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Graduation Date

2019

Document Type

Professional Paper

Degree

Master of Arts (MA)

School or Department

Mathematical Sciences

Abstract

The Common Core State Standards in Mathematics increased the emphasis on the skills of reasoning, justifying, and critiquing. Mathematics educators have struggled to meet this requirement, as it requires a distinct shift in classroom culture that both students and teachers find challenging. Visibly random groupings have been suggested as a way to effect a change in classroom norms, as students are asked to work with all members of the class. They thus learn to share their ideas as well as offer feedback on the thinking of other classroom participants. Students in three high school geometry classrooms were observed in an action research study focusing on how implementation of visibly random groupings affected discourse in the classroom. Data triangulation incorporated mathematical attitude surveys, open-ended questionnaires, teacher field notes, and student work samples. Different grouping methods were explored, and tasks and assessments were changed to accommodate the alterations that arose in the classroom culture. Pedagogical strategies also changed in response to the shifting norms. At the end of the research period, student attitudes had stayed relatively consistent, but their willingness to trust in their own reasoning as a valid source of knowledge had increased. Despite tensions around control of learning and the balance of content and process, teacher records indicate that a positive change had occurred in the classroom culture and expectations.

Keywords

High School Mathematics, Teaching, Proof, Discourse, Geometry

Encouraging Discourse in High School Mathematics

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