Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1981 A history of the "new math" movement in the United States Robert W. Hayden Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Science and Mathematics Education Commons Recommended Citation Hayden, Robert W., "A history of the "new math" movement in the United States " (1981). Retrospective Theses and Dissertations. 7427. https://lib.dr.iastate.edu/rtd/7427 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This was produced from a copy of a document sent to us for microfilming. 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Some pages in any document may have indistinct print, in all cases we have filmed the best available copy. Universi^ Micidnlms intematkxial 300 N /fct H RD , ANN AHBOH, Ml 48106 8209127 Hayden, Robert W. A HISTORY OF THE "NEW MATH" MOVEMENT IN THE UNITED STATES Iowa State University PH.D. 1981 University Microfilms Intern&tionâl 300N.ZMbRœd.AmDA**.MI4M06 Copyright 1981 by Hayden, RolDert W. All Rights Reserved A history of the "new math" movement In the United States by Robert W. Hayden A Dissertation Submitted to the Graduate Faculty In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Departments: Mathematics Professional Studies Co-majors: Mathematics Education Approved: Signature was redacted for privacy. In Charge of Major Signature was redacted for privacy. he Major Departments Signature was redacted for privacy. For the Gr Iowa State University Ames, Iowa 1981 Copyright Robert W. Hayden, 1981. All rights reserved. il TABLE OF CONTENTS Page I. PREFACE 1 II. THE MATHEMATICAL BACKGROUND OF THE "NEW MATH" 5 A. Introduction S B. The Foundations of Geometry and the Reformation of Analysis 7 C. The Development of Set Theory 17 D. Non-Euclidean Geometry 20 E. Modem Abstract Algebra 24 F. The Spread of Modern Mathematics 27 G. The Impact ' Modern Mathematics 36 H. Conclusion 45 III. EDUCATIONAL REFORM PRIOR TO THE "NEW MATH" 47 IV. THE SECOND WORLD WAR AND MATHEMATICS EDUCATION 72 A. The Importance of Mathematics to Society 72 B. New Uses for Mathematics 74 C. The Impact of the War on Applied Mathematics 76 D. The Impact of the War on Society's Support of Mathematics 80 E. The Impact of the War on School Mathematics 83 F. The Impact of the War on College Mathematics 87 V. SECONDARY SCHOOL "NEW MATH" 100 A. The University of Illinois Committee on School Mathematics (UlCSM) 100 B. The University of Maryland Mathematics Project (UMMaP) 107 C. The Commission on Mathematics of the College Entrance Examination Board (CEEB) 109 D. Sputnik 116 E. The School Mathematics Study Group (SMSG) 120 F. Other Programs 139 G. Dissemination 143 H. Reaction 157 VI. ELEMENTARY SCHOOL "NEW MATH" 173 A. The Problem of Teacher Training 173 B. The Early Elementary School "New Math" Programs 176 C. Training Teachers to Teach the "New Math" 190 Hi D. Dissemination 202 E. The Conflict Between Elementary School "New Math" and the Progressive Tradition in Education 207 F. The Neo-progressives 222 VII. CONCLUSION 235 VIII. REFERENCES 246 IX. ACKNOWLEDGMENTS 270 iv LIST OF TABLES Page Table 1, Topics covered in "new oath" college textbooks 95 Table 2. Comparison of two eleventh grade "new math" texts 138 Table 3. Elementary school "new math" textbook series 187 Table 4. NSF summer institutes for elementary school personnel (as announced in The American Mathe­ matical Monthly (1959-1960) and The Arithmetic Teacher (1961-1965)) 191 Table 5. Articles on geometry in The Arithmetic Teacher during selected five year periods 192 Table 6. Semester hours of mathematics required of future elementary school teachers in 1962 and 1966 194 Table 7. Popular magazine articles on elementary school "new math" 203 V LIST OF FIGURES Page Figure 1. Diagonal of a square 10 Figure 2. Euclid's fifth postulate 23 Figure 3. Growth In NCTM memberships during "new math" era 147 Figure 4. NSF expenditures on developing course content 149 1 I. PREFACE The 19508 and 19608 8aw a major upheaval In the content and viewpoint of school mathematics. The changes that took place during those years were part of a coherent movement to reform mathematics education. The various reforms advocated by the leaders of this movement became known collectively as the "new math." The present work is a history of the "new math" movement in the United States. This movement brought about change in the school mathematics curriculum on a scale and at a rate unknown before—or since. The 1970s and 1980s have seen a drift in the opposite direction. For example, there have been demands to go "back to the basics." While it is not always clear what is basic, such demands clearly challenge recent reforms and call for a return to a more traditional curriculum. Unfortunately, such reaction against the "new math" has often caused us to lose sight of its entirely valid criticisms of "old math." What is needed is not to go back, but to go forward more wisely. Part of that wisdom can come from examining the history of the "new math." The "new math" did more than simply criticize the old. It also provided answers to some of the problems of mathematics education. It did not answer every question, nor was every question that it answered answered correctly, but it did give some answers. These answers can be relevant to the educational problems of today. 2 For example, while writing this history, the author was teaching a remedial college mathematics course in beginning algebra. The chosen text was written as if the "new math" had never existed. A successful effort was made to have the text changed the next time the course was offered. The new text had as one of its coauthors a leader in the "new math" movement. The new text was not a "new math" book, but its authors had learned from the "new math," and what they learned made theirs a much better text. One of the purposes of this history is to prevent the lessons learned in the "new math" experience from being lost. Another purpose is to keep alive an awareness of basic issues in mathematics education that were raised by the "new math." There have been no previous attempts to write a history of the "new math." It is true that many articles, pamphlets, and books explaining "new math" appeared during the 1960s. These often contained a sketch of the historical background of the movement. However, none of these sketches pretended to be serious scholarly studies. They represented instead the Impressions of those involved in the movement in the nature of its roots. The one serious scholarly work that treats the "new math" is the Thirty-second Yearbook of the National Council of Teachers of Mathematics, A History of Mathematics Education in the United States and Canada (1970). Although this work is well-documented, it naturally only gives a part of its attention to the "new math." In addition, it puts too much emphasis on what was said about mathematics 3 education, by various experts and commissions, and too little emphasis on what was done. A final earlier work relevant to the present study is a history of the largest "new math" group written by one of its members (Wooton, 1965). While invaluable in its own area, the book is far too narrow to give an adequate appreciation of the entire movement and its origins. In writing the present work, an attempt has been made to make it as useful as possible. This attempt has influenced the final work in two main ways.