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Allyson Hallman-Thrasher

Algebra 1 students compare multiple representations and justify the development of recursive and explicit formulas.

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Allyson Hallman-Thrasher and Denise A. Spangler

We share ideas for preparing for and enacting high-cognitive demand tasks in ways that support students in articulating and justifying their ideas. We offer strategies for developing and posing several types of purposeful questions: (1) eliciting thinking, (2) generating ideas, (3) clarifying explanations, and (4) justifying claims.

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Denise A. Spangler and Allyson Hallman-Thrasher

We describe an activity designed to help preservice elementary school teachers develop mathematical knowledge for teaching in the domain of facilitating mathematical discussions. The activity involved preservice teachers writing task dialogues, imaginary conversations between a child and teacher about a problem-solving task, in which they practice responding to correct, partially correct, and incorrect student responses. Preservice teachers then implemented these same tasks with children in a field experience setting. We describe 2 different iterations of the activity and field experience in detail as well as the insights into preservice teacher knowledge each iteration afforded us.

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Allyson Hallman-Thrasher, Erin T. Litchfield and Kevin E. Dael

Frozen custard recipes are the starting point for students to derive and explain a method for multiplying matrices.

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Allyson Hallman-Thrasher, Courtney Koestler, Danielle Dani, Amanda Kolbe and Katie Lyday

Through trial and error and ultimate success, students create a graph to model a real-world situation.