Pre-service primary teachers' approaches to mathematical generalisation

Abstract

In our teaching with primary pre-service teachers (PSTs), each of us includes generalising tasks in the context of mathematical reasoning. We set out to explore the value of such activity from the perspective of PSTs and their approaches to generalisation. In this paper, we focus on one PST’s mathematical reasoning when working on the ‘flower beds’ problem. We analyse the ways in which this PST attends to: looking for a relationship; seeing structure within a single figure in a sequence; and seeing sameness and difference between figures in a sequence. We consider what motivates shifts in attention, we reflect on the significance of students’ prior experience, and of student collaboration in our teaching sessions.