Mathematics teachers’ noticing of argumentation within small groups

Abstract While small-group argumentation is seen as central to mathematics learning, teachers’ noticing of moments with potential for argumentation during group work remains underexplored. This study, conducted with Israeli secondary-school mathematics teachers, introduces the construct of Critical Events associated with Group Mathematics Argumentation (CEGMAs)—moments that teachers identify as opportunities for argumentation to develop—as a lens for analyzing teacher noticing. We aim to examine how these teachers notice such events by analyzing how they attend to, interpret, and respond, and how these components are connected. Seven teachers participated in interviews in which they analyzed videos of their own students working in small groups. They identified CEGMAs, interpreted them, and proposed instructional responses. Events were coded by the structural or dialogic focus of argumentation, and interpretations and responses were further analyzed across cognitive, social, and affective dimensions of the learning context, considering how professional narratives shaped teachers’ reasoning. Findings show that teachers identified structurally and dialogically focused CEGMAs in nearly equal proportions. Their interpretations emphasized students’ reasoning as well as their interactions in discussion, mainly within the cognitive dimension, followed by social. Responses were directed more toward dialogic engagement, again primarily cognitive then social. Patterns across noticing components revealed alignments and shifts shaped both by the nature of the event and by prevailing professional narratives. The study advances noticing research by showing how teachers’ attending, interpreting, and responding are shaped by both classroom dynamics and broader professional narratives, and by offering CEGMAs as an analytical tool for examining small-group mathematical argumentation.