Deep and shallow approaches to learning mathematics are not mutually exclusive.

Abstract

From time to time, students are characterised as having a deep or shallow approach to learning. A deep approach to learning tends to attract more approval than a shallow approach, at least in the West. Students on a university-based Foundation course to prepare them for undergraduate studies were divided into those likely to have a deep approach (26) and those likely to have a shallow approach (18). Their performance in a test of problem solving in an aspect of applied mathematics was compared. Contrary to expectations, the test scores and interviews with the students indicated that those with a deep approach did not benefit when asked to apply their learning in new contexts, and those with a shallow approach were not markedly disadvantaged. It is suggested that, at least amongst learners, neither approach is likely to be entirely self-sufficient, but should be seen as acceptable starting points of potential routes to success. Although a small scale study, mathematics tutors should be able to relate the findings and suggestions to their own experiences and practices.