HANDLING PUPILS’ MISCONCEPTIONS

Abstract

This paper will briefly delineate a theory for learning mathematics as a basis to reflect on (some particular) misconceptions of pupils in mathematics. Such a theory should enable us • to predict what errors pupils will typically make • to explain how and why children make (these) errors • to help pupils to resolve such misconceptions. 1. THE ROLE OF THEORY Teachers are often wary of theory- they want something practical. Yet, as Dewey has said, “in the end, there is nothing as practical as a good theory. ” How come? Theory is like a lens through which one views the facts; it influences what one sees and what one does not see. “Facts ” can only be interpreted in terms of some theory. Without an appropriate theory, one cannot even state what the “facts ” are. Let me illustrate with a story, taken from Davis (1984). It is said that in Italy in the 1640’s, the water table had receded so far that a very deep well had to be sunk in order to reach water. This was done. Then pumps were fitted to the pipes, and... disaster!... no water poured out of the spigot. It was clear that something was wrong, but what? Their understanding of the situation, i.e. their theory of pumping water, was that it was the pumps that pulled (sucked) the water to the surface. So the fault had to be with

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