Learning Mathematics with Digital Resources: Reclaiming the Cognitive Role of Physical Movement

In 1837, Fröbel introduced a pedagogical regimen focused on a set of simple tangible objects, beginning with a yarn ball, that children were invited to manipulate in various ways. Montessori and other educational luminaries followed this tradition of designing instructional manipulatives. Later, when digital technologies were invented for information management, computation, and telecommunication, these new media were adopted by educators eager to offer individualized learning, reach remote students, and create multimedia experiences that would augment on traditional classroom resources, such as textbooks, writing instruments, and authentic objects of inquiry, including natural phenomena and cultural artifacts. While early electric technologies privileged the visual and auditory sensory modalities and were not interactive (e.g., television), human–computer interaction innovations and the advent of personal platforms increasingly evolved toward state-of-the art devices, content, and activities offering immersive multimodal experiences in imaginary landscapes (e.g., virtual reality). What might be the educational promise of these media? How do digital technologies serve mathematics students differently than yarn balls? How might theories of learning guide the design of digital environments? To investigate these questions, we survey the history of digital resources for mathematics education through the prism of philosophical and psychological theories – enactivist cognition and ecological dynamics – that look to capture the role of embodied interaction in cognitive development and conceptual learning. Then, through three case studies of contemporary digital educational resources, a proposal is put forth for how these embodied theories of learning could inform the design of educational technologies compatible with how people naturally learn. First, students should learn to enact new physical movement forms that have been designed to instantiate the targeted concepts. Students learn to move in these new ways by developing perceptual orientations that enable them to solve situated motor-control problems. Only then are these new cognitive skills formalized in disciplinary semiotic forms. Perhaps future technology can be as powerful a learning tool as the historical yarn ball.