1 This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI The opinions and information provided do not necessarily reflect the views of the National Science Foundation

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. Final Report of the MAA/NCTM Joint Commission The Place of Mathematics in Secondary Education

3 The Place of Mathematics in Secondary Education Final Report of the Joint Commission of the Mathematical Association of America and the National Council of Teachers of Mathematics The National Council of Teachers of Mathematics Fifteenth Yearbook, 1940

4 The 1930s Dominant Forces School population was increasing due to a growing commitment of families to universal secondary education and to new school attendance laws. Social utility was primary determinant of content. Percentage of students enrolling in mathematics courses was decreasing. Students were dissatisfied with the mathematics curriculum. Large numbers of students were failing secondary school mathematics. Uncertain economic outlook fostered a sense of aimlessness and lack of enthusiasm among young people. Important Issues Is mathematics just a “tool subject?” How best to accommodate individual differences in an increasingly diverse student population? Is drill the best way to teach a child mathematics?

5 A Response from the Mathematics Community The Joint Commission of MAA and NCTM members was organized to take over the work of separate committees studying secondary mathematics The Commission made very little progress up to this point; however, they received a $6,500 grant from the General Education Board to complete the work The Commission published The Place of Mathematics in Secondary Education which became the 15th Yearbook of NCTM.

6 The Joint Commission Representing the Mathematical Association of America K. P. Williams, Chairman, Indiana University, Bloomington, IN A. A. Bennett, Brown University, Providence, RI H. E. Buchanan, Tulane University, New Orleans, LA F. L. Griffin, Reed College, Portland, OR C. A. Hutchinson, University of Colorado, Boulder, CO H. F. MacNeish, Brooklyn College, Brooklyn, NY U. G. Mitchell, University of Kansas, Lawrence, KA Representing the National Council of Teachers of Mathematics William Betz, Rochester Public Schools, Rochester, NY M. L. Hartung, University of Chicago, Chicago, IL G. H. Jamison, State Teachers College, Kirksville, MO Ruth Lane, State University of Iowa, Iowa City, IA J. A. Nyberg, Hyde Park High School, Chicago, IL Mary A. Potter, Supervisor of Mathematics, Racine, WI W. D. Reeve, Teachers College, Columbia University, New York, NY

7 The Place of Mathematics in Secondary Education IntroductionThe Role of Mathematics in Civilization Chapter 1Looking at Modern Education and its General Aims Chapter 2General Objectives for Secondary Education Chapter 3The Place of Mathematics in Education Chapter 4The Mathematics Curriculum Chapter 5On Distribution and Organization of the Materials of Instruction, Grades 7-12 Chapter 6 A Second Curriculum Plan Chapter 7 The Problems of Retardation and Acceleration Chapter 8 Mathematics and the Junior College Chapter 9 Evaluation of the Progress of Pupils Chapter 10 The Education of Teachers

8 Secondary Education Objectives Ability to think clearly - gathering and organizing data - representing data - drawing conclusions - establishing and judging claims of proof Ability to use information, concepts, and general principles Ability to use fundamental skills Desirable attitudes - respect for knowledge - respect for good workmanship - respect for understanding - social-mindedness - open-mindedness Interests and appreciations Other objectives - health - citizenship - worthy home membership

9 The Place of Mathematics in Education School mathematics contributes in important ways to the achievement of secondary education objectives. Mathematical Study as Training in Clear Thinking Mathematical Information, Concepts, and Principles Mathematical Skills Mathematics and Desirable Attitudes Mathematical Appreciations Remarks All mathematically capable students should take as much mathematics as possible in secondary school. Mathematics is so important in our civilization that a minimum education in mathematics leads to limitations in the choice of a profession later in life.

10 The Mathematics Curriculum Since mathematics has a cumulative nature, a mathematics program should be formed as a connected sequence of units, that is, it should unify concepts of mathematics. Basic considerations –Continuity and organic growth –The importance of flexibility –The work of elementary schools A tentative list of guiding principles –Considerations governing the selection of materials of instruction, grades 7-12 –Principles of arrangement Mathematical categories as a basis of organization of the curriculum –Expressing the mathematics curriculum in terms of broad categories Essentials of a general program in secondary mathematics Guiding principles for selecting curriculum materials and the sequencing of the materials:

11 A Complete Mathematics Curriculum Number and Computation Geometric Form and Shape Perception Graphic Representation Elementary Analysis Logical (or Straight) Thinking Relational Thinking Symbolic Representation and Thinking The Commission recommended a complete curriculum for grades 7 to 12 that covered the following areas:

12 Number and Computation Basic Concepts and Principles Students should be able to name or identify concepts; give examples or informal explanations of the terms; develop formal definitions of terms (e.g. operations, rounding of numbers, relations, ratio, proportion, equality, increase, decrease, etc.). Fundamental Skills Students should be able to use the four basic operations with integers, fractions, and decimals; use the measurement units in real life; read simple numerical tables.

