Chaining embodied learning: a system to help develop an integrated understanding of proportion, slope and rate of change

This paper presents the design of a sequenced chain of embodied learning systems, to support students' transition from basic concepts (such as proportion) to more advanced ideas like slope and rate of change, and thus integrate the three concepts. Drawing on Tall's (2003) notion of embodiment as a cognitive basis for formal mathematics, and informed by enactivist pedagogy (Abrahamson et al., 2022), the approach highlights how bodily actions can ground and enrich complex reasoning. In this design, learners progress through a series of embodied experiences that focus on 3 different kinds of understanding - spatial, numerical, and graphical. By sequencing interconnected systems - rather than providing isolated systems - we aim to examine how such chained embodied learning designs influence students' meaning-making across mathematical ideas.