Problems of Teaching Topology in Schools

Extract

There is a natural argument about teaching topology in schools which goes something like this. Here is a modern subject that is flourishing at the research level, it is truly geometrical in flavour (more so than geometry itself we gather) and its elementary notions are more primitive in the learning of the young child (according to Piaget)f than the ideas of triangle, rectangle or circle. Moreover, we understand that, as well as having an intrinsic interest and beauty in itself, this subject has elegant applications in other branches of mathematics, such as the calculus, which we think of as part of the traditional syllabus in schools. Surely, then, there is the strongest possible case for bringing this topic to the attention of the children while their geometrical intuition is still uninhibited by perfectly straight lines and perfectly round circles and to give them the advantage of the more intuitive proofs of the theorems in calculus which topology can furnish.