers 32 9.4 Summary 33 10 Concluding Remarks 34 References 34 Research Literature 34 Textbooks 36 2 Real Numbers in School: 1960s Experiments in France and Brazil 38 Abstract 38 1 Introduction 38 2 The Expansion of Secondary Schooling in France and Brazil 40 3 Real Numbers in the Early 1960s Programs 41 4 Real Numbers from the Perspective of the Modern Mathematics Movement 43 5 Real Numbers in French Reform and Experiments 45 6 The Introduction of Real Numbers in Ginásio 49 7 Final Considerations 52 References 54 3 The Revolution in Mathematics Education During the Meiji Era (1868–1912): A Study of the Textbooks Used to Teach Computation, Geometry and Algebra 59 Abstract 59 1 Introduction 59 2 The Teaching of Computation in Elementary Schools 61 3 Algebra and Geometry Textbooks During the Meiji Era 64 3.1 Studying the Mathematical Language to Understand the Contrast Between Algebra and Geometry Cases 65 3.2 The Evolution of Geometry Teaching in Middle Schools of the Meiji Era: A Study of the Textbooks 66 4 The Installation of Algebra Notations and Curricula in Japanese Universities 70 5 Conclusion 72 References 73 4 Early Experiments with Modern Mathematics in Belgium. Advanced Mathematics Taught from Childhood? 75 Abstract 75 1 Introduction 75 2 A First Experiment with Modern Mathematics in Two Schools for Future Kindergarten Teachers 77 3 Papy’s Experiments: Towards a Generalized Introduction of Modern Mathematics in Belgium 79 4 Libois’s Experiments at the École Decroly: A World of Difference 82 5 Commentaries on the Belgian Experiments... 84 6 Conclusions and Discussion 86 Sources 87 References 88 5 The Role of a Journal on Teaching Mathematics and Sciences Issued at the Beginning of the 20th Century in Professionalizing Italian Primary School Teachers 92 Abstract 92 1 Introduction 92 2 The Scuola Normale (Normal School) for Educating Primary School Teachers 94 3 The Journal Il Bollettino di Matematiche e di Scienze Fisiche e Naturali 97 3.1 The Foundation of the Journal 97 3.2 The Editors 100 3.3 The Mission and Vision of the Journal 104 3.4 The Content of the Journal 106 3.5 The Contributors 109 4 Conclusions 112 Acknowledgements 113 Appendix 1: The Editors and Their Schools During the Editorship 113 Appendix 2: The Publishers/Printers 113 Appendix 3: Distribution of the Issues 114 References 114 6 Russian Mathematics Teachers, 1830–1880: Toward a Group Portrait 119 Abstract 119 1 Introduction 119 2 Some Remarks on Methodology 120 3 Beginnings 121 4 Gymnasia and Mathematics in Gymnasia 122 5 Teachers at Gymnasia: Several Lives 123 6 Real Schools and Their Mathematics Teachers 126 7 Teachers at Military Institutions 127 8 Teachers at Commercial Academies 129 9 Teachers’ Workload and Methodological Work 130 10 The Position of Mathematics Teachers 135 11 Discussion and Conclusion 136 References 139 7 Arithmetic Patterns in the Arithmetic of Petros Argyros 143 Abstract 143 1 Introduction 143 2 Mathematics Education in the West and the Abaci Tradition 144 3 Mathematics Education in Greek Territories During the Ottoman Era 146 4 The Content of Arithmetic 148 5 Arithmetic Patterns in Arithmetic 148 6 Discussion and Conclusion 152 Acknowledgements 152 References 153 8 Frans van Schooten Sr. (1581–1645) Lecture Notes for the First Dutch Course for Engineers, Leiden, 1600–1681 155 Abstract 155 1 Introduction 156 2 The Dutch Republic Around 1600 157 3 Publications on Dutch Mathematics and Mathematics Education in the 17th Century 159 4 The Duytsche Mathematique 160 4.1 The “Instruction” 161 4.2 Teachers and Students 162 5 Frans van Schooten 164 6 BPL 1013 165 6.1 Interesting Features of BPL 1013 166 6.2 Arithmetic (See Table 1, Row 1) 166 6.3 Examples from (Advanced) Practical Geometry (See Table 1, Row 3–5) 168 7 Comparison with Other Texts 171 8 Discussion and Conclusion 174 References 176 Manuscripts 176 Publications 177 9 Arithmetic in the Spanish Army at the End of the 19th Century: The Textbooks by Salinas and Benítez 179 Abstract 179 1 Introduction 179 2 Methodological Issues 182 3 Bio-Bibliographical Sketch 183 4 Aritmética (Arithmetic) 186 5 Reactions to Aritmética 189 6 The Pizarras Por Papeletas Para El Examen de Aritmética En La Academia General Militar (Slates by Sheets for the Arithmetic Exam at the General Military Academy) 192 7 The Manual Para Las Clases de Tropa (Manual for Teaching the Troops) 192 8 A Final Comment 194 Acknowledgements 195 References 195 10 The New Math and School Governance: An Explanation of the Decline of the New Math in Sweden 200 Abstract 200 1 Introduction 200 2 Disposition and Sources 201 3 Survey of the Literature 202 4 Centralization of the Swedish School System, 1900–1970 203 5 Changes in the Textbook Market 207 6 Preparations for the New Math Reform, 1960–1968 209 7 Implementations of New Math—Failures and Successes, 1969–1980 213 7.1 Intended Curriculum 214 7.2 Implemented Curriculum 216 7.3 Achieved Curriculum 217 8 An Explanation of the Decline of the New Math in Sweden 219 Sources 222 References 224 11 History of Mathematics Instruction in Colonial and Early Post-colonial Cambodia 228 Abstract 228 1 Introduction: Mathematics Education in Colonial Cambodia 228 2 The Methodology 230 3 Summary