Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A particularly important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. Conceptual metaphor theory, a branch of cognitive linguistics, describes how abstract mathematical concepts are grounded in concrete physical representations. In this paper, we consider the implications of this research for the metaphysics and epistemology of mathematics. In the case of metaphysics, we argue that (...) embodied mathematics is neutral in the sense of being compatible with all existing accounts of what mathematical entities really are. However, embodied mathematics may be able to revive an older position known as psychologism and overcome the difficulties it faces. In the case of epistemology, we argue that the evidence collected in the embodied mathematics literature is inconclusive: It does not show that abstract mathematical thinking is constituted by metaphor; it may simply show that abstract thinking is facilitated by metaphor. Our arguments suggest that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how we come to have knowledge of it. (shrink)

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body‐based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the cognitive relevance of particular body states to associated math concepts. We test competing models of action‐cognition transduction to investigate the cognitive relevance of directed actions to students’ mathematical reasoning in the area of geometry. The hypotheses we test include (1) that cognitively relevant directed actions have a direct (...) effect on performance (direct cognitive relevance hypothesis), (2) that cognitively relevant directed actions lead to more frequent production of gestures during explanations, which leads to improved performance (mediated cognitive relevance hypothesis), and (3) that performance effects of directed actions are influenced by the presence or absence of gesture production during mathematical explanations (moderated cognitive relevance hypothesis). We explore these hypotheses in an experiment where high school students (N = 85) evaluated the truth of geometry conjectures after performing cognitively relevant or cognitively irrelevant directed actions while playing a movement‐based video game. Contrary to the direct and mediated cognitive relevance hypotheses, we found no overall differences in performance or gesture production between relevant and irrelevant conditions. Consistent with the moderated cognitive relevance hypothesis, cognitive relevance influenced mathematical performance, as measured by the accuracy of students’ intuitions, insights, and the validity of their proofs, provided that students produced certain kinds of gestures during mathematical explanations (i.e., with explanatory gestures as the moderator). Implications for theories of grounded and embodied cognition and the design of embodied forms of educational interventions are discussed. (shrink)

Embodied cognition theory posits that concept representations inherently rely on sensorimotor experiences that accompany their acquisitions. This is well established through concrete concepts. However, it is debatable whether representations of abstract concepts are based on sensorimotor representations. This study investigated the causal role of associated motor experiences that accompany concept acquisition in the involvement of the motor system in the abstract verb processing. Through two experiments, we examined the action–sentence compatibility effect, in the test phase after an increase in motor (...) features during the learning phase for abstract verbs with low motor features or novel words with no conceptual features at all. After associated motor experiences were added in the word learning phase, action–sentence compatibility effect was found in the semantic processing tasks during the test phase for abstract verbs and novel words. This was lacking in the word font color judgment task requiring no semantic processing. Coupled with our previous study, these findings suggest that motor features formed during word learning could causally affect embodiment in the motor system for abstract verbs, and reactivation of motor experiences in abstract verb processing depends on a given task’s demands. Our study supports the view that conceptual representations, even abstract concepts, can be grounded in sensorimotor experiences. (shrink)