Dragan Trninic

The mathematical imagery trainer: from embodied interaction to conceptual learning

We introduce an embodied-interaction instructional design, the Mathematical Imagery Trainer (MIT), for helping young students develop grounded understanding of proportional equivalence (e.g., 2/3 = 4/6). Taking advantage of the low-cost availability of hand-motion tracking provided by the Nintendo Wii remote, the MIT applies cognitive-science findings that mathematical concepts are grounded in mental simulation of dynamic imagery, which is acquired through perceiving, planning, and performing actions with the body. We describe our rationale for and implementation of the MIT through a design-based research approach and report on clinical interviews with twenty-two 4th-6th grade students who engaged in problem-solving tasks with the MIT.

Toward an embodied-interaction design framework for mathematical concepts

Recent, empirically supported theories of cognition indicate that human reasoning, including mathematical problem solving, is based in tacit spatial-temporal simulated action. Implications of these findings for the philosophy and design of instruction may be momentous. Here, we build on design-based research efforts centered on exploring the potential of embodied interaction (EI) for mathematics learning. We sketch two emerging, reciprocal contributions: (1) a sociocognitive view on the role of automated feedback in building the perceptuomotor schemes that undergird conceptual development; and (2) a heuristic EI design framework. We ground these ideas in vignettes of children engaging an EI design for proportion. Increasing ubiquity and access to mobile devices geared to avail of EI principles suggests the feasibility of mass-disseminating materials evolving from this line of research.

Embodied Interaction as Designed Mediation of Conceptual Performance

Can conceptual understanding emerge from embodied interaction? We believe the answer is affirmative, provided that individuals engaged in embodied-interaction activity enjoy structured opportunities to describe their physical actions using instruments, language, and forms pertaining to the targeted concept. In this chapter, we draw on existing literature on embodiment and artifacts to coin and elaborate on the construct of an embodied artifact—a cognitive product of rehearsed performance such as, for example, an arabesque penchee in dance or a flying sidekick in martial arts. We argue that embodied artifacts may encapsulate or “package” cultural knowledge for entry into disciplinary competence not only in explicitly embodied domains, such as dance or martial arts, but also implicitly embodied domains, such as mathematics. Furthermore, we offer that current motion-sensitive cyber-technologies may enable the engineering of precisely the type of learning environments capable of leveraging embodied artifacts as both means of learning and means for studying how learning occurs. We demonstrate one such environment, the Mathematical Imagery Trainer for Proportion (MIT–P), engineered in the context of a design-based research study investigating the mediated emergence of mathematical notions from embodied-interaction instructional activities. In particular, we discuss innovative features of the MIT–P in terms of the technological artifact as well as its user experience. We predict that embodied interaction will become a focus of design for and research on mathematical learning.