Title: This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI-0333879. The opinions and information provided do not necessarily reflect the views of the National Science
1This resource was developed by CSMC faculty and
doctoral students with support from the National
Science Foundation under Grant No. ESI-0333879.
The opinions and information provided do not
necessarily reflect the views of the National
Science Foundation. 3-6-05
2Committees and Reports that Have Influenced the
Changing Mathematics Curriculum
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 1959
http//www.mathcurriculumcenter.org
3Program for College Preparatory Mathematics
Report of theCommission on Mathematics1955-1959
College Entrance Examination Board New York
4What 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
5The 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).
6Commission Members
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
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
7Contents of the CEEB Report
- Chapter 1Orientation An urgent need for
curricular revision - Chapter 2Secondary Education The Commissions
premises - Chapter 3Recommendation The Commissions
program - Chapter 4Organization A proposed sequence for
the Commissions program - Chapter 5Implementation The vital role of
teacher education - Chapter 6Articulation The school and the
college
8The Commissions 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.
9RecommendationsNine-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 reasoningin 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 ideassets,
variables, functions, and relations - 5. Treatment of inequalities along with equations
10Nine-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
trigonometrycentered 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
11Mathematics for Grade 9Elementary 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)
12Mathematics for Grade 10Elementary Mathematics
II
- Informal geometry
- Deductive reasoning
- Sequence of theorems culminating in the
Pythagorean theorem - Coordinate geometry
- Additional theorems and originals
- Solid geometry
13Mathematics for Grade 11Intermediate 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
14Mathematics for Grade 12Advanced
MathematicsThree Possible ProgramsFirst
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 3 Selected topics that largely
included extensions of topics from the first
semester
Option 1 Introduction to probability with
statistical applications
Option 2 Introduction to modern algebra
(fields and groups)
15Teacher Education
- Secondary school teachers are the key to
carrying out the Commissions 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.
16Reactions 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).
17Reactions 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).
18ArticulationSecondary 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.
19Significance 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 Commissions intentions
(historical significance)
20References
- 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, 7-12. In P. Jones (Ed.), A history
of mathematics education in the United States and
Canada (32nd Yearbook pp. 235-266). Reston, VA
National Council of Teachers of Mathematics.