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1. How a teaching practice that builds on student thinking helps teachers draw out conceptual connections

   Ruk, Joshua M; Van_Zoest, Laura R (October 2023, North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lamberg, T; Moss, D (Ed.)

   Past research has identified factors that help maintain the cognitive demand of tasks, including drawing conceptual connections. We investigated whether teachers who were engaging in the teaching practice of building—and thus focusing the class on collaboratively making sense of their peers’ high-leverage mathematical contributions—drew conceptual connections at a higher rate than has been found in previous work. The rate was notably higher (54% compared to 14%). By comparing multiple enactments of the same task, we found that this higher rate of drawing conceptual connections seemed to be supported by (1) eliciting student utterances that delve more deeply into the underlying mathematics, (2) giving students more time to explore the underlying math, and (3) using previously learned abstractions to help move the class toward understanding the new abstract concepts underlying a task. 

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2. Tracing take-up across practice-based professional development and collaborative lesson design

   Valerio, J. (January 2021, Proceedings of the 43rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Olanoff, D.; Johnson, K.; Spitzer, S. (Ed.)

   This study explored how two professional development approaches to reforming math instruction with different mechanisms for fostering change might have valuable synergies when used in tandem to support take-up, i.e., teachers’ acceptance, adoption, and incorporation of ideas into practice. This investigation of Practice-Based Professional Development and Collaborative Lesson Design found that take-up was a recursive process that occurred across both PD types as teachers iteratively moved between building and deploying knowledge. Both overarching and practice-specific struggles occurred during enactment, triggering shifts back to knowledge building. Struggles associated with learning to facilitate productive struggle included making sense of student thinking, identifying and providing appropriate scaffolds without lowering the cognitive demand, and helping students move from intuitive to mathematical arguments. 

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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 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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