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We investigate teachers’ initial in-the-moment responses to instances of high-potential student mathematical thinking (SMT) during whole class discussion to understand what it means to productively incorporate SMT into instruction. Teachers’ initial responses were coded using the Teacher Response Coding scheme, which disentangles the teacher action, who the response is directed to, and the degree to which the SMT is honored. We found that teachers incorporated students’ actions and ideas in their response, but tended to address the SMT themselves and did not fully take advantage of the SMT. We consider the productivity of teachers’ initial responses in relation to principles of productive use of SMT and compare the results to those of a previous study of teachers’ hypothetical initial responses to SMT in an interview setting. 

We investigate teachers’ initial in-the-moment responses to instances of high-potential student mathematical thinking (SMT) during whole class discussion to understand what it means to productively incorporate SMT into instruction. Teachers’ initial responses were coded using the Teacher Response Coding scheme, which disentangles the teacher action, who the response is directed to, and the degree to which the SMT is honored. We found that teachers incorporated students’ actions and ideas in their response, but tended to address the SMT themselves and did not fully take advantage of the SMT. We consider the productivity of teachers’ initial responses in relation to principles of productive use of SMT and compare the results to those of a previous study of teachers’ hypothetical initial responses to SMT in an interview setting. 

Research has shown that listening to and interpreting student thinking is challenging, yet critical for effective incorporation of student mathematical thinking (SMT) into instruction. We examine an exemplary teacher’s interpretations of SMT, his inference of the potential of the SMT to foster learning, and the rationale for his responses to that thinking. Our findings reveal some reasons why teachers may fail to successfully act on SMT that emerges during whole class discussion. This study confirms previous research findings, that in order to incorporate SMT into instruction in a way that fosters learning, teachers must correctly interpret that SMT. The study also shows that even good teachers may need support in developing skills that will enable them accurately interpret SMT and its potential to foster learning. 

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations— their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations. To that end, the purpose of this study is to characterize teachers’ orientations toward using student mathematical thinking as a resource during whole-class instruction. We analyzed a collection of 173 thinking-as-a-resource orientations inferred from scenario-based interviews conducted with 13 teachers. The potential of each orientation to support the development of the practice of productively using student mathematical thinking was classified by considering each orientation’s relationship to three frameworks related to recognizing and leveraging high-potential instances of student mathematical thinking. After discussing orientations with different levels of potential, we consider the cases of two teachers to illustrate how a particular collection of thinking-as-a-resource orientations could support or hinder a teacher’s development of the practice of building on student thinking. The work contributes to the field’s understanding of why particular orientations might have more or less potential to support teachers’ development of particular teaching practices. It could also be used as a model for analyzing different collections of orientations and could support mathematics teacher educators by allowing them to better tailor their work to meet teachers’ specific needs.