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Learn why collecting, clarifying, and revoicing—often great teaching moves—do not always work. 

Do your students ever share ideas that are only peripherally related to the discussion you are having? We discuss ways to minimize and deal with such contributions. 

This work-in-progress paper shares preliminary results from a research project that addresses three primary objectives: (1) to develop a conceptual model of technology adoption among engineering faculty through qualitative interview research; (2) to propose an adaption of existing models for technology adoption with appropriate constructs for engineering faculty; and (3) to propose one or more specific interventions to increase faculty adoption of new engineering technologies. In this paper, we focus primarily on the work in progress to meet the first objective. Specifically, we highlight how our preliminary findings about the factors affecting technology adoption, identified from interviews with engineering faculty, align with or differ from factors in previous models for technology adoption. Subjective norm, voluntariness, utility, technology cost, and facilitating conditions, were all preliminary factors found in our data that align at least somewhat with constructs from previous models [1], [2]. Time, access to the technology, efficiency/ease of work, and self regulation are factors that we have identified which are absent from the most widely applied models of technology adoption. We consider what our findings might imply in engineering education contexts. 

We draw on our experiences researching teachers’ use of student thinking to theoretically unpack the work of attending to student contributions in order to articulate the student mathematics (SM) of those contribution. We propose four articulation-related categories of student contributions that occur in mathematics classrooms and require different teacher actions:(a) Stand Alone, which requires no inference to determine the SM; (b) Inference-Needed, which requires inferring from the context to determine the SM; (c) Clarification-Needed, which requires student clarification to determine the SM; and (d) Non-Mathematical, which has no SM. Experience articulating the SM of student contributions has the potential to increase teachers’ 

We argue that progress in the area of research on mathematics teacher responses to student thinking could be enhanced were the field to attend more explicitly to important facets of those responses, as well as to related units of analysis. We describe the Teacher Response Coding scheme (TRC) to illustrate how such attention might play out, and then apply the TRC to an excerpt of classroom mathematics discourse to demonstrate the affordances of this approach. We conclude by making several further observations about the potential versatility and power in articulating units of analysis and developing and applying tools that attend to these facets when conducting research on teacher responses. 

Teacher responses to student mathematical thinking (SMT) matter because the way in which teachers respond affects student learning. Although studies have provided important insights into the nature of teacher responses, little is known about the extent to which these responses take into account the potential of the instance of SMT to support learning. This study investigated teachers’ responses to a common set of instances of SMT with varied potential to support students’ mathematical learning, as well as the productivity of such responses. To examine variations in responses in relation to the mathematical potential of the SMT to which they are responding, we coded teacher responses to instances of SMT in a scenario-based interview. We did so using a scheme that analyzes who interacts with the thinking (Actor), what they are given the opportunity to do in those interactions (Action), and how the teacher response relates to the actions and ideas in the contributed SMT (Recognition). The study found that teachers tended to direct responses to the student who had shared the thinking, use a small subset of actions, and explicitly incorporate students’ actions and ideas. To assess the productivity of teacher responses, we first theorized the alignment of different aspects of teacher responses with our vision of responsive teaching. We then used the data to analyze the extent to which specific aspects of teacher responses were more or less productive in particular circumstances. We discuss these circumstances and the implications of the findings for teachers, professional developers, and researchers. 

We draw on our experiences researching teachers’ use of student thinking to theoretically unpack the work of attending to student contributions in order to articulate the student mathematics (SM) of those contribution. We propose four articulation-related categories of student contributions that occur in mathematics classrooms and require different teacher actions:(a) Stand Alone, which requires no inference to determine the SM; (b) Inference-Needed, which requires inferring from the context to determine the SM; (c) Clarification-Needed, which requires student clarification to determine the SM; and (d) Non-Mathematical, which has no SM. Experience articulating the SM of student contributions has the potential to increase teachers’ abilities to notice and productively use student mathematical thinking during instruction. 

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. 

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.