Teacher support in collective argumentation to foster student understanding of parallelism based on the Toulmin model and Pirie-Kieren theory

Dialogue-oriented mathematics learning requires teachers not only to facilitate discussion but also maintain mathematical accuracy while preserving students’ ownership of reasoning. This study investigates how teacher support shapes collective argumentation and students’ understanding of parallelograms in a junior high school classroom. Using the Teacher Support for Collective Argumentation (TSCA) framework in combination with the full Toulmin argumentation model, the study examines how specific teacher moves contribute to the emergence, development, and coherence of students’ argument structures, with particular attention to the coordination of warrants, qualifiers, and rebuttals. Students’ conceptual development is further analyzed through the Pirie–Kieren framework to trace shifts from visual intuition to formal justification. Drawing on qualitative analysis of the recordings of class discussions, student artifacts, and interaction transcripts from geometry lessons, the findings indicate that teacher support enacted to probing questions, revoicing, and visual representation management sustains students’ ownership of arguments while enhancing the coherence of mathematical argument structures. Integrating TSCA with the Toulmin model enables more precise identification of argument maturity, especially in the correspondence between warrant types and the levels of claim certainty. These findings suggest that collective argumentation functions as an important socio-epistemic pathway toward formal proof and highlight pedagogical implications for question design and teacher interventions in the geometry classroom.