There are certain topics connected with the teaching of mathematics which seem to present themselves periodically for review. The aims or objectives of mathematical teaching is one of them ; the foundations of school mathematics is another. I have selected for review to-day one of the fundamental concepts of mathematics, that of functionality.

May I begin my discussion with a brief historical survey ? The idea that the function concept should have a prominent, even a dominant, place in the mathematical programme of the schools may be said to have originated with Klein. Others before him, in France, England and America, as well as in Germany, had advocated the inclusion of “ variables ” and “ functions ” in the school programme, but Klein was the first to press the view that “ functional thinking ” should be made the binding or unifying principle of school mathematics. Klein was equally distinguished as a mathematician and as a leader in the pedagogy of mathematics in Germany, but some years elapsed before his views became generally accepted, even in his own country.