UNIVERSITY OF ILLINOIS COMMITTEE ON SCHOOL MATHEMATICS

I. Name

University of Illinois Committee on School Mathematics (UICSM)

II. Information

Inquiries may be addressed to Dr. Max Beberman, University of Illinois, 1208 West Springfield, Urbana, Illinois.

III. Date

1952‑

IV. Membership

The Committee is a joint committee of the College of Education, the College of Engineering, and the College of Liberal Arts and Sciences at the University of Illinois. Director of the program is Dr. Max Beberman.

V. Procedure

Since 1952, the University of Illinois Committee on School Mathematics has been working on materials of instruction, the development of teaching methods, and the training of teachers for a new curriculum in mathematics for the secondary schools. The UCISM has developed students' texts and teachers' guides for the four high school grades. These were used during 1957‑58 in 12 pilot schools by 40 teachers and about 1700 students. During the 195859 school year, 33 additional schools participated. The courses were used in 21 states and involved 104 teachers and over 3900 students. Since 1956, the Project has been supported largely by a $277,000 grant from the Carnegie Corporation of New York. In 1958 another grant of $282,600 was allocated to the Project.

VI. Grade Level

9-12

VII. Purpose

To develop materials and train teachers for a new secondary mathematics curriculum

VIII. Results and Recommendations

A. Considerations for courses

1. That the language of both textbook and teacher be made as

unambiguous as possible

2. That discovery of generalizations by the student be encouraged and fostered. This results in

a) power in mathematical thinking;

b) a developing interest in mathematics.

B. Content of the courses

1.First course

a. Distinction between numbers and numerals

b. Real numbers

c. Principles of real numbers (associativity, commutativity, etc.)

d. Inverse operations

e. Relations of inequality

f. Numerical variables ('pronumerals")

g. Generalizations about real numbers

h Notation and some concepts of the algebra of sets

i. Solution of equations, linear and quadratic

j. Solution of "worded" problems

k. Ordered pairs of numbers

j. Graphing equations and inequalities.

2. Second course

a. Sets and relations

b. Linear and quadratic functions

c. Systems of linear equations

d. Measures of intervals, arcs, angles, and plane regions

e. Elementary properties of angles, polygons, and circles

f. Further study of manipulations of algebraic expressions

3. Third course

a. Mathematical induction (generalizations, hereditary properties, recursive definitions, progressions, sigma‑notation)

b. Exponents and logarithms (continuity and the limit concept, geometric progressions, the binomial series)

c. Complex numbers (field properties, systems of quadratic equations)

d. Polynomial functions (the factor theorem, synthetic division, curve tracing)

4. Fourth course

a. Circular functions (winding functions, periodicity, evenness and oddness, monotoneity, "analytical trigonometry" rather than "triangle solving," inverse circular functions)

b. Deductive theories (abstraction of postulates from a model, deduction of theorems from these postulates without reference to a model, reinterpretation of the theory to yield information about other models)

C. Teachers associateship program

1. Purpose to provide long‑range dissemination of the program

2. Members college teachers who spent much of their time training teachers: supervisors from large school systems

3. Procedure:

a. Teacher associate takes a year's leave of absence and joins the staff at Urbana.

b. He teaches courses at the University High School, participates in staff seminars, corresponds with participating teachers, and visits pilot schools.

4. Results when the teacher associate returns to his own system the UICSM cooperate with him to improve teaching in his own locality.

D. Implications

The UICSM believes that (1) a consistent exposition of high school mathematics is possible; (2) high school students are greatly interested in ideas; (3) acquiring manipulative skill and understanding basic concepts are complementary activities. In the development of the program, topics from contemporary mathematics are used, but more concern is given to consistency than to up-to-dateness. Experience of the early years of the program indicates that contemporary mathematics contains much that is interesting and valuable for high school students. Also, high school teachers can teach these newer concepts when given help.