## Abstract

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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## Notes

- 1.
One teacher did not respond to A3 because they were not able to envision posing the task in that way, and another teacher was not able to respond to G4 because their interview was cut short.

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## Acknowledgments

The authors would thank Napthalin Atanga, Rachel Bernard, Elizabeth Fraser, Lindsay Merrill, Mary Ochieng, Kylie Palsky, and Annick Rougee for their contributions to work that informed this paper.

## Funding

This work was funded in part by the U.S. National Science Foundation (NSF) under Grant Nos. 1220141, 1220357, and 1220148. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.

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Stockero, S.L., Van Zoest, L.R., Freeburn, B. *et al.* Teachers’ responses to instances of student mathematical thinking with varied potential to support student learning.
*Math Ed Res J* (2020). https://doi.org/10.1007/s13394-020-00334-x

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### Keywords

- Classroom discourse
- Instructional activities and practices
- Mathematics
- Secondary
- Student thinking
- Teacher moves
- Teacher responses