Embodied and dis-embodied affordances in mathematics education

In this paper, we discuss a two-way mechanism for acquiring mathematical knowledge: dis-embodied-to-embodied and embodied-to-dis-embodied shifts. Shifting from an embodied representation to a dis-embodied representation enables mathematics learners to discover general rules and patterns that can be applied to a wide range of mathematical problems, while shifting from a dis-embodied representation to an embodied representation allows mathematics learners to acquire a more graspable knowledge of mathematics. After discussing these two shifts in mode of processing, we describe a two-way mechanism through which a parallel employment of these two modes of thought allows mathematics learners to acquire a grounded and deep knowledge of mathematics. Therefore, any mathematics education program should engage learners in both modes of processing. Finally, we conclude that it is not possible to have an efficient education program by focusing on just one mode of mathematical thought.