The study of pivotal teaching moments (PTMs) offers significant insights into mathematics classroom interactions. PTMs are student-generated instances within a lesson that provide opportunities for teachers to modify planned instruction (Stockero & Van Zoest, 2013). Given the importance of interactions and discourse in students’ mathematical growth and understanding, we examine them in the context of PTM episode triples. PTM episode triples consist of three main elements: (1) a PTM, (2) a teacher response to the PTM, and (3) the immediately ensuing student utterance. Analysis of data from nine elementary mathematics lessons shows that teacher responses that explicitly “pursued students’ thinking” elicited significantly higher cognitive levels of student discourse than teachers who "ignored or dismissed" PTMs or simply "acknowledged [PTMs] but continued as planned." While many researchers have focused on PTM episode “doubles” (combinations of student-generated interruptions and the teacher’s response), no studies to our knowledge have addressed PTM episode “triples” as we have. Implications of these findings prove helpful for identifying concrete ways that educators can increase the cognitive level of student discourse within their classrooms. Further, our integration and modification of existing theory and frameworks for analyzing PTM episode triples—incorporating the relationship between PTMs and teachers’ responses to them, on the one hand, and the cognitive level of the ensuing student utterance, on the other hand—are a unique contribution to the field and provide a method by which researchers and educators can study classroom practice.

关键教学时刻（PTM）的研究为数学课堂互动提供了重要的见识。PTM是一堂课中由学生生成的实例，为教师提供了修改计划教学的机会（Stockero和Van Zoest，2013）。鉴于互动和话语对于学生的数学成长和理解的重要性，我们在PTM情节三倍的背景下对其进行了研究。PTM情节三部分包括三个主要元素：（1）PTM，（2）老师对PTM的回应，以及（3）紧随其后的学生话语。对来自9个基础数学课程的数据进行的分析表明，与“忽略或驳回” PTM或简单地“承认[PTM]但按计划继续进行”的教师相比，明确“追求学生的思维”的教师回答所引起的学生话语认知水平明显更高。尽管许多研究人员将注意力集中在PTM情节“双打”（学生产生的打断和老师的反应相结合）上，但是我们对知识的研究还没有像PTM情节“三联”那样。这些发现的含义被证明有助于确定教育者可以在课堂上提高学生话语认知水平的具体方式。