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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 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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3. A Decomposition of the Teaching Practice of Building

   Leatham, K. R.; Van Zoest, L. R.; Peterson, B. E.; Stockero, S. L. (September 2022, NCTM Research Conference)

   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. 

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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