1 This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI The opinions and information provided do not necessarily reflect the views of the National Science Foundation

2 This set of PowerPoint slides is one of a series of resources produced by the Center for the Study of Mathematics Curriculum. These materials are provided to facilitate greater understanding of mathematics curriculum change and permission is granted for their educational use. Program for College Preparatory Mathematics College Entrance Examination Board Commission on Mathematics Committees and Reports that Have Influenced the Changing Mathematics Curriculum

3 College Entrance Examination Board New York Report of the Commission on Mathematics Program for College Preparatory Mathematics

4 What stimulated this report? Emerging national concern for excellence in education Organized efforts to provide improved programs for gifted students Recent developments in mathematics and its applications not reflected in secondary school curricula Continuing debate over goals of school mathematics: disciplinary, utilitarian, and cultural Mounting criticism of secondary education by the popular press

5 The College Entrance Examination Board (CEEB) Commission Research Mathematicians High School Teachers Teachers of Teachers of Mathematics These three groups were the ones most immediately concerned with mathematics in the schools. “The purpose of the Commission on Mathematics was ‘to review the existing secondary school mathematics curriculum, and to make recommendations for its modernization, modification, and improvement’” (NCTM, 32nd Yearbook, p. 73).

6 Commission Members Albert W. Tucker (Chairman) Princeton University Albert E. Meder, Jr. (Executive Director) Rutgers University Samuel S. Wilks Princeton University George B. Thomas, Jr. M.I.T. Frederick Mosteller Harvard University Carl B. Allendoerfer University of Washington Howard F. Fehr Teachers College, Columbia University Eugene P. Northrop University of Chicago Henry Van Engen Iowa State Teachers College Edwin C. Douglas The Taft School, Connecticut Martha Hildebrandt Proviso Township High School, Illinois Morris Meister Bronx High School of Science, New York Robert E. K. Rourke Kent School, Connecticut Ernest R. Ranucci Weequahic High School, New Jersey

7 Contents of the CEEB Report Chapter 1—Orientation: An urgent need for curricular revision Chapter 2—Secondary Education: The Commission’s premises Chapter 3—Recommendation: The Commission’s program Chapter 4—Organization: A proposed sequence for the Commission’s program Chapter 5—Implementation: The vital role of teacher education Chapter 6—Articulation: The school and the college

8 The Commission’s Premises All students who are “college-capable” should take as much mathematics as possible in secondary school. High school students should be taught in two tracks so that the gifted students can proceed to the more challenging material. New areas of mathematics, such as probability and statistics, modern algebra, and mathematical logic should be included in the secondary school curriculum. Prospective secondary school teachers should take four years of mathematics while in high school.

9 Recommendations Nine-Point Program 1.Strong preparation, both in concepts and skill, for college mathematics at the level of calculus and analytic geometry 2.Understanding of the nature and role of deductive reasoning—in algebra, as well as in geometry 3.Appreciation of mathematical structure (patterns)— properties of natural, rational, real, and complex numbers 4.Judicious use of unifying ideas—sets, variables, functions, and relations 5.Treatment of inequalities along with equations

10 Nine-Point Program (cont.) 6.Incorporation with plane geometry of some coordinate geometry, and essentials of solid geometry and space perception 7.Introduction in grade 11 of fundamental trigonometry— centered on coordinates, vectors, and complex numbers 8.Emphasis in grade 12 on elementary functions (polynomial, exponential, circular) 9.Recommendation of additional alternative units for grade 12: either introductory probability with statistical applications or an introduction to modern algebra

11 Mathematics for Grade 9 Elementary Mathematics I Operations with simple algebraic expressions Positive and negative numbers Linear equations and inequalities in one variable Variation (optional) Linear equations and inequalities in two variables Polynomial expressions Rational (fractional) expressions Informal deduction in algebra Quadratic equations Descriptive statistics (optional) Numerical trigonometry of the right triangle (optional)

12 Mathematics for Grade 10 Elementary Mathematics II Informal geometry Deductive reasoning Sequence of theorems culminating in the Pythagorean theorem Coordinate geometry Additional theorems and originals Solid geometry

13 Mathematics for Grade 11 Intermediate Mathematics Basic concepts and skills (the real number system) Linear functions Radicals Quadratic functions and equations Systems of equations Exponents and logarithms Series Number fields Plane vectors Coordinate trigonometry Trigonometric formulas

14 Mathematics for Grade 12 Advanced Mathematics Three Possible Programs First Semester Elementary Functions Sets and combinations Functions and relations from a set theoretic approach Polynomial functions Exponential functions Logarithmic functions Circular functions Second Semester Option 1 Introduction to probability with statistical applications Option 2 Introduction to modern algebra (fields and groups) Option 3 Selected topics that largely included extensions of topics from the first semester

15 Teacher Education Secondary school teachers are the key to carrying out the Commission’s program. New courses and programs need to be designed to in-service the secondary school teachers during the summer months. Undergraduate programs should include a study of contemporary mathematical content. Undergraduate preparation must include pedagogical content.

16 Reactions to the Report “After hundreds of speeches and articles which dealt with symbolic logic, topology, abstract algebra, and sets and after creating uneasiness and alarm among teachers over all the country, the Commission has ended up with few real changes and these are undesirable. Of all the new topics only the notion of sets is retained and this is used to make the solution of equations, the concept of function, coordinate geometry, and a few other topics more abstract and hence less teachable” (Kline, 1960, p. 62).

17 Reactions to the Report Edward Begle (director of the School Mathematics Study Group) commented that the formation of the Commission on Mathematics was, “probably the most important step in the improvement of the mathematics curriculum in the United States” (Begle, 1963, p. 137).

18 Articulation: Secondary School to College College entrance requirements Due to curricular changes, some subject unit requirements no longer have precise definitions. Cooperative action between schools and colleges can avoid roadblocks to students. New designations needed Colleges requiring three years of high school mathematics may specify the requirement as Elementary Mathematics I & II and Intermediate Mathematics. Colleges requiring four years of mathematics may specify Advanced Mathematics as well as the above College Board test requirements Tested subject matter will not change immediately but will do so over time to give schools time to adapt.

19 Significance of the Report Recommended new and more abstract, higher-level mathematical topics for high school Omitted discussion of consumer mathematics Facilitated the “new math” movement Provided a framework that guided revisions of mathematics curricula, particularly that of the School Mathematics Study Group (SMSG) Produced a statistics/probability textbook to demonstrate the Commission’s intentions (historical significance)

20 References Begle, E. G. (1963). The reform of mathematics education in the United States of America. In H. Fehr (Ed.), Mathematical Education in the Americas. New York: Bureau of Publications, Teachers College, Columbia University. Commission on Mathematics. (1959). Appendices. New York: College Entrance Examination Board. Commission on Mathematics. (1959). Program for college preparatory mathematics. New York: College Entrance Examination Board. Kline, M. (1960, April). New curriculum or new pedagogy? New York State Mathematics Teachers Journal, 10, 62. National Council of Teachers of Mathematics. (1970). A history of mathematics education in the United States and Canada (32nd Yearbook). Reston, VA: National Council of Teachers of Mathematics. Osborne, A. R., & Crosswhite, F. J. (1970). Forces and issues related to curriculum and instruction, In P. Jones (Ed.), A history of mathematics education in the United States and Canada (32nd Yearbook; pp ). Reston, VA: National Council of Teachers of Mathematics.