Metaphor Retheorized



How does metaphor work? Actually, how do simile, metonymy, or synecdoche work? Let’s talk about learning to do stuff. When you’re learning to do something, and I suggest you do it as if you’re doing something else, how do you pick that up and run with it? So, pat your cat like you’re spreading butter. (Or, your cat is bread, your hand is the butter knife.) Immediately, we have introduced a constraint into your activity. The metaphorical instruction foregrounds selected sensorial features of the experience, and you modify your motor action so as to enhance your perception of those features. Perhaps you’re now patting softer, exuding the fur from your hand as a uniform voluminous substance, your gliding palm sensing the warm tingle of viscous velvety texture.


Traditionally, metaphor theories from cognitive linguistics have focused on motor action — the ‘doing’ of metaphorical instruction. We wish to foreground sensory perception — the ‘feeling’ of metaphorical instruction. Our approach draws on empirical research from enactivist philosophy, the movement sciences, and dynamic systems theory, that have demonstrated the formative role of imagery perception, including imagination, in the organization of motor action. When people learn from metaphor, they explore for motor actions that would enhance their sensory perception of target imagery. By “explore” we mean that this is a dynamical process of interacting with the environment, where unexpected sensations emerge in our experience, drawing our attention and reflection. Once we have distilled those sensations, figured out what motor actions enhance them, and practiced operating in this new way, we have grounded the metaphor in the target context. We may now molt the metaphor, as it has served its discursive function.


What is the relevance of all this for a research program on mathematics education? We theorize mathematics learning as grounded in developing new sensorimotor perceptual structures. In learning to do so, teachers can play important roles by attending to how students are making sense — literally — of the concept in question. But to do so, teachers must understand the sensorimotor perceptual constitution of mathematical concepts; they must shift their engagement with students toward discourse about sensorimotor perceptions; they must legitimize students’ idiosyncratic metaphor; they must make the invisible visible, the ineffable effable.


All this begins from teachers themselves shifting their attention to their own discreet phenomenology —  their subtle sensorimotor perceptions of mathematical concepts. These experiences are not arcane curiosities peripheral to the serious  paper-pushing rote work of manipulating symbolic notation. No, these experiences are the thing itself. Talking mathematics is talking action and sensation. Mathematics is (like) poetry. Learning is moving in new ways.