7 - Journeys through Embodiment and Symbolism

Summary

In this chapter we make a more detailed analysis of the parallel development of embodiment and symbolism as children learn to count collections of objects, to operate with whole numbers, and move on to fractions, signed numbers and the generalized arithmetic of algebra.

Following the vision of Bruner, one would expect a steady growth from enactive and iconic representations to symbolic representations in a transition from the actions and perceptions of the embodied world to the operations in the symbolic world. A closer analysis of the relationship between embodiment to symbolism reveals a more subtle story.

When performing operations on objects, the attention may focus on the objects, on how to perform the operations, or both. The operational compression from process to mental object has two aspects, which I term embodied compression, focusing on the objects and symbolic compression focusing on the symbols. Focusing on the objects offers the possibility of sensing what happens as a consequence of the operation. It has an effect that can be seen.

For instance, once the child realizes that counting a set is independent of the order of counting then the positioning of the objects doesn’t matter and counting a set of ‘two’ and ‘four’ to give ‘six’ can be seen to give the same result as rearranging the objects and counting ‘four’ and ‘two’. Shifting one of the four objects over to the other collection gives ‘three and three’, which is also ‘six’. Lining them up in rows gives ‘two lots of three’ or ‘three lots of two’. Focusing on the embodied effect of an operation encourages a general sense of the relationships between operations and numbers.