The role of gestural polysigns and gestural sequences in teaching mathematical concepts

In this paper, we examine the conceptual pedagogical value of representational gestures in the context of teaching halving to first graders. We use the concept of the ‘polysign’ as an analytical tool and introduce the notion of a ‘mathematics gesture sequence’ to assess the conceptual role gestures play in explicating mathematical concepts. In our study of four teachers each teaching a lesson on halving, they produced representational polysign gestures that provided multiple layers of information, and chained these gestures in mathematical gestural sequences to spatially represent the operation of halving. Their use of gestures and their ability to use gestures accurately to convey mathematical concepts varied. During the lesson, learners, whose teachers used few representational gestures or used gestures that were conceptually incongruent with the mathematical concept, expressed more confusion than learners whose teachers used conceptually appropriate gestures. While confusion can be a productive part of the learning process, our analysis shows that producing conceptually appropriate gestures may be important in mediating concepts and the transition from concrete and personal symbolic processes to institutional mathematical signs.