“Single paper” presented at the annual meeting of the European Association for Research on Learning and Instruction (EARLI) Special Interest Groups 10, 17, 21 & 25. University of Augsburg, Augsburg, Germany.
ABSTRACT: Solving geometry problems often depends on introducing auxiliary lines to reveal latent structural relations among figurally disparate diagrammatic components. Yet generating such lines is challenging, as students must envision new elements that are not yet materially available. Meanwhile, a phenomenologically comparable dynamic occurs in movement learning, such as in dance: to coordinate the enactment of independent multi-limb actions, dancers generate attentional anchors—imagined perceptual structures that coherently organize kinesiological intentionality. Building on Reed and Bril’s theoretical construct field of promoted action, the Geometry Resources in Dance (GRiD) design-based research project conjectures that, given appropriate cultural mediation that includes semiotic resources and attentive guidance, students can objectify their covert attentional anchors from dance practice as overt auxiliary lines for geometry discourse. We report on results from micro-analyzing the multimodal social interactions of four Balinese 5th-grade students as they coordinated their actions to form a circle in a dancing context. Attentional anchors, first evidenced in their gaze and bodily orientation, gradually materialized in response to joint-action constraints into a geometric system of auxiliary lines inscribed on a provided floor-mat template. We speculate that the Balinese cultural ecology— where sitting, kneeling, and working on the ground are normative—facilitated the literal grounding of perception as geometric inscription. Within the GRiD context, action and inscription are not dichotomized but epistemically continuous: tracing lines of perceptual intentionality on the floor is experienced not as mathematizing, modeling, or abstracting but as gestured marking of enactive practice.