Modern Mathematics: An International Movement?

Description

The international New Math developments between about 1950 through 1980, are regarded by many mathematics educators and education historians as the most historically important development in curricula of the twentieth century. It attracted the attention of local and international politicians, of teachers, and of parents, and influenced the teaching and learning of mathematics at all levels―kindergarten to college graduate―in many nations. After garnering much initial support it began to attract criticism. But, as Bill Jacob and the late Jerry Becker show in Chapter 17, some of the effects became entrenched. This volume, edited by Professor Dirk De Bock, of Belgium, provides an outstanding overview of the New Math/modern mathematics movement. Chapter authors provide exceptionally high-quality analyses of the rise of the movement, and of subsequent developments, within a range of nations. The first few chapters show how the initial leadership came from mathematicians in European nations and in the United States of America. The background leaders in Europe were Caleb Gattegno and members of a mysterious group of mainly French pure mathematicians, who since the 1930s had published under the name of (a fictitious) “Nicolas Bourbaki.” In the United States, there emerged, during the 1950s various attempts to improve U.S. mathematics curricula and teaching, especially in secondary schools and colleges. This side of the story climaxed in 1957 when the Soviet Union succeeded in launching “Sputnik,” the first satellite. Undoubtedly, this is a landmark publication in education. The foreword was written by Professor Bob Moon, one of a few other scholars to have written on the New Math from an international perspective. The final “epilogue” chapter, by Professor Geert Vanpaemel, a historian, draws together the overall thrust of the volume, and makes links with the general history of curriculum development, especially in science education, including recent globalization trends. Foreword References Contents List of Figures List of Tables Abstracts Preface to the Series Preface to the Book Author Biographies Chapter 1: Modern Mathematics: An International Movement Diversely Shaped in National Contexts Introduction An American Cradle and a European Cradle Dissemination of the Reform Characterization of the Reform A Failed Reform? References Part I: Preparing the Reform on Both Sides of the Atlantic Chapter 2: The Rise of the American New Math Movement: How National Security Anxiety and Mathematical Modernism Disrupted the School Curriculum Introduction Emergence of Mathematical Workforce Demands in the 1940s The Promotion of “Modern” Mathematics for Undergraduates Emergence of Secondary School Reform Sputnik and Its Aftermath Concluding Remarks References Chapter 3: The Early Roots of the European Modern Mathematics Movement: How a Model for the Science of Mathematics Became a Model for Mathematics Education Introduction The International Commission for the Study and Improvement of Mathematics Teaching Modern Mathematics as an Educational Project Structures in Mathematics and Child Psychology The Preparatory Meetings: Defining an Agenda A Decisive Meeting Between the Bourbakists and Piaget Dissemination and Early Developments at National Levels The Ongoing Debate Within CIEAEM Early National Developments Discussion References Chapter 4: The Royaumont Seminar as a Booster of Communication and Internationalization in the World of Mathematics Education Introduction Meetings on Mathematics Education Before Royaumont Royaumont Bodies Promoting Internationalization in Mathematics Education The Seminar of Royaumont: Not Only “Euclid Must Go!” In the Aftermath of Royaumont Aarhus, Denmark Zagreb-Dubrovnik, Yugoslavia Bologna, Italy Stockholm, Sweden. Modern Mathematics at the International Congress of Mathematicians in 1962 Athens, Greece In the United States of America: The Conference in Cambridge (MA) Frascati, Italy From Milano Marittima, Italy, to Echternach, Luxembourg Modern Mathematics Goes Beyond the Iron Curtain Budapest, Hungary Moscow, USSR. Modern Mathematics at the International Congress of Mathematicians in 1966 Bucharest, Romania Modern Mathematics in Other Hemispheres Latin America Africa and Asia Toward New Horizons Utrecht 1964, Netherlands Utrecht 1967, Netherlands Conclusions Dramatis Personae Much Ado About Nothing? References Part II: Implementation of the Reform Around the World Chapter 5: The Modern Mathematics Movement in France: Reforming to What Ends? The Contribution of a Cross-Over Approach to Modernity Introduction New Goals Assigned to the French Education System: Democratize, Orientate, Select for a Cultural, Social, and Economic Modernity The 1950s—Changing Educational Paradigm: The Reversal of Priorities The 1960s—Thinking Democratization and Modernization: Structural Reforms and Disciplinary Issues The 1970s—Disillusionment and Controversy Mathematics and Lettres: Competition and Emulation of Modernizing Ambitions Disciplinary Issues of Democratization General Education for All and Specialization Dissimilar Dynamics of Reform Mathematics: A Discipline in the Field of Science Teaching Science and Science Teaching: The