How can transforming representation of mathematical entities help us employ more cognitive resources?

Motor strength as a feature of concepts and visual representations

In this article, we define motor strength as the extent to which a concept is associated with body movements and the motor system that guides body movements. We extend this notion to one of the features of visual representations of some concepts and discuss the role of the motor system in understanding concepts and visual representations that have a significant degree of motor strength. It is suggested that when a concept is understood in its literal sense, the employment of the motor system and gestures in processing that concept depends on its degree of motor strength. If a concept is understood in its metaphorical sense, the employment of the motor system and gestures is dependent on the degree of motor strength of the base of the metaphor through which that concept is understood. The degree of motor strength of a concept relies on its motor affordances and its associations with people's past experiences. Because the motor system plays an essential role in the grounding of many abstract concepts in the physical environment, the notion of motor strength can help psychologists acquire a clearer understanding of how concepts with varying degrees of motor strength are grounded in the physical environment.

The role of perceptual and action effector strength of graphs and bases of mathematical metaphors in the metaphorical processing of mathematical concepts

Metaphors that describe an abstract concept in terms of a motion concept are widely used to enhance our understanding of abstract concepts. These metaphors are used not only in our daily language but also in learning mathematics. As an example, in the process of understanding the abstract representation of a mathematical concept, a graphical representation may play the role of a mediatory domain. This graphical representation could have a high degree of perceptual and action effector strength. This is particularly the case when a gestures (as a motion) is used to depict the graphical representation. After looking at this example, we discuss perceptual and action effector strength of the base domains of several mathematical metaphors that describe mathematical concepts in terms of spatial and motion concepts. Then, based on the data in the Lancaster Sensorimotor Norms, it is suggested that high degrees of perceptual and action effector strength of the base domains of these metaphors play an important role in the grounding of abstract mathematical concepts in the physical environment.