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.
Author(s): Dirk De Bock
Series: History of Mathematics Education
Publisher: Springer
Year: 2023
Language: English
Pages: 614
City: Cham
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
