Towards an ecological-dynamics design framework for embodied-interaction conceptual learning: the case of dynamic mathematics environments

Abstract

Designers of educational modules for conceptual learning often rely on procedural frameworks to chart out interaction mechanics through which users will develop target understandings. To date, however, there has been no systematic comparative evaluation of such frameworks in terms of their consequences for learning. This lack of empirical evaluation, we submit, is due to the intellectual challenge of pinning down in what fundamental sense these various frameworks differ and, therefore, along which parameters to conduct controlled comparative experimentation. Toward an empirical evaluation of educational-technology design frameworks, this conceptual paper considers the case of dynamic mathematics environments (DME), interactive modules for learning curricular content through manipulating virtual objects. We consider user activities in two paradigmatic DME genres that utilize similar HCI yet different mechanics. To compare these mechanics, we draw from complex dynamic systems theory a constraint-based model of embodied interaction. Task analyses suggest that whereas in one DME genre (GeoGebra) the interaction constraints are a priori inherent in the environment, in another DME genre (Mathematics Imagery Trainer) the constraints are ad hoc emergent in the task. We conjecture differential learning effects of these distinct constraint regimes, concluding that ad hoc emergent task constraints may better facilitate the naturalistic development of cognitive structures grounding targeted conceptual learning. We outline a future empirical research design to compare the pedagogical entailments of these two design frameworks.