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

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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.

Mathematics in General Education
A report of the Committee on the Function of
Mathematics in General Education for the
Commission on Secondary School Curriculum
Progressive Education Association 1940
http//www.mathcurriculumcenter.org
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• Progressive Education Committee
• on the Function of Mathematics in General
  Education
• Appointed 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 attended
• secondary 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
Purpose of the Report
Address the communication gap between
mathematics and other disciplines. Defend the
relation of mathematics to the purposes
of general education. Assist teachers of
mathematics to better meet student needs.
Organization of the Report

• Part I Basic educational philosophy and role of
  the teacher
• Part II Problem solving
• Part IIIHelping students appreciate the
  development and nature
• of mathematics
• Part IVStudent as a human being, evaluating
  growth of the
• student toward the objectives of general
  education

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Purpose of General Education

• Development of adolescent
• Educational needs
• Ideals of democracy

• 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)

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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
  institutions
• that 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

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.

• 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)

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Mathematical Behaviors Growing Out of
Mathematical Experiences
Categories 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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Mathematical Behaviors

• 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

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Mathematical Behaviors

• 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 ones
  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 and
• distinguish between logical deduction, truth,
  and fact
• Symbolism
• effectively use symbols in and outside of
  mathematics

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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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Development of Mathematical Understandings
Teach for transfer of learning by focusing on
big mathematical ideas (e.g., formulation and
solutions). Provide applications of mathematics
to everyday situations. Connect history of
mathematics to the rest of history. Develop
aesthetic appreciation of mathematics.
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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Developments in Mathematics

• Mathematics was responding to the needs of the
  times in the areas
• of commerce, surveying, and architecture.
• Necessity not only driving factor curiosity,
  competition, and genius
• were appreciated.
• Connections were discovered between problems
  once viewed as
• unrelated, such as the relationship between
  conic sections and laws
• of motion.
• Practical applications were found for abstract
  mathematics, such as
• boolean algebra.
• Global influences on unification of school
  matheamtics included Felix
• Klein (Germany), John Perry (England) and E. H.
  Moore (United
• States).

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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 solvingstudents 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