Introducing students and prospective teachers to the notion of proof in mathematics
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Authors
Stylianides, AJ
Stylianides, GJ
Publication Date
2022-06Journal Title
Journal of Mathematical Behavior
ISSN
0732-3123
Publisher
Elsevier BV
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Stylianides, A., & Stylianides, G. (2022). Introducing students and prospective teachers to the notion of proof in mathematics. Journal of Mathematical Behavior https://doi.org/10.1016/j.jmathb.2022.100957
Abstract
Although the notion of proof is important for all learners’ mathematical experiences, there has been limited attention to what it might involve and look like to introduce students and prospective teachers to proof. In this paper we argue for the importance of having a coherent approach to introducing students and prospective teachers to proof, and we discuss the theoretical basis of a learning trajectory relevant to both groups. We also discuss an instructional sequence that aimed to promote the learning trajectory among English secondary students and U.S. prospective elementary teachers, drawing on data from two multi-year design experiments. The learning trajectory comprises two milestones: (1) seeing a need to learn about proof and (2) developing an operationally functional conceptualization of proof. The “need” in milestone 1 entails an aspect of epistemological justification applicable to both students and prospective teachers, and a further aspect of pedagogical justification applicable to prospective teachers.
Sponsorship
The paper is based on research supported by funds from the Spencer Foundation to both authors (grant numbers: 200700100, 200800104) and the Economic and Social Research Council (ESRC) in England to the first author (grant reference: RES-000-22-2536).
Funder references
Economic and Social Research Council (RES-000-22-2536-A)
Identifiers
External DOI: https://doi.org/10.1016/j.jmathb.2022.100957
This record's URL: https://www.repository.cam.ac.uk/handle/1810/336228
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
Licence URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
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