Mathematical learning and gesture Character viewpoint and observer viewpoint in students' gestured graphs of functions

This paper reports on a research project in mathematics education involving the use of gesture, movement and vocal sound to highlight mathematically salient features of the graphs of polynomial functions. Empirical observations of students' spontaneous gesture types when enacting elicited gestures of these graphs reveal a number of useful binaries (proximal/distal, being the graph/seeing the graph, within sight/within reach). These binaries inform an analysis of video-taped gestural and interview data and appear to predict teachers' assessments of student mathematical engagement and understanding with great accuracy. Reframing this data in terms of C-VPT and O-VPT adds a further layer of sophistication to the analysis and connects it with deeper findings in cognitive and neuroscience and gesture studies.