The Missing Bodies of Mathematical Thinking and Learning Have Been Found

For a long time, the body has had a bad rap among some big names in the Western philosophical tradition. Plato and Descartes come quickly to mind as particularly bad rappers (cue Monty Python-esque skit). But it appears that the body is making a comeback in the cognitive and learning sciences. Long banished from the main stage by an idealized, inside-the-head information-processing worldview, the body is steadily being rediscovered in the work of thinking and learning. I say rediscovered because there have been substantive anticipations of this movement in 20th-century philosophical traditions like phenomenology and later Wittgenstein, and then in recent empirical extensions of these philosophical ideas in ethnomethodology and conversation/interaction analysis. In the current cognitive and learning sciences that are rediscovering the body, these anticipations are not always acknowledged. A reasonably active mind has been with us since the beginning of the so-called cognitive revolution. That active mind is now being reintroduced to a sensing, feeling, thinking body in action. Mathematics has commonly been construed as among the forms of human activity most distant from the body’s experiences and its understandings (Rotman, 1993). As early as high school geometry, we are taught that our intuitions about line segments drawn on paper, with their minimal thickness and finite lengths, mislead us from the real phenomena of geometry, “lines” that go on infinitely across imagined infinite planes, lines without thickness. We are told that if we wish to understand“abstractions”—whatmanyregardas the realphenomenaofdisciplinary mathematics—we must do it through tangible but misleading objects, marks, and movements. These teachings have a long history. “Plato [said] that numbers and