Committees and Reports that Have Influenced the Changing Mathematics Curriculum

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. 2-28-05

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. 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

3. 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.”

4. 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

5. 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. Part I — Basic educational philosophy and role of the teacher Part II— Problem solving Part III—Helping students appreciate the development and nature of mathematics Part IV—Student as a human being, evaluating growth of the student toward the objectives of general education Organization of the Report

6. 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)

7. 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

8. “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) 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.

9. 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

10. 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

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

12. 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)

13. 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)

14. 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).

15. 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.

16. 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