> Context • Radical embodied approaches to cognition propose a drastic alternative to representation-based models of the mind by way of theorizing and empirically demonstrating the constitutive roles of perception–action loops in human behavior. However, applying those approaches to higher-order processes – such as mathematical thinking and learning – remains one of the hottest debates within contemporary cognitive science. > Problem • How might a radical embodied perspective theoretically explain semiotic mediation? For example, how can we theorize the understanding of trigonometric relations expressed through the symbolic form of “sin 2a = sin a”? > method • Revisiting the nature of semiotic mediation, we pursue a historically grounded theoretical analysis that integrates perspectives from Lev Vygotsky and Nikolai Bernstein; to make the theoretical proposal accessible, we illustrate it by empirical data from a dual-eye-tracking study on teaching/learning trigonometry. > Results • We show how semiotic mediation of mathematical ideas is constituted as direct intercorporeal sensorimotor coordination between interlocutors. We treat semiotic actions as directly transforming an environment for the interlocutor, inviting new sensorimotor processes. New sensorimotor routines potentially lead to the emergence of pedagogically desired perception and action orientations, that is, new enactive capacity as the cognitive vehicle of mathematical reasoning. As such, Vygotskian cultural–historical ideas of semiotic mediation become a natural continuation of a radical embodied project developed by Bernstein, Kelso, Turvey, and others. Semiotic actions do not represent mind-independent reality as standalone tokens – rather, they present the environment itself, for the interlocutor, in a new way. > Implications • The proposed perspective avoids ontologically problematic views of pedagogical discourse as the negotiation of minds, instead focusing educators’ attention on transformations of the students’ environment that foster desired perceptions and actions. > Constructivist content • We develop an alternative to a social-constructivist reading of cultural-historical ideas, thus contributing to the understanding of higher-order cognition as direct extension of perception and action.

Vygotsky conceptualized the teaching/learning process as inherently collaborative. We extend prior evaluations of this claim by enlisting eye-tacking instruments to monitor the perceptual activity of four teacher–student dyads, as the student solves a challenging manipulation problem designed to ground the scientific notion of parabolas in their new sensorimotor routines. Analyzing each dyad's gaze paths led us to model the teaching/learning process as the emergence and dynamic transformation of intersubjective coupling between the student and tutor perception–action systems. While the student's sensory-motor coordination gradually gravitates toward an effective routine, the tutor's perception is iteratively launched from the student's current action, until the tutor detects an optimal moment for verbal intervention. In this micro-zone of proximal development, the student's motor action comes to align with the tutor's cultural-perspective strategy. Our elaboration of the cultural–historical approach to teaching/learning draws on research on joint attention and joint action from the cognitive sciences as well as the embodied-design approach from the educational sciences and demonstrates a compatibility of Vygotsky's heritage and complex dynamic systems theory. Finally, we discuss the educational value of the observed student–tutor intersubjective coupling phenomena, thus grounding the contribution of this multidisciplinary study within educational concerns.

As technologies that put the body at the center of mathematics learning enter formal and informal learning spaces, we still know little about the teaching methods educators can use to support students’ learning with these specialized systems. Drawing on ethnomethodology and conversation analysis (EMCA) and the Co-Operative Action framework, we present three multimodal ways that educators can be responsive to learners’ embodied ideas and help them transform sensorimotor patterns into mathematically significant perceptions. These techniques include (1) encouraging learners to use gesture to express and reflect on their ideas, (2) presenting multimodal candidate understandings to check comprehension of learners’ embodied ideas, and (3) co-constructing multimodally expressed embodied ideas with learners. We demonstrate how these techniques create opportunities for learning and discuss implications for a multimodal, embodied practice of responsive teaching.