A Technique of Presenting the Function Concept in the Secondary Schools

There are four main branches of mathematics; namely, algebra, geometry, analysis, and topology. The third, analysis, may be defined as the study of functions. The word, function is used commonly in a nonmathematical sense to denote simply the ideal of one thing depending on another. It may be said, A man\u27s success is a function of his ability and industry, even though the relationship involved cannot be expressed in mathematical terms. The theory of functions as the mathematician thinks of it was begun by the Frenchman, Augustin Cauchy (1789-1857). He was a civil engineer, but permitted his interest in theoretical mathematics to absorb the greater part of his time. In the high schools, students must face many problems. Sometime just the idea of numbers that are not known are represented by letters. The introduction of function has been invented to give an idea of the meaning or the relationship between two or more quantities. This shifting of mathematics has not reached its end, a considerable change may be anticipated as the result of the demand of modern science that the student be prepared to make constant use of the tools and concepts of mathematics. The writer wishes to show how the function concept may be taught in a high school algebra class