Future of the Country “The False Quarrel” of Modern Mathematics The Ambitions of Modernity of the Mathematics Reform: Confrontation with Realities Aims and Content of the Premier Cycle Programs The Problematic Reality of the Teaching Staff The Pitfall of the Different Goals of the Premier Cycle Save the Reform Concluding Remarks References Chapter 6: West German Neue Mathematik and Some of Its Protagonists Introduction Modern University Mathematics and Backward School Mathematics University Mathematicians Who Wanted to Modernize School Mathematics The Royaumont Seminar as a Theoretical Cradle or Practical Beginning of German New Math The Networks The New Math Reform vs. Meraner Reform The Radical Nuremberg Curriculum The End in the Beginning References Chapter 7: New Mathematics in the United Kingdom: Projects and Textbooks as Driving Forces of Curriculum Reform Socio-Political and Educational Context of the Reform The Dominant Paradigm Changes in the Primary and Secondary Schools The “New Mathematics” and the Creation of a New Association of Teachers Developments During the 1950s in Europe and in the USA The Beginnings of the Association of Teachers of Mathematics Some Curriculum Development Projects Radical Mathematics in ATM Publications Zooming in on the School Mathematics Project The End of Modern Mathematics in the UK References Chapter 8: Modern Mathematics in Italy: A Difficult Challenge Between Rooted Tradition and Need for Innovation Traditions in Italian Mathematics Education The Reconstruction After World War II in Italy: National Initiatives and International Contacts in Mathematics Education From Royaumont to Bologna The Italians at Royaumont Bologna Conference First Cautious Steps Toward Modern Mathematics in Italy Proposals of New Programs for High School The (Blunt) Top of Modern Mathematics in Italy Initiatives in Grades 1–8 The Primary School The Middle School Experimental Projects for Mathematics A New Student Population From Projects to Textbooks Conclusions References Chapter 9: The Distinct Facets of Modern Mathematics in Portugal Introduction Context of the Modern Mathematics Reform Beginnings Laying the Ground—The Sebastião e Silva Experiment Teacher Formation Evaluating the Experiment Mathematics as a Language—The Program for CPES The New Programs Looking at the Textbooks Teacher Formation The Struggle to Apply Modern Mathematics to Real-World Situations—The Technical School Experiment Purpose and Methods for the Experiment The Experimental Textbooks Teacher Formation Structuring Geometry—Curso Geral in Liceus The New Curricula, as Expressed in the Unique Textbooks Evaluating the New Curricula Mathematics as Logic—The Program for the Last Years of Liceus The Reliance on Logic The Absence of Teacher Formation The Primary Schools The New Programs The End of Modern Mathematics Concluding Remarks References Chapter 10: Papy’s Reform of Mathematics Education in Belgium: Development, Implementation, and Controversy Introduction Toward Modern Mathematics at the Secondary Level The First Experiment with Future Kindergarten Teachers A Ten-Year Experimental Trajectory at the Secondary Level Mathématique Moderne Large-Scale Recycling of Teachers: The Days of Arlon Implementation and Controversy Modern Mathematics in Belgian Primary Schools A Reform Prepared in Various Experiments Modern Mathematics in Daily Primary School Practice Discussion References Chapter 11: A Tale of Two Systems: A History of New Math in The Netherlands, 1945–1980 Introduction The Dutch School System(s) Episode 1: 1945–1960, New Math Rising Episode 2: The 1960s, a New Curriculum Committee Episode 3: The 1970s, IOWO Aftermath: The End of a Didactical Institute Final Remarks References Chapter 12: Nordic Cooperation on Modernization of School Mathematics, 1960–1967 Introduction The Nordic Countries Modern Mathematics Nordic Cooperation in School Mathematics Nordic Committee for the Modernization of School Mathematics Experimental Texts and Experimental Teaching Grades 1–6 Grades 4–6—SMSG Material Grades 7–9 Grades 10–12 Aftermath Denmark Sweden Finland Norway IMU—An Individual Mathematics Teaching Project A Case Study: Modern Mathematics in Iceland Discussion Concluding Remarks Sources in Archives Riksarkivet (RA B) [Swedish National Archives] B1 Utgående skrivelser [Outgoing Letters] B2 Experimental texts Riksarkivet (RA E) (Swedish National Archives) E1 Inkomna skrivelser [Incoming Letters] References Chapter 13: Reforms Inspired by Mathématique Moderne in Poland, 1967–1980 Early Polish Efforts to Modernize Mathematics Education Krygowska’s Role in Poland and in International Reform Debates The 1967 Change in the Mathematics Curriculum for Secondary Schools in Poland Changes in the Polish Mathematics Curriculum for the Early Grades During the Period 1970–1980 Closing Reflections References Chapter 14: The New Math in Hungary: Tamás Varga’s Complex Mathematics Education Reform Introduction A Brief Chronology of the Reform Tamás Varga, the Leader of the Reform The Political and Institutional Context The Hungarian Reform in the Context of the International New Math Movement Pedagogical and Psychological Background: A Complex Situation A “Heuristic” Epistemology of Mathematics The “Complexity” of