This paper examines the conceptual pedagogical value of representational gestures in the context of teaching halving to first graders. It uses the concept of the ‘polysign’ as an analytical tool and introduces the notion of a ‘mathematics gesture sequence’ to assess the conceptual role gestures play in explicating mathematical concepts. In this 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, this 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.