Probing understanding through example construction: The case of integration

Abstract

Activities that reveal something about learners as they become aware of aspects of mathematical concepts that were not previously focussed upon can be very useful for the learners themselves as well as for teachers and researchers. In this paper I consider example construction tasks as research probes to reveal learners' awareness of the concept of integration. Forty students studying A-level, engineering, mathematics and education have been invited to construct relevant mathematical objects meeting specified constraints. What learners choose to change in mathematical examples reveals the dynamics and depth of their awareness and acts to promote and enrich their appreciation of the concept.