Embodied design using augmented reality: the case of the gradient

We study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of tasks based on embodied design, including perception-based, action-based and incorporation-based tasks. Tiago’s work demonstrates the affordances of the ARSB, e.g. to trace a height line and to manipulate plastic planes either with or without feedback from projected height lines. Tiago’s reasoning about mathematical concepts, e.g. the parameters in a plane equation and the gradient vector, is supported by perceptual structures that he discovers during these embodied tasks. We distinguished two ways in which ARSB affordances were used in the learning sequence. In perception-based and action-based tasks, the affordances of the ARSB were immediately available and intensively involved in the interaction. In incorporation tasks, on the contrary, a critical affordance was deliberately removed and the student was able to reproduce its functionality without technology.