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Mata-Pereira, Joana; da Ponte, João-Pedro – Educational Studies in Mathematics, 2017
A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students' mathematical reasoning, we conduct design research where whole-class…
Descriptors: Mathematics Instruction, Mathematical Logic, Generalization, Validity
Stylianides, Gabriel J.; Stylianides, Andreas J. – Educational Studies in Mathematics, 2017
The concept of "proof" has attracted considerable research attention over the past decades in part due to its indisputable importance to the discipline of mathematics and to students' learning of mathematics. Yet, the teaching and learning of proof is an instructionally arduous territory, with proof being recognized as a hard-to-teach…
Descriptors: Validity, Mathematical Logic, Intervention, Mathematics Instruction
Komatsu, Kotaro – Educational Studies in Mathematics, 2017
In contrast to existing research that has typically addressed the process from example generation to proof construction, this study aims at enhancing empirical examination after proof construction leading to revision of statements and proofs in secondary school geometry. The term "empirical examination" refers to the use of examples or…
Descriptors: Secondary School Mathematics, Mathematics Instruction, Geometry, Mathematical Logic
Pedemonte, Bettina; Reid, David – Educational Studies in Mathematics, 2011
This paper offers a typology of forms and uses of abduction that can be exploited to better analyze abduction in proving processes. Based on the work of Peirce and Eco, we describe different kinds of abductions that occur in students' mathematical activity and extend Toulmin's model of an argument as a methodological tool to describe students'…
Descriptors: Mathematics Instruction, Inferences, Logical Thinking, Models
Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron – Educational Studies in Mathematics, 2012
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…
Descriptors: Reading Comprehension, Mathematics Education, Mathematical Logic, Number Concepts
Larsen, Sean; Zandieh, Michelle – Educational Studies in Mathematics, 2008
In his 1976 book, "Proofs and Refutations," Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an…
Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Logic, Validity
Pedemonte, Bettina – Educational Studies in Mathematics, 2007
The paper presents a characterisation about argumentation and proof in mathematics. On the basis of contemporary linguistic theories, the hypothesis that proof is a special case of argumentation is put forward and Toulmin's model is proposed as a methodological tool to compare them. This model can be used to detect and analyse the structure of an…
Descriptors: Persuasive Discourse, Linguistic Theory, Mathematical Logic, Validity
Weber, Keith; Alcock, Lara – Educational Studies in Mathematics, 2004
In this paper, we distinguish between two ways that an individual can construct a formal proof. We define a syntactic proof production to occur when the prover draws inferences by manipulating symbolic formulae in a logically permissible way. We define a semantic proof production to occur when the prover uses instantiations of mathematical…
Descriptors: Mathematical Logic, Validity, Mathematical Concepts, Case Studies