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Abstract
The purpose of this study was to understand how prospective middle school teachers used strip diagrams and double number lines in a content course. Representations play a critical role in mathematics teaching and learning. They help students and teachers solve problems, communicate their thinking, and access mathematics. However, teachers largely privilege symbols over non-symbolic representations such as drawings and diagrams, thus restricting their own and their students mathematical thinking and communication. I conjecture the genesis of a culture shift to legitimizing drawings in school mathematics begins in mathematics teacher education content courses, an under-researched space. In this study, I analyzed a year-long content course for prospective middle school teachers where they learned to consistently use two drawings, strip diagrams and double number lines, to solve mathematical problems. I collected video data of classroom lessons and analyzed how the teachers created their drawings. To analyze the drawings, I constructed an explicit set of methods heavily shaped by Geoffrey Saxes Papua New Guinea and classroom studies. I distilled the teachers drawings down to a set of coarse formssets of inscriptions used to create drawings to serve certain functions. I also identified three task features shaping which coarse forms teachers used when creating their drawings. Using these methods and results, I provided an account of a community of teachers who reasoned with drawings to understand, organize, and connect critical concepts in middle grades mathematics.