of the Interviews 231 3.1 Interview 1 231 3.2 Interview 2 233 3.3 Interview 3 235 3.4 Interview 4 240 3.5 Interview 5 244 3.6 Interview 6 247 4 Summary and Directions for Future Research 250 References 251 12 Patterns for Studying History of Mathematics: A Case Study of Germany 252 Abstract 252 1 Introduction 252 2 Interdisciplinary Research 253 2.1 The Disciplinary Net 253 2.2 Italy—A Local Case? 255 3 Germany: A Case for Studying Some Global and Local Elements 257 3.1 The German Situation 257 3.2 The Case of the Hochstift Münster 258 3.3 Münster Becoming Part of the Prussian Province Westphalia 263 3.4 Mathematics Between the States of the Deutscher Bund 264 3.5 Reconciling the Antagonisms Within the New German Reich from 1871 266 4 Conclusion 268 References 269 Sources 269 Publications 269 13 A Teacher of Mathematics in Times of Change 271 Abstract 271 1 Introduction 271 2 A Time of Great Changes 273 3 A Teaching Career 275 4 Teaching Arithmetic at an Elementary School 276 5 Teaching Arithmetic at a Vocational School 279 6 Teaching Mathematics at a Latin School 281 7 Teaching Mathematics for the Military and on Boarding Schools 284 8 An Epilogue 286 References 287 14 Visual Representations of Arithmetical Operations Performed with Counting Instruments in Chinese Mathematical Treatises 289 Abstract 289 1 Introduction 289 2 Procedures of Multiplication Performed with Counting Rods Found in the Shendao Dabian Lizong Suanhui 292 2.1 The First Procedure of Multiplication Described in Zhou’s Treatise 292 2.2 The Second Procedure of Multiplication Described in Zhou’s Treatise 295 3 Procedure of Division Performed with Counting Rods Found in the Shendao Dabian Lizong Suanhui 298 4 Images of Configurations of Beads on an Abacus 303 4.1 The Earliest Chinese Treatises Containing Visual Representations of Operations with the Abacus 303 4.2 Panzhu Suanfa 盤珠算法 (Computational Methods for “Pearls in a Tray” [= Abacus]): A Brief Introduction 303 4.3 Representation of Operations to be Performed with the Abacus Found in the Panzhu Suanfa 盤珠算法 305 4.3.1 Diagrams Related to the “Rules for Moving up” 307 4.3.2 Diagrams Related to the “Rules for Retreating” 307 4.3.3 Diagrams Accompanying Solutions of Problems 307 5 Conclusions 311 References 312 A. Primary Sources 312 B. Translations and Secondary Works 312 Author Index 315 Subject Index 322 Front Matter ....Pages i-xv Influences from the 1959 Royaumont Seminar. Proposals on Arithmetic and Algebra Teaching at Lower-Secondary Level in Iceland (Kristín Bjarnadóttir)....Pages 1-21 Real Numbers in School: 1960s Experiments in France and Brazil (Elisabete Zardo Búrigo)....Pages 23-43 The Revolution in Mathematics Education During the Meiji Era (1868–1912): A Study of the Textbooks Used to Teach Computation, Geometry and Algebra (Marion Cousin)....Pages 45-60 Early Experiments with Modern Mathematics in Belgium. Advanced Mathematics Taught from Childhood? (Dirk De Bock, Geert Vanpaemel)....Pages 61-77 The Role of a Journal on Teaching Mathematics and Sciences Issued at the Beginning of the 20th Century in Professionalizing Italian Primary School Teachers (Fulvia Furinghetti, Annamaria Somaglia)....Pages 79-105 Russian Mathematics Teachers, 1830–1880: Toward a Group Portrait (Alexander Karp)....Pages 107-130 Arithmetic Patterns in the Arithmetic of Petros Argyros (Elena Kiliari, Athanasios Gagatsis, Irene Papadaki)....Pages 131-142 Frans van Schooten Sr. (1581–1645) Lecture Notes for the First Dutch Course for Engineers, Leiden, 1600–1681 (Jenneke Krüger)....Pages 143-166 Arithmetic in the Spanish Army at the End of the 19th Century: The Textbooks by Salinas and Benítez (Antonio M. Oller-Marcén, Vicente Meavilla-Seguí)....Pages 167-187 The New Math and School Governance: An Explanation of the Decline of the New Math in Sweden (Johan Prytz)....Pages 189-216 History of Mathematics Instruction in Colonial and Early Post-colonial Cambodia (Sethykar SamAn)....Pages 217-240 Patterns for Studying History of Mathematics: A Case Study of Germany (Gert Schubring)....Pages 241-259 A Teacher of Mathematics in Times of Change (Harm Jan Smid)....Pages 261-278 Visual Representations of Arithmetical Operations Performed with Counting Instruments in Chinese Mathematical Treatises (Alexei Volkov)....Pages 279-304 Back Matter ....Pages 305-314 This book offers insights into the history of mathematics education, covering both the current state of the art of research and the methodology of the field. History of mathematics education is treated in the book as a part of social history. This book grew out of the presentations delivered at the International Congress on Mathematics Education in Hamburg. Modern development and growing internationalization of mathematics education made it clear that many urgent questions benefit from a historical approach. The chapters present viewpoints from the following countries: Belgium, Brazil, Cambodia, China, Cyprus, Germany, Iceland, Italy, the Netherlands, Russia, Spain and Sweden. Each chapter represents significant directions of historical studies. The book is a valuable source for every historian of mathematics education and those interested in mathematics education and its development