Technology-enhanced embodied learning has gained traction in HCI, yet deeper insights into how children’s physical actions interplay with their cognitive and emotional states remain underexplored. This study investigates MOVES-NL, an embodied digital learning environment, as a medium for advancing understanding of the dynamic relationship between movement, engagement, and cognitive processes such as stress and learning. MOVES-NL combines movement and immediate formative feedback to foster arithmetic understanding of integers, offering a novel perspective on the integration between embodied interactions and conceptual development. Moving beyond traditional evaluations of learning impact or media comparisons, this work employs multimodal learning analytics (MMLA) integrating motion capture with physiological data to explore the nuanced dynamics of embodied learning. Through a mixed-methods approach integrating both qualitative and quantitative analyses, this study reveals how students’ physical movements relate to cognitive and emotional states, offering actionable insights to support engagement and learning processes. This research advances the understanding of how children’s physical movements relate to their cognitive processes and highlights key considerations for integrating embodied technologies into curricula to foster student engagement and deepen their conceptual understanding, adding value to ongoing conversations about the role of digital technology in children’s education and development.

In the context of a design-based research effort to develop a technology-enabled constructivist algebra unit, a new activity architecture emerged that steps students through discovery levels. As they build a virtual model of a problem situation, students figure out technical principles for assuring the model's fidelity to the situation. These construction heuristics, we find, are precisely the conceptual foundations of algebra, such as tinkering with the model to assure that the variable quantity is of consistent size throughout the model. We articulated these principles as situated intermediary learning objectives (SILOs). At each interaction level, the student discovers a SILO, and then the technology takes over by automatizing that SILO, thus freeing the student for further discovery. We call this architecture reverse scaffolding, because the cultural mediator thus relieves learners from performing what they know to do, not from what they do not know to do. In a quasi-experimental evaluation study (Grades 4 & 9; n=40), reverse-scaffolding students outperformed direct-scaffolding students, for whom the technical features were pre-automatized. We speculate on the architecture's generalizability.

In a retrospective analysis of my own pedagogical design projects over the past twenty years, I articulate and compare what I discern therein as two distinct activity genres for grounding mathematical concepts. One genre, "perception-based design," builds on learners' early mental capacity to draw logical inferences from perceptual judgment of intensive quantities in source phenomena, such as displays of color densities. The other genre, "action-based design," builds on learners' perceptuomotor capacity to develop new kinesthetic routines for strategic embodied interaction, such as moving the hands at different speeds to keep a screen green. Both capacities are effective evolutionary means of engaging the world, and both bear pedagogical potential as epistemic resources by which to build meaning for mathematical models of, and solution processes for situated problems. Empirical studies that investigated designs built in these genres suggest a two-step activity format by which instructors can guide learners to reinvent conceptual cores. In a primary problem, learners apply or develop non-symbolic perceptuomotor schemas to engage the task effectively. In a secondary problem, learners devise means of appropriating newly interpolated mathematical forms as enactive, semiotic, or epistemic means of enhancing, explaining, and evaluating their primary response. Whereas my analysis distills activities into two separate genres for rhetorical clarity, ultimately embodied interaction may interleave and synthesize the genres' elements.

In the course of developing an experimental algebra unit, the researchers noted variability in their design's instructional potential across a set of implementation media. In an effort to explain this variability, we revisited the classical theoretical construct of transparency. Transparency is the perceptual and conceptual accessibility of the mechanism, logic, and application of a tool. Corroborating earlier literature, it appears that participants saw only what they had built---transparency is a subjective achievement of a learner rather than an inherent feature of a device. Our first design prompted students with an algebraic proposition, for example "3x+2=4x-1". The two equivalent expressions were to be interpreted by students as alternative quantifications of a single linear spatial interval; namely, the path that a giant took on two separate occasions to bury and recover treasure. Problem solving required manually adjusting the modeling media to coordinate two types of equivalence: (a) the total length represented by each expression; and (b) the length represented by the variable and known units. The researchers found that successful coordination was predicated on the subjective transparency of the models' perceptual. Therefore, in redesigning the activity as a computer-based application we will have learners first construct tools and only then automatize them.

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.

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.