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

1
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 Foundation. 2-15-05
2

Committees 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.
The Reorganization of Mathematics in Secondary
Education
National Committee on Mathematical Requirements
Final Report 1923
http//www.mathcurriculumcenter.org
3
The National Committee on Mathematical
Requirements (NCMR)
The Reorganization of Mathematics in Secondary
Education
Appointed by MAA 1916 Preliminary Report
1920Summary Report 1922Final Report 1923
4
Prepared in response to . . .
the conflict of opinions on the problems of
mathematics in secondary education with a focus
on the following questions

• What should be taught?
• How much of it?
• To whom?
• How?
• Why?

5
NCMR Members

• Mathematicians
• J. W. Young, chairman, Dartmouth College,
  Hanover, NH
• A. R. Crathorne, University of Illinois
• C. N. Moore1, University of Cincinnati
• E. H. Moore, University of Chicago
• David Eugene Smith,Teachers College, Columbia
  University
• H. W. Tyler, Massachusetts Institute of
  Technology
• Oswald Veblen1, Princeton University
• Representatives of secondary mathematics
  teachers associations
• J. A. Foberg, vice chairman, State Department of
  Public Instruction, Harrisburg, PA,
• Vevia Blair, Horace Mann School, Association of
  Teachers of Mathematics in the Middle States
• and Maryland
• W. F. Downey2, English High School, Boston
• G. W. Evans2, Charlestown High School, Boston
• Added later
• A. C. Olney, Commissioner of Secondary Education
  for California
• Raleigh Schorling, The Lincoln School, New York
  City
• P. H. Underwood, Ball High School, Galveston
• Eula A. Weeks, Cleveland High School, St. Louis

6
Organization of Report

• Two Major Parts
• General Principles and Recommendations
• Investigations Conducted for the Committee

7
Principles and Recommendations
Chapter 1 A brief outline of the
report Chapter 2 Aims of mathematical
instruction general
principles Chapter 3 Mathematics for grades 7,
8, 9 Chapter 4 Mathematics for grades 10, 11,
12 Chapter 5 College entrance
requirements Chapter 6 Listing of propositions
in plane and solid
geometry Chapter 7 The function concept in
secondary
mathematics Chapter 8 Terms and symbols in
elementary mathematics
8
Investigations Conducted for the Committee
Chapter 9 The present status of disciplinary
values in
education Chapter 10 The theory of correlation
applied to school
grades Chapter 11 Mathematical curricula in
foreign countries Chapter 12 Experimental
courses in mathematics Chapter 13 Standardized
tests in mathematics for
secondary schools Chapter 14 The training of
teachers of mathematics Chapter 15 Certain
questionnaire investigations Chapter 16
Bibliography on the teaching of mathematics
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Aims of Mathematical Instruction

• Practical Aims
• Disciplinary Aims
• Cultural Aims

The primary purposes of the teaching of
mathematics should be to develop those powers of
understanding and of analyzing relations of
quantities and of space which are necessary to an
insight into and control over our environment and
to an appreciation of the progress of
civilization in its various aspects, and to
develop those habits of thought and of action
which will make these powers effective in the
life of the individual. (NCMR, 1923)
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Practical Aims

1. Understand and apply the fundamental processes of
   arithmetic
2. Understand and use the language of algebra
3. Understand and use elementary algebraic methods
   to solve problems
4. Understand and interpret graphical
   representations
5. Be familiar with common geometric forms and their
   properties and relations develop and utilize
   space perception and spatial imagination

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Disciplinary Aims

• 1. Acquisition of mathematical ideas or concepts
  that promote quantitative thinking
• 2. Development of ability to think clearly in
  terms of such ideas and concepts
• 3. Acquisition of mental habits and attitudes
  which enable use of these ideas and concepts (1
  and 2 above) in the life of the individual
• 4. Development of functional thinkingthinking
  in terms of and about relationships between
  variables

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Cultural Aims

1. Appreciation of beauty in the geometrical forms
   found in nature, art, and industry
2. Appreciation of the importance of logical
   structure, precision of statement and of
   thought, logical reasoning, discrimination
   between the true and the false
3. Appreciation of the power of mathematics and the
   role that mathematics and abstract thinking have
   played in the development of civilization

13
Mathematics for Years 7, 8, 9
All junior high students in Grades 7, 8, and 9
should have the opportunity to study and attain
mathematical knowledge and training likely needed
by all citizens.

• Mathematics content should be presented in a
  correlated/unified fashion.
• Mathematics should focus on concrete and verbal
  problems instead of formal exercises.
• Mathematics should be practical for everyday
  life.

