Orchestrating the emergence of conceptual learning: a case study in a geometry class

This paper is about orchestrating the emergence of conceptual learning in a collaborative setting. We elaborate on the idea of critical moments in group learning, events which may lead to a particular development at the epistemic level regarding the shared object. We conjecture that teachers' identification of critical moments may help them guide students to the emergence of conceptual learning. The complexity of small group settings in classrooms prevents teachers from noticing these critical moments, though. Here we present an environment, SAGLET (System for Advancing Group Learning in Educational Technologies), based on the VMT (Virtual Math Teams) environment (Stahl 2009), which allows teachers to observe multiple groups engaging in problem-solving in geometry. SAGLET capitalizes on machine learning techniques to inform teachers about on-line critical moments by sending them alerts, so that they can then decide whether (and how) to use the alerts in guiding their students. One teacher in an elementary school used SAGLET to help multiple groups of students solve difficult problems in geometry. We observed how the teacher mediated two cohorts of multiple groups at two different times in a mathematics classroom. We show that in both cases the teacher could detect the needs of the groups (partly thanks to the alerts) and could provide adaptive guidance for all the groups.