Transforming dis-embodied mathematical representations into embodied representations, and vice versa: a two-way mechanism for understanding mathematics

Since formal mathematics is discussed in terms of abstract symbols, many students face difficulties to acquire a clear understanding of mathematical concepts and ideas. Transforming abstract or dis-embodied representations of mathematical concepts and ideas into embodied representations is a strategy to make mathematics more tangible and understandable. This representational transformation allows us to actively employ our sensorimotor resources in the process of mathematical understanding. However, a one-way transformation of dis-embodied mathematical representations into embodied representations cannot always be the best strategy to understand mathematics. In order to omit or suppress contextually irrelevant information, we may need to transform an embodied representation into the dis-embodied representation. In other words, a dynamic mechanism in which the individual shifts between the two types of representational transformation could be the best way to acquire a better understanding of mathematical concepts/ideas and solve mathematical problems.