All experts agree that mere possession of information is of little value in mathematics. To know mathematics means to be able to do mathematics, to use matheamtical language, to find the unknown, to check a proof and so on. Therefore to teach mathematics, we must give opportunity to the student to do mathematics. There are many ways of doing mathematics, but from several view points, solibf problems appears as the most cardinal mathematical activity. In fact, solving problems may be considered as the specific achievment of intelligence, and intelligence is the special giftm of mankind. Solving mathematical problems at thier level comes early and quite spontaneously to some children, and I think that all children could be made ready for it pretty early by the right approach. At any rate, higher matheamtical activities(such as framing new concepts, building theories, constructing axiomatic systems) presuppose considerable mathematical experience which must be acquired mainly by solving problems. Hence it is well justified that all mathematical textbooks beginning with the Rhind Papparus contain problems. The problems may even be regarded as the most essential contents of textbooks and problem solving by the students as the most essential component of mathematical instruction.
G.Polya