Varga’s Reform Varga’s Curriculum Textbooks, Teachers’ Guides, and Expected Teaching Practices An Example: Probability in Varga’s Curriculum The Reasons to Teach Probability The Probability Curriculum Examples of Activities Conclusions on the Case of Teaching Probability The Impact and the Reception of the Reform Conclusion and Discussion References Chapter 15: New Math and the South Slavs The Context of Yugoslavian Mathematics Before the Royaumont Seminar Yugoslavia at the Royaumont Seminar Yugoslavian Political and Educational Framework Đuro Kurepa (1907–1993) Kurepa’s Principles Miloš Radojčić (1903–1975) Judita Cofman (1936–2001) Conclusion References Chapter 16: The Kolmogorov Reform of Mathematics Education in the USSR Introduction Prehistory: The Start of the Olympiad Movement in the 1930s Mathematicians in the Reform Andrey Kolmogorov The Olympiad Stream Didactic Transformation A First Case Study: Vectors A Second Case Study: Probability Theory Social Blindness The Golden Age of Soviet Mathematics Education A Lesson for Our Times? References Chapter 17: The Influence of Royaumont on Mathematics Education in the USA Introduction Emerging Ideas on Problem Solving and a “Modern Curriculum” Post-Royaumont Geometry in the USA Post-Royaumont Sets, Logic, and Structure Post-Royaumont Thinking About Problem Solving Post Royaumont Research Mathematicians in the USA and K–12 Concluding Remarks References Chapter 18: Aspects of Canadian Versions of So-Called “Modern” Mathematics and Its Teaching: Another Visit to the Old “New” Math(s) Introduction From International to National From National to Provincial On British Columbia On Ontario On Québec A Couple of Cross-Cutting Items and Themes On Books On Professional Organizations and Journals Conclusion References Chapter 19: New Math in Latin America (and a Glimpse at Costa Rica) Introduction Three Factors Within the Modern Mathematics Reform Reform in Latin America Stone and the Inter-American Perspective The Reform Through the CIAEM and Its Conferences The Road to Breaking with New Math Three Conferences An Assessment of the Five Conferences IACME and the Support from ICMI, IMU, and Other International Institutions Details on Names The Case of Costa Rica The Implementation of the Reform A Second “Breath” Breaking with the New Math Costa Rica and CIAEM Concluding Remarks References Chapter 20: Modernizing Mathematics Teaching: International Dialogues from Brazil Initial Considerations Brazil and the First International Movement to Modernize Mathematics Education Brazil and the Modern Mathematics Movement The Modern Mathematics Movement and the Expansion of the School System in Brazil A Change in Mind Brazil, the World Conference on Education for All, and Mathematics Education Final Considerations References Chapter 21: Australian School Mathematics and “Colonial Echo” Influences, 1901–1975 The Tyranny of Distance ICMI, Bombay, Royaumont, and a Revival of an Exclusive Club Australasian Universities Caleb Gattegno’s Global Influence First Contact: Gattegno’s Meeting with Georges Cuisenaire in 1953 The Rise and Fall of “Numbers in Colour” as an International Phenomenon Zoltán Pál Dienes’s Influence on School Mathematics in Australia, 1961–1975 Dienes’s Theory and His Influence on School Mathematics in Australia The Four Main Components of Dienes’s Theory The Immediate Impact of Dienes’s Theories on Thinking About the Teaching and Learning of Mathematics The Impact of Dienes’s Theories and Teaching Approaches on School Mathematics in Australia Dienes and His Influence in Victoria in the 1970s SGML in Victoria in the 1970s Four Factors Contributing to the Declining Influence of Dienes’s Theories The Entry of New Mathematics into Secondary School Curricula in Australia Influence of “Modern Mathematics” on Secondary School Mathematics in Australia The School Mathematics Research Foundation The Curriculum Canon Changes, But the Colonial Echo Continues References Chapter 22: What Did the “New Math Movement” Bring to Hong Kong in the 1960s and the 1970s (and Beyond)? Introduction Prequel: 1960–1965 The Launching: 1965–1970 The Close of the Scene: Beyond 1970 (Indirect) Harvest of the New Math Movement Past Experience as a Guide for the Future Epilogue References Chapter 23: Modern Mathematics: An International Movement, the Experience of Morocco Introduction: Characterization of Modern Mathematics Implementation of Modern Mathematics in Morocco: Main Stages Description of the Implementation Process Notes and Comments Textbooks Accompanying the Implementation of Modern Mathematics Criticisms of the Reform of Modern Mathematics Conclusion References Chapter 24: Modern Mathematics Curriculum Reforms in Ghana: UK and USA Influences Introduction School Mathematics Before Independence Roles Played by International Anglophone Organizations in the Reforms The American-Led Curriculum Initiatives The UK-Led Curriculum Initiatives Influence of Monopolistic State Publishing Houses on the Curriculum Initiatives Particularities of the Reforms Influence of the Curriculum Initiatives on School Mathematics Conclusion References Epilogue: From Center to Periphery? The Global Dynamics of the New Math Movement References Composite Reference List Author Index Subject Index