### Exercising Mathematical Authority: Three Cases of Preservice Teachers’ Algebraic Justifications

#### Abstract

Students’ ability to reason for themselves is a crucial step in developing conceptual understandings of mathematics, especially if those students are preservice teachers. Even if classroom environments are structured to promote students’ reasoning and sense-making, students may rely on prior procedural knowledge to justify their mathematical arguments. In this study, we employed a multiple-case-study research design to investigate how groups of elementary preservice teachers exercised their mathematical authority on a growing visual patterns task. The results of this study emphasize that even when mathematics teacher educators create classroom environments that delegate mathematical authority to learners, they still need to attend to the strength of preservice teachers’ reliance on their prior knowledge.

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