Alternative approaches to teaching, learning and assessing mathematics

In this article I describe two different models of teaching mathematics and the different forms of knowledge that students developed in response to these. Five different assessments were used to assess students in two schools, as part of a longitudinal, ethnographic study of mathematics learning. The outcomes of these assessments are reported alongside the students' reflections of their knowledge use, within and outside school. Students at a 'traditional' school are shown to;have developed an inert knowledge that, they claimed: was of no use to them in the 'real world'. Students at a school using 'progressive' methods are shown to have developed more flexible and useful forms of knowledge that they were able to use in a range of settings. The results of the three-year study are used, both to problematise traditional models of teaching and assessing and to inform the perspective of situated cognition. (C) 1998 Elsevier Science Ltd. All rights reserved.