Chapter 18. Seeing the graph vs. being the graph

This study is situated within a body of new work in mathematics education that involves studies of gesture, kinesthetic learning and embodied metaphor and mathematical understandings (for example, Lakoff & Núñez, 2000; Nemirovsky & Borba, 2003; Goldin-Meadow, Kim & Singer, 1999). This chapter reports findings from the first two years of the author’s multi-year study exploring variations of secondary students’ gestures when asked to describe mathematical graphs. Three diagnostic categories emerged from this data with regard to learners’ degree of imaginative engagement and ability to notice mathematically salient features when encountering graphs.