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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. 2-28-05

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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.

A report of the Committee on the Function of Mathematics in General Education for the Commission on Secondary School Curriculum

Progressive Education Association • 1940

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Mathematics in General Education

http://www.mathcurriculumcenter.org

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Progressive Education Committeeon the Function of Mathematics in General

EducationAppointed 1932

Impetus for the Committee Formation• Social and economic conditions were changing in light of the Great

Depression.

• Revised theories of learning were being implemented.

• Confidence in the educational values of mathematics was diminishing.

• Society educational needs were changing.

• More students were attending secondary school: in 1900, 11.4% attendedsecondary school compared to 64% in 1934.

• Curriculum for all students in school was needed.Goal of the Committee To examine “the study and teaching of mathematics for their values in relation to the whole process of general education.”

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Members of the PEA Committee

• Albert A. Bennett, Brown University

• Cuthbert Daniel, Editorial Consultant, Radio Research Project, Princeton University

• Harold Fawcett, Ohio State University School

• Maurice L. Hartung, University of Chicago

• Robert J. Havighurst, Director for General Education, General Education Board

• Joseph Jablonower, Board of Examiners, New York, N.Y.

• Ruth Kotinsky, Secretary of Commission on Secondary School Curriculum, PEA

• V. T. Thayer, Educational Director of Ethical Culture Schools; Chairman of Commission on Secondary School Curriculum, PEA

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Mathematics in General Education

Part I — Basic educational philosophy and role of the teacher

Part II— Problem solving

Part III—Helping students appreciate the development and natureof mathematics

Part IV—Student as a human being, evaluating growth of thestudent toward the objectives of general education

Purpose of the Report

Organization of the Report

• Address the communication gap between mathematicsand other disciplines.

• Defend the relation of mathematics to the purposes ofgeneral education.

• Assist teachers of mathematics to better meet studentneeds.

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Purpose of General Education

“The purpose of general education is to provide rich and significant experiences in the major aspects of living, so directed as to promote the fullest possible realization of personal potentialities, and the most effective participation in a democratic society.” (p. 43)

• Development of adolescent• Educational needs• Ideals of democracy

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Role of Mathematics in General Education

• Assist students in becoming knowledgeable consumers

• Improving the students’ ability to solve problems

• Familiarize students with persons, groups, and institutionsthat use mathematics

• Provide tools for analyzing social issues

• Instill social sensitivity in interpreting data

• Inspire the esthetic appreciation for mathematics

• Increase “mathematization” of all fields

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Role of Mathematics in Meeting Student Needs

“Problem is here to be interpreted not as an exercise of the traditional sort assigned for solution in mathematics classes, but as a difficulty appreciated by the student and awakening in him a desire for its solution.” (p. 44)

Adolescents encounter certain problems as they strive to meet their needs in the basic aspects of living. Helping them solve their problems is one way of helping them to meet their needs.

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Mathematical Behaviors Growing Out of Mathematical

ExperiencesCategories of mathematical behaviors seen as broadly applicable to the problem solving of life:

• Formulation and Solution

• Data• Approximation• Function• Operations• Proof• Symbolism

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Formulation and Solution• formulate and solve their own real-world problems• focus on the process of coming up with solutions to their

everyday problems

Data• gather and understand data• organize data• use tables and graphs

Approximation• use approximation in measurement• understand and use statistical concepts such as central

tendencies and measures of dispersion

Mathematical Behaviors

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Function• identify connections between what data says and if there is a

relationship• realize that the function concept is useful in many situations

Operations• move beyond the emphasis of drill and rote performance of

operations• identify importance and value in checking one’s answer

Proof• train the mind in logical thinking• understand logical proof and apply it in a variety of life

situations• use if-then statements, understand deduction and induction

anddistinguish between logical deduction, truth, and fact

Symbolism• effectively use symbols in and outside of mathematics

Mathematical Behaviors

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Organization of the Curriculum

• Concepts should not be taught in isolation.

• Curricular sequences should be planned on the basis of concrete problems, focusing on: personal living, immediate personal-social relationships, social-civic relationships, or economic relationships.

• Applications should be diverse, but applicable to more specific situations.

• Curricular decisions should strive to achieve the “values of the democratic way of life and to develop related desirable qualities of personality.” (p. 43)

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• Teach for transfer of learning by focusing on bigmathematical ideas (e.g., formulation and solutions).

• Provide applications of mathematics to everydaysituations.

• Connect history of mathematics to the rest of history.

• Develop aesthetic appreciation of mathematics.

Development of Mathematical Understandings

“In these days when one hears so often the accusation that mathematics is dull and without human interest, the teacher can ill afford to neglect the historical side-lights that may serve to illumine the whole subject for some students.” (Osborne, p. 264)

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• Mathematics was responding to the needs of the times in the areasof commerce, surveying, and architecture.

• Necessity not only driving factor; curiosity, competition, and geniuswere appreciated.

• Connections were discovered between problems once viewed asunrelated, such as the relationship between conic sections and lawsof motion.

• Practical applications were found for abstract mathematics, such asboolean algebra.

• Global influences on unification of school matheamtics included FelixKlein (Germany), John Perry (England) and E. H. Moore (UnitedStates).

Developments in Mathematics

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Far Reaching Implications

“If mathematics is to be a field for creative activity, the approach to problems must involve a type of investigational experience which is an adventure into the unknown--it must provide constant opportunity for discovery.” (p. 52)

“General classroom methods may lead to growth in intelligent self-direction in creativeness or may retard such growth.” (p. 51)

Teachers of mathematics have the responsibility to society to teach problem solving—students need to use this skill in all classes, as well as in life.

All activities should enable students to resolve a problem situation where intelligent decision making is needed.

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Significance of the Report

• Broad focus on mathematics beyond arithmetic, algebra, and geometry

• Direction given for dealing with diverse populations of students enrolling in school

• Extension of the curriculum to include components outside the typical academics

• Focus on problem solving and reflective thinking to preserve democracy

• Recommendations set aside as the focus of the world shifted to World War II