Action-based embodied design for mathematics learning: A decade of variations on a theme

Abstract

Embodied cognition theory emphasizes that bodily interaction with the environment is important for all forms of learning, including mathematics. This theoretical trend coincides well with developments in motion responsive technology, and has resulted in numerous embodied technologies for mathematics learning. This review aims to contribute to clarifying theoretically and empirically grounded design principles of action-based embodied designs for mathematics learning. We analyzed 79 publications between 2010 and 2019, containing 15 studies assessing 15 sensorimotor problems for five mathematical domains (proportion, angle, area, parabola, and sine function), and explicated the characteristics of the technologies, their learning sequences and elicited learning processes, and the influence of within-topic ask variations on students’ learning. We found that action-based designs pose motor control problems using continuous motion feedback to facilitate learners to discover and practice a challenging new ways of moving their hand(s) in which to ground mathematical cognition. The state of discovery of the sensorimotor solution is important, and passive and readymade designs are cautioned. The learning sequence in which these technologies are embedded, elicit mathematical knowing through necessary and sequential phases in which personal idiosyncratic experiences increasingly converge into a culturally shared mathematical discourse. In the qualitative stage, an acting step elicits students to actively establish new motor coordination-patterns through the emergence of new perceptual structures known as attentional anchors. In the subsequent reflecting step, students’ personal sensorimotor experiences and attentional anchors become the ground for referencing in (a shared) mathematical discourse through multimodal (words, gestures) collaboration with a tutor. In the quantitative stage, measuring artifacts (grids, protractors, numbers, variables) are included in students’ field of promoted action, which discretize and formalize students’ actions and subsequent reflections into culturally recognizable quantitative forms. Critically, task factors such as the type of objects students manipulate (cursors icons, bars, rectangle), and the direction these objects are moved (parallel, orthogonal), affect students’ attentional anchors and subsequent reflections in the qualitative stage, but converge to similar mathematical insights in the quantitative stage. These insights help to better use (new) motion responsive technology in eliciting child–computer interaction that can lead to mathematical cognition and beyond.