Materialized Action: Reformulating the “Doing of” Math Through Fiber Crafting

This article examines how fiber crafting as a category of activity can develop mathematics learning and the conditions under which various fiber crafting traditions differentially cultivate mathematical understanding. Modifying the constructionist paradigm with relational materialist principles, this paper advances the notion of “materialized action,” which describes the natural inquiry process that results through emergent patterns between learners and the materialized traces of their actions. This paper takes a qualitative approach, combining a design and intervention phase to look closely across a set of materials (i.e., three fiber crafts, knitting, crochet, and pleating) and engagement in a “powerful idea” (i.e., the role of unitizing in multiplicative proportional reasoning), as instantiated across three youth case studies, and as an illustration of how we can better understand micro-developmental learning processes. We identified three levels of unitizing that make up the larger idea of enacting proportional reasoning (PR) through materialized action, which build and catalyze toward one another and support emergent understanding of PR from the intra-action of the material and the learner. In their engagement with PR, youth employed different strategies based on personal choice, affordances of the materials, and practices of the crafting traditions. Materialized actions as a theoretical advancement has the potential to reformulate what counts as mathematics and can guide the design of mathematics learning that is embracing (rather than reducing) worldly concreteness in learning key domain ideas, with implications for the design of more equitable learning environments.