Chinese teachers’ professional noticing of students’ reasoning in the context of Lakatos-style proving activity.

Abstract

Despite the pedagogical values of Lakatos-style proving activity in school mathematics, little is known about how teachers react to students’ reasoning in this kind of activity. As an attempt to unpack the underlying decision-making processes, this study examines teachers’ noticing of students’ justification and refutation of conjectures in the context of Lakatos-style proving activity. Twelve Chinese pre-service and in-service secondary mathematics teachers participated in semi-structured, vignette-based interviews where they were presented with realistic classroom scenarios. These were based on actual classroom episodes reported in the literature and covered various aspects of Lakatos- style reasoning in the context of geometry. Findings show that teachers can better notice students’ justifications than students’ refutations, and better notice students’ valid arguments than invalid arguments. Key themes are identified to characterise their noticing of various student arguments.