Embodied Action, Effect and Symbol in Mathematical Growth

This study of the learning of vectors is situated in the intersection of embodied theory relating to physical phenomena, and process-object encapsulation of actions as mathematical concepts. We consider the subtle effects of different contexts such as vector as displacement or force, and focus on the need to create a concept of vector that has greater flexibility. Our approach refocuses the development from ‘action to process’ as a shift of attention from ‘action to effect’ in a way that we hypothesise is more meaningful to students. At a general level we embed this development from enactive action to mental concept within a broad theoretical perspective and at the specific level of vector we report initial experimental data.