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Direct linkHanna, Gila; Yan, Xiaoheng – For the Learning of Mathematics, 2021
The paper argues that there is a need for new approaches to teaching proof with newly-available technology. It contributes to filling this need by opening a discussion on digital proof assistants, programs that allow one to do mathematics with the aid of a computer, construct proofs, and check their correctness. The paper starts by exploring such…
Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Teaching Methods
Pinto, Alon; Karsenty, Ronnie – For the Learning of Mathematics, 2020
While proof is often presented to mathematics undergraduates as a well-defined mathematical object, the proofs students encounter in different pedagogical contexts may bear salient differences. In this paper we draw on the work of Dawkins and Weber (2017) to explore variations in norms and values underlying a proof across different pedagogical…
Descriptors: Validity, Mathematical Logic, Undergraduate Study, College Mathematics
Gabel, Mika; Dreyfus, Tommy – For the Learning of Mathematics, 2020
In this paper, we discuss the relationship between rhetoric and mathematics, focusing on mathematical proofs. We offer a theoretical framework based on Perelman's New Rhetoric for analyzing the teaching of proof, taking into account rhetorical aspects. We illustrate the practicality and applicability of the proposed framework and methodology by…
Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic
Brown, Stacy – For the Learning of Mathematics, 2019
Recognizing identity not only as an important educational outcome but also as being inter-related to students' knowledge and practice, this paper explores an affordance of proof scripts; exploring students' identities. Specifically, drawing on data from teaching experiments and the construct of perceptual ambiguity, this paper presents an analysis…
Descriptors: Mathematical Logic, Validity, Mathematics Instruction, College Mathematics
Lai, Yvonne; Baldinger, Erin E. – For the Learning of Mathematics, 2021
In this paper, we propose a potential interactional explanation of tertiary-to-secondary (dis)continuity: that of authority relations. Using secondary mathematics teachers' proof validations across two contexts, we suggest that secondary teachers' conceptions of authority shape their capacity to reconcile their positions as former mathematics…
Descriptors: Mathematics Teachers, Mathematics Instruction, Secondary School Teachers, Teacher Attitudes
Dawkins, Paul Christian – For the Learning of Mathematics, 2012
Weber and Alcock's (2004, 2009) syntactic/semantic framework provides a useful means of delineating two basic categories of proof-oriented activity. They define their dichotomy using Goldin's (1998) theory of representation systems. In this paper, I intend to clarify the framework by providing criteria for classifying student reasoning into…
Descriptors: Semantics, Syntax, Models, Mathematical Logic
