Arithmetical abstractions—progress toward maturity of concepts under differing programs of instruction

Abstract

The assumption basic to my investigation is that school instruction in arithmetic should be organized to help children to think abstractly about quantitative matters, and that to achieve this end they need to acquire a large body of mathematical concepts and be able to use intelligently another large body of mathematical relationships, generalizations, and principles. I doubt that many will quarrel with this assumption. Differences of opinion center around the particular mathematical content to be taught and around the rate at which children should be urged toward abstractions.