The role of executive functions in symbolic and situational mathematical abilities

In this paper, we discuss the role of executive functions in shifting between symbolic and situational mathematical representations. Through the process of inhibition, an abstract representation is separated from concrete features and represented in terms of abstract symbols. This is a shift from a situational representation to a symbolic one. Cognitive flexibility can play an important role in the opposite direction of this shift. This involves a shift from an abstract mode of thought to a concrete mode. Since this change starts with the processing of a symbolic representation, areas of the brain that handle symbolic representations are initially activated. As there is a move toward a situational representation, sensorimotor networks become more and more activated because situational representations have more sensorimotor features than symbolic representations. We call this process meta-embodiment. Meta-embodiment enables the individual to actively employ sensorimotor networks to create new concrete situational representations on the basis of already-known symbolic representations. This is an ability that allows the individual to connect to a situational representation in the concrete environment, to perceive it by active employment of sensorimotor networks, and to find out how it fits into an already-known symbolic representation. Finally, educational implications of our proposal are discussed.