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Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovell, 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 broad ways teachers used public records—manipulating and referencing—to support establishing and maintaining students’ thinking as objects in sense-making discussions.more » « less
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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
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We share a decomposition of building on MOSTs—a teaching practice that takes advantage of high-leverage instances of student mathematical contributions made during whole-class interaction. This decomposition resulted from an iterative process of teacher-researchers enacting conceptions of the building teaching practice that were refined based on our study of their enactments. We elaborate the four elements of building: (a) Establish the student mathematics of the MOST as the object to be discussed; (b) Grapple Toss that object in a way that positions the class to make sense of it; (c) Conduct a whole-class discussion that supports the students in making sense of the student mathematics of the MOST; and (d) Make Explicit the important mathematical idea from the discussion. We argue for the value of this practice in improving in-the-moment use of high-leverage student mathematical thinking during instruction.more » « less
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D. Olanoff, K. Johnson (Ed.)Productive use of student mathematical thinking is a critical yet incompletely understood aspect of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four subpractices that comprise it. In this paper we begin to unpack this complex practice by looking closely at its first subpractice, establish. Based an analysis of secondary mathematics teachers’ enactments of building, we describe two critical components—make precise and make an object—as well as important subtleties of the establish subpractice.more » « less
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null (Ed.)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.more » « less
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D. Olanoff, K. Johnson (Ed.)Productive use of student mathematical thinking is a critical yet incompletely understood aspect of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four subpractices that comprise it. In this paper we begin to unpack this complex practice by looking closely at its first subpractice, establish. Based an analysis of secondary mathematics teachers’ enactments of building, we describe two critical components—make precise and make an object—as well as importantsubtleties of the establish subpractice.more » « less
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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’more » « less
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