Mathematics teachers’ noticing of critical events associated with argumentation

This study explores secondary-school mathematics teachers’ noticing of Critical Events Associated with Argumentation (CEAs), moments when students’ reasoning or interactions become evident, offering teachers opportunities to promote argumentation in the classroom. Thirty-one teachers analyzed a written classroom scenario, identifying CEAs, interpreting their potential for fostering argumentation, and proposing teaching alternatives. The findings reveal that teachers identified CEAs emphasizing either mathematical arguments, collaborative interactions in constructing and evaluating arguments, or both, with a primary focus on dialogic interactions. The identified CEAs, along with their interpretations and proposed strategies, demonstrated alignment, by focusing on common underlying aspects. The dynamic interconnection among components of noticing—attending, interpreting, and responding—challenges linear models, suggesting iterative and holistic processes. By framing CEAs as opportunities to integrate structural and dialogic aspects of argumentation, this study contributes to refining noticing frameworks and advancing teachers' professional development. Theoretical and practical implications for research on noticing and argumentation in mathematics education are discussed, alongside recommendations for future studies.