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  1. We share three suggestions for how teachers can more productively use board work to scaffold joint sense making: (1) make the public record precise; (2) purposefully organize the public record; and (3) take advantage of the public record by referencing it in meaningful ways. 
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    Free, publicly-accessible full text available July 1, 2024
  2. 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. 
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  3. 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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  4. Lischka, A. E. ; Dyer, E. B. ; Jones, R. S. ; Lovett, J. N. ; Strayer, J. ; Drown, S. (Ed.)
  5. 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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  6. Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)
  7. We investigated teachers’ responses to a common set of varied-potential instances of student mathematical thinking to better understand how a teacher can shape meaningful mathematical discourse. Teacher responses were coded using a scheme that both disentangles and coordinates the teacher move, who it is directed to, and the degree to which student thinking is honored. Teachers tended to direct responses to the same student, use a limited number of moves, and explicitly incorporate students’ thinking. We consider the productivity of teacher responses in relation to frameworks related to the productive use of student mathematical thinking. 
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