Task-solving in mathematics: the significance of visual imagery

Abstract

Mathematics education research argues that mathematical problem solving relies heavily on visualisation in its different forms and at different levels, far beyond the obvious field of geometry. Mathematics educators are thus encouraged and inspired to ‘see’ not only what comes ‘within sight’ but also what we are unable to see when reviewing their students’ work. The qualitative case study described in this paper speaks to this research as it examines the use of visualisation processes (as called visual imagery) in word problem solving. In our study, 17 Grade 11 learners participated in one-on-one task-based interviews. They answered 10 word problems, which we compiled in a worksheet, whose aim was to analyse the evidence of visual imagery in the participants’ solutions and problem solving strategies. To analyse this evidence, we developed a visual imagery analytical framework that facilitated the analysis of the participants’ responses in the worksheet, their interview transcripts as well as gestures in video-recordings. The findings suggest that developing tasks that encouraged the use of visual imagery to solve mathematical problems help learners to improve their problem solving functionality. Thus, all the 17 participants managed to use some kind of visual imagery during task-based interviews, although at different levels and in many different ways.