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1. Articulating the student mathematics in student contributions

   https://doi.org/https:/doi.org/10.51272/pmena.42.2020-354  

   Van Zoest, L. R. ; Stockero, S. L. ; Leatham, K. R. ; Peterson, B. E. ; Ruk, J. M. ( October 2020 , Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Sacristán, A. I. ; Cortés-Zavala, J. C. ; Ruiz-Arias, P. M. (Ed.)

   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 contributions. 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. 

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2. Articulating the student mathematics in student contributions

   https://doi.org/10.51272/pmena.42.2020-354  

   Van Zoest, Laura R. ; Stockero, Shari L. ; Leatham, Keith R. ; Peterson, Blake E. ; Ruk, Joshua M. ( December 2020 , Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Sacristán, A ; Cortés-Zavala, J ; null (Ed.)

   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’ 

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3. Undergraduates' perceptions of the benets of working tasks focused on analyzing student thinking as an application for teaching in abstract algebra

   Álvarez, James A. ; Kercher, Andrew ; Turner, Kyle ( January 2020 , Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S.S. ; Reed, Z. ; Higgins, A. (Ed.)

   The Mathematical Education of Teachers as an Application of Undergraduate Mathematics project provides lessons integrated into various mathematics major courses that incorporate mathematics teaching connections as a legitimate application area of undergraduate mathematics. One feature of the lessons involves posing tasks that require undergraduates to interpret or analyze the work of another student. This paper reports on thematic analysis of hour-long interviews for eight participants enrolled in an undergraduate abstract algebra course from two different implementation sites. We focus on student work and reactions to these interpreting or analyzing student thinking (AST) applications as they relate to their perceptions regarding the use of AST applications as a mechanism to both deepen their content knowledge and improve their skills for communicating mathematics. Several participants identify positive benefits, but more research is needed to determine the how to incorporate AST applications to accommodate some participants’ reluctance to engage in new mathematical contexts. 

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4. 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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5. Establishing student mathematical thinking as an object of class discussion

   Leatham, K. R. ; Van Zoest, L. R. ; Freeburn, B. ; Peterson, B. E. ; Stockero, S. L. ( October 2021 , Proceedings of the 43rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)

   Productive use of student mathematical thinking is a critical yet incompletely understood dimension of effective teaching practice. 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 first element, establish. Based on an analysis of secondary mathematics teachers' enactments of building, we describe two critical aspects of establish—establish precision and establish an object—and the actions teachers take in association with these aspects. 

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