Some processes through which mathematics is lost

Summary

This paper presents a detailed examination of a collection of mistakes made by people learning mathematics. The style of the reporting is anecdotal, but each anecdote is supported by a detailed analysis. All the research took place in classrooms with the aim of generating hypotheses rather than employing formal means of measurement.

There has been a tradition in mathematics teaching to regard mistakes simply as things to be corrected. In this paper that viewpoint is replaced by one which suggests that mistakes are a source of learning about the thought processes of others.

Attempting to bridge the gap between class teaching and educational research is not easy. The aim here is, in part, to show that close observation purely on a scale which can be managed by individuals in schools ‐‐ given the necessary time ‐‐ can yield insights on a level with research hypotheses.