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.
Read more about this topic: New Math
Famous quotes containing the words modern and/or exercises:
“... in the fierce competition of modern society the only class left in the country possessing leisure is that of women supported in easy circumstances by husband or father, and it is to this class we must look for the maintenance of cultivated and refined tastes, for that value and pursuit of knowledge and of art for their own sakes which can alone save society from degenerating into a huge machine for making money, and gratifying the love of sensual luxury.”
—Mrs. H. O. Ward (1824–1899)
“Almost every man we meet requires some civility,—requires to be humored; he has some fame, some talent, some whim of religion or philanthropy in his head that is not to be questioned, and which spoils all conversation with him. But a friend is a sane man who exercises not my ingenuity, but me.”
—Ralph Waldo Emerson (1803–1882)