Where is the bigger picture in the teaching and learning of mathematics?

Abstract

This article presents an interpretive analysis of three different mathematics teaching cases to establish where the bigger picture should lie in the teaching and learning of mathematics. We use pre-existing data collected through pre-observation and post-observation interviews and passive classroom observation undertaken by the third author in two different Grade 11 classes taught by two different teachers at one high school. Another set of data was collected through participant observation of the second author’s Year 2 University class. We analyse the presence or absence of the bigger picture, especially, in the teachers’ questioning strategies and their approach to content, guided by Tall’s framework of three worlds of mathematics, namely the ‘conceptual-embodied’ world, the ‘proceptual-symbolic’ world and the ‘axiomatic-formal’ world. Within this broad framework we acknowledge Pirie and Kieren’s notion of folding back towards the attainment of an axiomatic-formal world. We argue that the teaching and learning of mathematics should remain anchored in the bigger picture and, in that way, mathematics is meaningful, accessible, expandable and transferable.