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1. Teachers' initial responses to high leverage instances of student mathematical thinking

   Stockero, S. L.; Peterson, B. E.; Ochieng, M. A.; Ruk, J. R.; Van Zoest, L. R.; & Leatham, K. R. (July 2019, Proceedings of the 43rd Annual Conference of the International Group for the Psychology of Mathematics Education)

   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. 

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2. Teachers' Initial Responses to High Leverage Instances of Student Mathematical Thinking

   Stockero, Shari L.; Peterson, Blake E.; Ochieng, Mary A.; Ruk, Joshua R.; Van Zoest, Laura R.; Leatham, Keith R. (July 2019, Proceedings of the 43rd Annual Conference of the International Group for the Psychology of Mathematics Education)

   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. 

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3. Teachers’ responses to instances of student mathematical thinking with varied potential to support student learning

   https://doi.org/10.1007/s13394-020-00334-x  

   Stockero, Shari L.; Van Zoest, Laura R.; Freeburn, Ben; Peterson, Blake E.; Leatham, Keith R. (January 2020, Mathematics Education Research Journal)

   null (Ed.)

   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. 

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4. Teacher-Responses: Highlight characteristics of low response process validity for item(s) measuring teachers' pedagogical content knowledge

   Epstein, M. L. (January 2022, Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E. (Ed.)

   Response Process Validity (RPV) reflects the degree to which items are interpreted as intended by item developers. In this study, teacher responses to constructed response (CR) items to assess pedagogical content knowledge (PCK) of middle school mathematics teachers were evaluated to determine what types of teacher responses signaled weak RPV. We analyzed 38 CR pilot items on proportional reasoning across up to 13 middle school mathematics teachers per item. By coding teacher responses and using think-alouds, we found teachers' responses deemed indicative of low item RPV often had one of the following characteristics: vague answers, unanticipated assumptions, a focus on unintended topics, and paraphrasing. To develop a diverse pool of items with strong RPV, we suggest it is helpful to be aware of these symptoms, use them to consider how to improve items, and then revise and retest items accordingly. 

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5. The complexity of interpreting student thinking and inferring its potential to foster learning

   Ochieng, M. A.; Ruk, J. M.; Leatham, K. R.; Peterson, B. E.; Stockero, S. L.; & Van Zoest, L. R. (July 2019, Proceedings of the 43rd Annual Conference of the International Group for the Psychology of Mathematics Education)

   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. 

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