13 Geometric Form and Shape Perception Basic Concepts Students should be able to name figures; sketch or draw figures to illustrate geometric terms; develop formal definitions of basic terms (parts of figures, geometric relationships, etc.). Fundamental Skills Students should be able to draw, measure, and construct common geometric figures; develop essential geometric relationships.

14 Graphic Representation Basic Terms and Concepts Students should be able to name or identify concepts; give examples or informal explanations of the terms; develop formal definitions of terms (ordinate, axis, coordinate, distance, tangent, line, slope, graph, symmetry, etc.). Fundamental Skills Students should be able to construct a graph (with an appropriate scale and title) to represent a set of data from a table; interpret a given graph; (optional) draw a line that fits data that are approximately linear.

15 Elementary Analysis Basic Concepts Students should be able to name or identify concepts; give examples or informal explanations of the terms; develop formal definitions of terms (types of number, operations, structural and functional terms, etc.). Fundamental Principles Students should be able to use the fundamental principles of algebra and elementary analysis in related applications.

16 Logical (or Straight) Thinking Basic Terms and Concepts Students should be able to understand the basic terms; recognize actual use of terms in real life (assumption or postulate, proposition, converse, conclusion, etc.). Fundamental Principles Students should be able to understand the assumptions and principles on which the structure of mathematics is based.

17 Relational Thinking Basic Concepts Students should be able to recognize, name and define terms (constant, variable, independent and dependent variable, one-to- one correspondence, function, formula, table, etc.). Fundamental Skills and Abilities Students should be able to read tables of values; calculate formulas for values of independent variables; interpolate in tables and graphs; construct appropriate formulas from contexts; determine the constants for formulas to approximately fit a set of given data; recognize functional dependence.

18 Symbolic Representation and Thinking Students should be able to translate quantitative statements into symbolic form and conversely, and appreciate the power of such translation.

19 Further Recommendations The Commission provided two alternative curriculum organizations for grades The Commission also made recommendations addressing specific concerns in education during this period. Retardation and acceleration Junior colleges and general mathematics Evaluation and testing Education of teachers of mathematics

20 Significance of the Commission The authors “were able to rise above the negativism surrounding mathematics in the 1930s to produce positive, forward-looking statements” (NCTM 32nd Yearbook, p. 230). “While other forces were tending to produce a fragmented curriculum of brief, specialized courses in ‘consumer’ mathematics, the Commission made impressive pleas for the cultural and disciplinary values of a curriculum built around broad, unifying concepts” (NCTM 32nd Yearbook, p. 230). The commission “constructed what they felt was a blueprint for a program in mathematics that could stand on its own merits” (NCTM 32nd Yearbook, p. 230). It was not apologetic in its tone.

21 References Betz, W. (1940). The present situation in secondary mathematics, with particular reference to the new national reports on the place of mathematics in education. The Mathematics Teacher, 33(8), Breslich, E. R. (1940). Presenting the report of the Joint Commission to the National Council of Teachers of Mathematics. The Mathematics Teacher, 33(4), Douglass, H. R. (1940). Two important deliberative reports concerned with mathematics in the schools. The Mathematics Teacher, 33(8), Hartung, M. L. (1940). Some suggestions to readers of two recent reports on the mathematics curriculum. The Mathematics Teacher, 33(8), Joint Commission of the MAA and the NCTM. (1940). The Place of Mathematics in Secondary Education. Fifteenth Yearbook of the NCTM. New York, NY: Bureau of Publications, Teachers College, Columbia University. Jones, P. S. (Ed.). (1970). A history of mathematics education in the United States and Canada. Reston, VA: National Council of Teachers of Mathematics. National Committee on Mathematical Requirements. (1923). The reorganization of mathematics in secondary education. The Mathematical Association of America, Inc. Osborne, R. A., & Crosswhite, F. J. (1970). Forces and issues related to curriculum and instruction, In P. S. Jones (Ed.), A history of mathematics education in the United States and Canada (pp ). Reston, VA: National Council of Teachers of Mathematics. Potter, M. A. (1940). The two recent national reports on mathematics in general education. The Mathematics Teacher, 33(8), 370.