Abstract
A rising epistemological paradigm in the cognitive sciences—embodied cognition—has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students’ physical movements, eye-gaze paths, and verbal–gestural utterance so as to track and evaluate emerging conceptual capacity. We—a cohort of cognitive scientists and design-based researchers of embodied mathematics—survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for educational practice.
Highlights
Philosophy of cognitive science is undergoing considerable change
Graspable Math (GM) focuses on the perceptual strategies successful students use to read and transform equations and develops an intervention to connect these experiences to meaningful structures in a precise and fluid interface
GM allows the procedural advantages of physically moving symbols to seamlessly integrate into conceptually challenging lessons
Summary
Philosophy of cognitive science is undergoing considerable change. This change, dubbed the embodiment turn in the history of philosophy (Nagataki and Hirose, 2007, pp. 223–224; see Zlatev, 2007), challenges the classical Cartesian mind–body divide (Merleau-Ponty, 1945/2005), which dominated 20th century perspectives on the fundamental infrastructure and mechanism of the human mind. Dynamic gestures directly support students’ investigation of generalizable properties of space and shape through body movements by enacting various transformations on simulated mathematical objects Movement, such as dynamic gesture production, depends on the generation of goal-directed motor programs, which activate predictors (feedforward mechanisms) for many or all plausible outcomes of the proposed actions so that during movement execution the system can make rapid course corrections or quickly determine goal achievement (Wolpert et al, 2003). These predictors perform like mental models that “run through” the steps toward plausible outcomes, and in so doing, support model-based reasoning and inference making (Nathan and Martinez, 2015), which can enhance scientific and mathematical learning. We first give a general overview of research on gesture, and we discuss a specific design-based research program, in which learners engage in collaborative gestures within a mathematics learning game
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