“ Mathematics as an Educational Task ”

The Background In these days of change and " progress " in education, we are placed in the position of needing the wisdom of Solomon to decide which of a wide variety of views is appropriate, if indeed any of them are. The wave of " new mathematics " began to sweep the country in the 60's and now in the 70's we are looking back at the improvements and the debris. On the one hand we have advocates of new teaching methods, on the other a traditionalist backbone asks for retention of old arithmetical skills taught by rote. It is not even a simple choice of old or new for there is an embarrassing choice of " new " methods in mathematics teaching. The developmental psychology of Jean Piaget has greatly influenced teaching of mathematics at the primary level with the Nuffield Mathematics Project, for example, taking Piaget's views as axiomatic. Politics have entered the fray with the great debate over comprehensive education. Sociologists, philosophers, curriculum theorists, manufacturers of educational aids, educationists of all shades of opinion have added their voices. One wonders whether mathematical education is an intellectual discipline or a growth industry-all of this against a background where the latest U.K. government figures tell us that there is a shortage of 1200 qualified mathematics teachers in schools. Literally thrown into the maelstrom like a gauntlet we have the text Mathematics as an Educational Task by Hans Freudenthal. It is a monumental work in mathematical education terms, collecting together the ideas which Professor Freudenthal has developed over the years, forming the most comprehensive corpus of thought on the subject ever published in a single volume by one man. For those committed to mathematical education it is an essential book to read. Professor Freudenthal is a considerable force to be reckoned with. He is a leading light in mathematical education in Holland having previously established himself as a research mathematician of the first rank. He is also a perceptive critic who will not flinch from exposing the charlatan or from strongly stating his views when he simply holds a different opinion from another whom he respects. For a long and consistent period he has applied his energies to