New Math - Modern Exercises

Modern Exercises

Mathematicians describe their interesting objects with set-builder notation. This method of identification expands mathematical discussion beyond the stale exercises in common use. Under the stress of Russian engineering competition, American schools began to use textbooks based on set theory. For example, the process of solving an algebraic equation required a parallel account of axioms in use for equation transformation. To develop the concept of number, non-standard numeral systems were used in exercises. Binary numbers and duodecimals were new math to the students and their parents. Teachers returning from summer school could introduce students to transformation geometry. If the school had been teaching Cramer's rule for solving linear equations, then new math may include matrix multiplication to introduce linear algebra. In any case, teachers used the function concept as a thread common to the new materials.

It was stressed that these subjects should be introduced early. Some of this focus was seen as exaggerated, even dogmatic. For example, in some cases pupils were taught axiomatic set theory at an early age. The idea behind this was that if the axiomatic foundations of mathematics were introduced to children, they could easily cope with the theorems of the mathematical system later.

Other topics introduced in the New Math include modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra. Most of these topics (except algebraic inequalities) have been greatly de-emphasized or eliminated in elementary school and high school since the 1960s.