Shvarts, A., & Abrahamson, D. (2018, June). Vygotsky’s psychological systems as complex dynamical systems: Theorizing multimodal data of student–tutor collaboration on an embodied mathematical task. 

Paper presented at the annual meeting of the Jean Piaget Society, Amsterdam, May 31 – June 2.

This proposal draws theoretical parallels between Vygotsky’s socially originated psychological systems and complexity theory of teaching–learning processes as self-organizing, adaptive dynamical systems in flux. The proposed approach to educational research subsumes and integrates enactivist and sociocultural perspectives on teaching–learning phenomena, providing new theoretical perspectives on the micro-ontogeny of mathematical concepts. When individuals engage in goal-oriented social enactment of cultural practice, such as performing mathematical tasks, they come forth into a self-organizing complex dynamical system of student–tutor interaction. We investigate the nature and evolution of this collaborative system in the empirical context of a design research project, in which tutor–student dyads participated in a teaching–learning joint activity oriented on completing an interactive non-symbolic computer-based manipulation task. The data included dual eye-tracking (DUET)—computer reconstructions of the participants’ synchronous dynamical gazes—as superimposed onto videography of the virtual objects being manipulated as well as contemporaneous vocalized and gestural utterance. These multimodal data occasioned opportunities for the analysts to witness and model the phenomenon of teaching-learning as the nuanced, incremental co-action of two independent sensorimotor systems co-attending to problem-solving physical actions in a shared perceptual display. In particular, we model these data as evidencing a student–tutor complex dynamical system gravitating towards normative practice whence cultural mathematical meaning emerge. Findings suggest the hitherto under-theorized participatory role of tutors’ perceptual activity in supporting students’ idiosyncratic sensorimotor engagement and promoting its cultural objectification. Synchrony and coordination between a tutor’s perception and a student’s action reveal the emergence of inter-subjective coupling between the tutor and student’s respective perception–action systems. At a critical stage of embodied interaction, the tutor’s multimodal cultural intervention is interlaced with the student’s personal embodied activity through iterative open-ended attempts to re-orient the student’s attention towards the cultural meaning. Theorizing the student and tutor as constituting a complex dynamical system in action enables us to characterize and explain empirical data that would have remained opaque through analyzing individual activities per se.