Toward a taxonomy of design genres: fostering mathematical insight via perception-based and action-based experiences, in

In a retrospective analysis of my own pedagogical design projects over the past twenty years, I articulate and compare what I discern therein as two distinct activity genres for grounding mathematical concepts. One genre, “perception-based design, ” builds on learners ’ early mental capacity to draw logical inferences from perceptual judgment of intensive quantities in source phenomena, such as displays of color densities. The other genre, “action-based design, ” builds on learners ’ perceptuomotor capacity to develop new kinesthetic routines for strategic embodied interaction, such as moving the hands at different speeds to keep a screen green. Both capacities are effective evolutionary means of engaging the world, and both bear pedagogical potential as epistemic resources by which to build meaning for mathematical models of, and solution processes for situated problems. Empirical studies that investigated designs built in these genres suggest a two-step activity format by which instructors can guide learners to reinvent conceptual cores. In a primary problem, learners apply or develop non-symbolic perceptuomotor schemas to engage the task effectively. In a secondary problem, learners devise means of appropriating newly interpolated mathematical forms as enactive, semiotic, or epistemic means of enhancing, explaining, and evaluating their primary response. Whereas my analysis distills activities into two separate genres for rhetorical clarity, ultimately embodied interaction may interleave and synthesize the genres ’ elements