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1. 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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2. 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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3. Teachers' responses to instances of student mathematical thinking with varied potential to support student learning.

   Stockero, S. L. (October 2018, Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   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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4. Teachers' responses to instances of student mathematical thinking with varied potential to support student learning

   Stockero, S. L. (January 2018, Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   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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5. Teachers' responses to instances of student mathematical thinking with varied potential to support student learning.

   Stockero, S. L.; Freeburn, B.; Van Zoest, L. R.; Peterson, B. E.; Leatham, K. R. (November 2018, Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   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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