Adaptive leaming technologies are emerging in educational settings as a means to customize instruction to learners' background, experiences, and prior knowledge. Here, a technology-based personalization intervention within an intelligent tutoring system (ITS) for secondary mathematics was used to adapt instruction to students' personal interests. We conducted a learning experiment where 145 ninth-grade Algebra I students were randomly assigned to 2 conditions in the Cognitive Tutor Algebra ITS. For 1 instructional unit, half of the students received normal algebra story problems, and half received matched problems personalized to their out-of-school interests in areas such as sports, music, and movies. Results showed that students in the personalization condition solved problems faster and more accurately within the modified unit. The impact of personalization was most pronounced for 1 skill in particular-writing symbolic equations from story scenarios-and for 1 group of students in particular-students who were struggling to learn within the tutoring environment. Once the treatment had been removed, students who had received personalization continued to write symbolic equations for normal story problems with increasingly complex structures more accurately and with greater efficiency. Thus, we provide evidence that interest-based interventions can promote robust leaming outcomes-such as transfer and accelerated future learning-in secondary mathematics. These interest-based connections may allow for abstract ideas to become perceptually grounded in students' experiences such that they become easier to grasp. Adaptive leaming technologies that utilize interest may be a powerful way to support leamers in gaining fluency with abstract representational systems.

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We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants’ actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities. Our focus here is on pre-college geometry proof production. GEMC suggests that action alone can foster insight but is insufficient for valid proof production if action is not coordinated with language systems for propositionalizing general properties of objects and space. GEMC guides the design of a video game-based learning environment intended to promote students’ mathematical insights and informal proofs by eliciting dynamic gestures through in-game directed actions.GEMC generates several hypotheses that contribute to theories of embodied cognition and to the design of science, technology, engineering, and mathematics (STEM) education interventions. Pilot study results with a prototype video game tentatively support theory-based predictions regarding the role of dynamic gestures for fostering insight and proof-with-insight, and for the role of action coupled with language to promote proof-with-insight. But the pilot yields mixed results for deriving in-game interventions intended to elicit dynamic gesture production. Although our central purpose is an explication of GEMC theory and the role of action-cognition transduction, the theory-based video game design reveals the potential of GEMC to improve STEM education, and highlights the complex challenges of connecting embodiment research to education practices and learning environment design.

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.

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