Abstract
This manuscript focuses on how students make sense of proofs. Participants were students who engaged in peer-review conferences of each other’s attempted proofs in a graduate-level real analysis course for mathematics teachers. Building on the concept of distance from conversational analysis, we distinguish how three types of distance (epistemic, rhetorical, and ontological) between a student and a particular claim influence sensemaking. This article also explores the impact of students’ sensemaking on their perceptions of proof.
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Notes
Continuity: Let f: D → R, where D is a subset of R. We say that f is continuous on D, if for every x0 in D, f is continuous at x0. We say f is continuous at x0 if, for every ε > 0 there exists a δ > 0 such that for all x in D with |x−x0|< δ, |f(x)–f(x0)| < ε.
Uniform continuity: Let f: D → R, where D is a subset of R. We say that f is uniformly continuous on D, if for every ε > 0 there exists a δ > 0 such that for all s,t in D with |s−t|< δ, |f(s)–f(t)| < ε.
A single student discussed deep engagement in a prior inquiry-based proof course. This was the only instance of connection and exploration in the prior courses category.
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Acknowledgements
The authors thank Martha Byrne and Cathery Yeh for their invaluable support in revising this manuscript. They also thank V. Rani Satyam, Niral Shah, and Keith Weber for their suggestions to deepen the literature review.
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DLR wrote the first draft, created coding scheme, and led analysis. MEP supported double coding, provided edits and feedback on manuscript.
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Reinholz, D.L., Pilgrim, M.E. Student sensemaking of proofs at various distances: the role of epistemic, rhetorical, and ontological distance in the peer review process. Educ Stud Math 106, 211–229 (2021). https://doi.org/10.1007/s10649-020-10010-3
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DOI: https://doi.org/10.1007/s10649-020-10010-3