6. One of the most curious characteristics of American secondary-mathematics instruction is the obscurity in the teaching of the function notion. It is generally agreed that functional thinking (the dependence of one magnitude upon another) constitutes one of the most fundamental notions of mathematics. Because of the interrelations of the equation, the formula, the function, the graph, and the geometric relations inductively acquired, the material is easily correlated around the function idea as the organizing and unifying principle. The function concept (implicitly or explicitly) dominant throughout helps to lend concreteness and coherence to the subject. However, it would be false to assume that this material is presented to establish the principle of correlation. On the contrary, it happens that correlation around the function notion, though incidental, is a valuable instrument for accomplishing the larger aim, which is to obtain a composite introductory course in mathe maties that all future citizens of our democracy should be required to take as a matter of general scholarship.

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