Teaching aids for the secondary school mathematics teacher

Abstract

Statement of Problem: Within the past fifteen years, educators at all levels have become aware of a deficiency in methods of teaching and the content of courses now being taught in mathematics. They feel that a refinement of certain areas of concepts is necessary and that much improvement can be attained. Of these areas, the concept of the "place-value" number system and the concept of "set" are discussed in this paper. Both are important to the "new look" in the field of mathematics.

Method of Procedure: To construct a "place-value" number system, a base must be laid upon which to build. This is done by making tables with a given base and discussing the basic operations of arithmetic, with which the reader is familiar, using this base. The base "7" is used here. Reference is made also to other bases. "Set" theory is introduced by taking an everyday concept of "set" and weaving a link to general logic and showing how it can be used in abstract logic.

Findings and Conclusions: "Place-value" number systems other than base "10" are useful. Base "2" is used in electrically operated machines, and base "12" has been considered as a very usable base. The structure of all those systems, however, is the same and can be learned using any base from which to work. "Set" is becoming more and more the basis for building mathematical concepts. It should be introduced and used in elementary school and developed as higher levels of schooling are attained. Many texts now are being written building large parts of the mathematical structure around "set."