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1. Using public records to support the productive use of student mathematical thinking

   Freeburn, B.; Leatham, K. R.; Graff, S.; Kamlue, N.; Stockero, S. L.; Peterson, B. E.; Van Zoest, L. R. (January 2022, Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)

   The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers' use of public records appeared to support or inhibit their efforts to conduct a sense-making discussion around a particular student contribution. We use cognitive load theory to frame two broadways teachers used public records—manipulating and referencing—to support establishing and maintaining students' thinking as objects in sense-making discussions. 

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2. Orienting to Student Sense-Making: Using Simulations to Support the Development of Equitable Mathematics Teaching

   https://doi.org/10.4018/979-8-3693-1164-6.ch011  

   Shaughnessy, Meghan; Boerst, Timothy A; Garcia, Nicole; Claiborne, Brit (November 2024, IGI Global)

   This chapter reports on work from a decade-long project to develop and study the use of teaching simulations focused on the teaching practices of eliciting and interpreting student thinking to support preservice teachers' (PSTs') learning. The chapter describes how teaching simulations focused on these practices allow teacher educators to support PSTs in orienting to student sense-making that is at the heart of equitable mathematics instruction. The teaching simulation approach is described. Examples illustrate how the approach is designed and facilitated in ways that make visible PSTs' engagement with three teaching performance areas (eliciting the student's process, using mathematical knowledge and skill, and conveying respect for the student as a mathematical thinker and learner) that are crucial for more equitable mathematics instruction. Connections between each of the performance areas and more equitable eliciting and interpreting of student thinking are described alongside the ways in which teacher educators can provide feedback that supports PSTs' development. 

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3. Teachers’ orientations toward using student mathematical thinking as a resource during whole-class discussion

   https://doi.org/10.1007/s10857-018-09421-0  

   Stockero, Shari L.; Leatham, Keith R.; Ochieng, Mary A.; Van Zoest, Laura R.; Peterson, Blake E. (January 2019, Journal of Mathematics Teacher Education)

   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. 

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4. Conducting a whole class discussion about an instance of student mathematical thinking

   Stockero, S. L.; Peterson, B. E.; Leatham, K. R.; Van Zoest, L. R. (January 2022, Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)

   Productive use of student mathematical thinking is a critical aspect of effective teaching that is not yet fully understood. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper, we begin to unpack this complex practice by looking closely at its third element, Conduct. Based on an analysis of secondary mathematics teachers' enactments of building, we describe the critical aspects of conducting a whole-class discussion that is focused on making sense of a high-leverage student contribution. 

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5. CONDUCTING A WHOLE CLASS DISCUSSION ABOUT AN INSTANCE OF STUDENT MATHEMATICAL THINKING

   Stockero, S. L.; Peterson, B. E.; Leatham, K. R.; Van Zoest, L. R. (November 2022, Psychology of Mathematics Education)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)

   Productive use of student mathematical thinking is a critical aspect of effective teaching that is not yet fully understood. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at its third element, Conduct. Based on an analysis of secondary mathematics teachers’ enactments of building, we describe the critical aspects of conducting a whole-class discussion that is focused on making sense of a high-leverage student contribution. 

   more » « less