14
Mathematics for Years 7, 8, 9

• Recommended content
• Arithmetic
• Intuitive geometry
• Algebra
• Trigonometry

• Demonstrative geometry
• (optional)
• History
• Biography

Five models for junior high school course
sequencing were proposed, each reflecting some
variations of a basic model.
15
Basic Curriculum Model For Years 7, 8, 9 First
year Applications of arithmetic, particularly
as they relate to home, thrift, and to the
various school subjects such as intuitive
geometry.
Second year Algebra and applied arithmetic,
particularly as they relate to commercial,
industrial, and social needs. Third year
Algebra, trigonometry, demonstrative geometry.
In this model, arithmetic is practically
completed in the second year and demonstrative
geometry is introduced in the third year.
16
Mathematics for Years 10, 11, 12
All high schools should offer mathematics courses
for years 10, 11, 12 and encourage a large
proportion of students to take them.

• Courses should prepare students for possible
  vocations and life in the real world.
• Content should include ideas and processes
  important to contemporary applications.
• Material should be logically organized to
  facilitate the development of effective habits of
  mind.

17
Mathematics for Years 10, 11, 12
Recommended course offerings, in various
configurations, included

• Elementary calculus
• History
• Biography
• Additional electives

• Algebra
• Plane geometry
• Solid geometry
• Trigonometry
• Elementary statistics

Four plans for high school course sequencing with
slight variation to the above were proposed by
the Committee.
18
College Entrance Requirements

• Entrance requirements in mathematics should
  reflect the special mathematical knowledge and
  training required for the successful study of
  courses in the physical sciences and in the
  social sciences which the student will take in
  college.
• Entrance exams should
• Assess candidates ability to benefit from
  college instruction.
• Focus on elementary algebra and plane geometry.
• College admissions should be based on more than
  just
• test scores.

19
Propositions in Geometry
Identified a minimum set of propositions to be
included in any standard geometry course (reduced
list from the Committee of Fifteen)

• Selection based on
• Usefulness in other proofs and exercises
• Value in completing important pieces of theory

20
The Function Concept
Proposed use of function as a unifying concept in
the secondary curriculum

• At the junior high school level, function was
  seen embedded in and relevant to work with
  formulas, graphing, and interpretation of data.
• At the high school level, function provided a way
  of unifying the study of dependency relationships
  in algebra, geometry, trigonometry, and everyday
  life.

21
Terms and Symbols in Elementary Mathematics

• Recommended words and symbols to be used, and not
  to be used (e.g., trapezium)
• Proposed standardization of mathematical
  exposition in texts and mathematical journals
  (e.g. try to avoid vulgar mathematical slang such
  as tan, cos, and math)
• Proposed simplification of terms in elementary
  instruction

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Significance of 1923 NCMR

• Major areas of impact
• The purpose of mathematics in secondary education
  was defined and defended.
• The theory of mental discipline was rejected in
  favor of ideas of transfer.
• The function concept was suggested as a unifier
  of algebra and geometry.
• College entrance requirements were amended to
  include general tests to predict collegiate
  success in addition to examining achievement for
  specific mathematics courses.
• Model curricula were offered based on the work of
  the committee as well as descriptions of
  experimental work both nationally and
  internationally.

23
Significance of 1923 NCMR

• Other impacts
• The junior and senior high school curriculums
  (6-3-3) were solidified.
• An integrated course called general mathematics
  FOR ALL, less dominated by arithmetic, was
  created for junior high.
• New texts and methods were designed,
  nontraditional material was placed at the end of
  the book, implementation was minimal.
• Calculus was recommended for study in high
  school.
• Geometry texts with emphasis on thinking through
  original exercises, as opposed to memorization
  of book theorems evolved.
• Many Mathematics Teacher articles and yearbook
  chapters concerning the aims of mathematics were
  written in the two decades that followed.
• Teacher training programs began to include
  general knowledge, professional knowledge, and
  specialized knowledge.
• Mathematicians involvement with school
  mathematics increased.

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But ultimately. . . .

• No major change in practice was seen due to
  traditional inertia in educational practice and
  the depression of the 1930s.
• Over the next two decades, the views expressed in
  the Kilpatrick report, The Problem of Mathematics
  in Secondary Education, exerted more influence
  than the 1923 Report (Klein, 2003).

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References

• Bidwell, J. K., Clason R. G. (1970). Readings
  in the history of mathematics education.
  Washington, DC National Council of Teachers of
  Mathematics.
• Kilpatrick, W. H. (1920). The problem of
  mathematics in secondary education. A report of
  the Commission on the Reorganization of Secondary
  Education, appointed by the National Education
  Association. Bureau of Education Bulletin 1920,
  1, 1-24.
• Klein, D. (2003). A brief history of K-12
  mathematics education in the 20th century. In J.
  Royer (Ed.), Mathematical cognition. Information
  Age Publishing.
• National Committee on Mathematical Requirements
  (NCMR). (1923). The reorganization of
  mathematics in secondary education. The
  Mathematical Association of America.
• National Committee on Mathematical Requirements
  (NCMR). (1927). The reorganization of
  mathematics in secondary education (Part I).
  Boston Houghton Mifflin.
• National Council of Teachers of Mathematics.
  (1970). A history of mathematics education in
  the United States and Canada. Reston, VA
  National Council of Teachers of Mathematics.