Establishing a baseline for comparing classroom discourse from representative geometry lessons: pivotal teaching moments and cognitive levels of student discourse

Abstract Pivotal teaching moments (PTMs), when a student says something unanticipated by the teacher, offer key opportunities to shape learning and student discourse in a lesson, so studying teachers’ responses to them yields important descriptors of pedagogy and its impact on student mathematical thinking. Recent decades have seen developments in research on, and standards for, classroom mathematics, but no comprehensive examination of changes in the ways teachers respond to student discourse. This sequential mixed-methods study applies our novel framework for analyzing elements of PTM episodes to all available English-language Third International Mathematics and Science Study geometry lesson videos, as a first step to establishing a baseline description of mathematics teachers’ discourse practices in the 1990s. We find many of the PTMs stemmed from students’ incorrect mathematical statements, and the dominant teacher response focused on emphasizing correct answers and meanings rather than pursuing student thinking, with relatively low-cognitive-level student discourse ensuing. Discourse patterns are especially significant in geometry, where research has seen students struggle to articulate their understanding.