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1. Establishing student mathematical thinking

   Leatham, K. R. (January 2021, Proceedings of the 43rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   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. 

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2. Establishing student mathematical thinking

   Leatham, K. R. (November 2021, Proceedings of the 43rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   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. 

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3. 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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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. (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. 

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5. A conceptualization of the teaching practice of building

   https://doi.org/10.1007/s10857-026-09744-3  

   Stockero, Shari L; Peterson, Blake E; Leatham, Keith R; Van_Zoest, Laura R (February 2026, Journal of Mathematics Teacher Education)

   In this theoretical paper, we present a conceptualization of the teaching practice of building—a teaching practice that takes advantage of high-leverage student contributions we call Mathematical Opportunities in Student Thinking (MOSTs). Specifying this complex teaching practice is important because it provides the detail needed for mathematics education researchers to study the nuances of teachers’ in-the-moment use of student thinking and for mathematics teacher educators to support teachers in developing such use. We describe key aspects and teacher actions associated with the four elements of building: Establish, Grapple Toss, Conduct, and Make Explicit. Throughout the paper we compare and contrast this decomposition with teaching moves and practices from the literature to illustrate the contribution of this work to understanding responsive teaching practices. 

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