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Recent developments in cognitive and educational science highlight the role of the body in learning. Novel digital technologies increasingly facilitate bodily interaction. Aiming for understanding of the body’s role in learning mathematics with technology, we reconsider the instrumental approach from a radical embodied cognitive science perspective. We highlight the complexity of any action regulation, which is performed by a complex dynamic functional system of the body and brain in perception-action loops driven by multilevel intentionality. Unlike mental schemes, functional systems are decentralized and can be extended by artifacts. We introduce the notion of a body-artifact functional system, pointing to the fact that artifacts are included in the perception-action loops of instrumented actions. The theoretical statements of this radical embodied reconsideration of the instrumental approach are illustrated by an empirical example, in which embodied activities led a student to the development of instrumented actions with a unit circle as an instrument to construct a sine graph. Supplementing videography of the student’s embodied actions and gestures with eye-tracking data, we show how new functional systems can be formed. Educational means to facilitate the development of body-artifact functional systems are discussed.

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Embodied learning and the design of embodied learning platforms have gained popularity in recent years due to the increasing availability of sensing technologies. In our study, we made use of the Mathematical Imagery Trainer for Proportion (MIT-P) that uses a touchscreen tablet to help students explore the concept of mathematical proportion. The use of sensing technologies provides an unprecedented amount of high-frequency data on students' behaviors. We investigated a statistical model called mixture Regime-Switching Hidden Logistic Transition Process (mixRHLP) and fit it to the students' hand motion data. Simultaneously, the model finds characteristic regimes and assigns students to clusters of regime transitions. To understand the nature of these regimes and clusters, we explore some properties in students' and tutor's verbalization associated with these different phases.

Analogical reasoning, the ability to learn about novel phenomena by relating it to structurally similar knowledge, develops with great variability in children. Furthermore, the development of analogical reasoning coincides with greater working memory efficiency and increasing knowledge of the entities and relations present in analogy problems. In figural matrices, a classical form of analogical reasoning assessment, some features, such as color, appear easier for children to encode and infer than others, such as orientation. Yet, few studies have structurally examined differences in the difficulty of visual relations across different age-groups. This cross-sectional study of figural analogical reasoning examined which underlying rules in figural analogies were easier or more difficult for children to correctly process. School children (N = 1422, M = 7.0 years, SD = 21 months, range 4.5–12.5 years) were assessed in analogical reasoning using classical figural matrices and memory measures. The visual relations the children had to induce and apply concerned the features: animal, color, orientation, position, quantity and size. The role of age and memory span on the children's ability to correctly process each type of relation was examined using explanatory item response theory models. The results showed that with increasing age and/or greater memory span all visual relations were processed more accurately. The “what” visual relations animal, color, quantity and size were easiest, whereas the “where” relations orientation and position were most difficult. However, the “where” visual relations became relatively easier with age and increased memory efficiency. The implications are discussed in terms of the development of visual processing in object recognition vs. position and motion encoding in the ventral (“what”) and dorsal (“where”) pathways respectively.