The constructive role of conceptual metaphor in children’s arithmetic: a comparison and contrast of Piagetian and embodied learning perspectives

The purpose of this paper is to propose that the notion of the conceptual metaphor, as defined in the theoretical framework of embodied learning, can have a role in the construction of children’s arithmetic and, in particular, in their invention of calculation strategies. In doing so it acknowledges the role of the sensory perceptual world in the development of children’s arithmetic. A Piagetian framework makes a distinction between an embodied world of learning and the operational world of arithmetic. The two theoretical frameworks are compared in relation to children’s realisation of the equality of commuted pairs in addition. The proposal is that the conceptual metaphor can be seen as an additional cognitive tool to explore children’s analogous reasoning in abstractions from the results of operations. The potential of the conceptual metaphor in this role would be to provide a theoretical framework to explore children’s development of arithmetic in terms of their everyday, perceptual experiences. In doing so it supports the notion of analogy as a key part in the creative process of arithmetic.