The role of the researcher’s epistemology in mathematics education: an essay on the case of proof

Balacheff, Nicolas

doi:10.1007/s11858-008-0103-2

Cited by 43 publications

(22 citation statements)

References 7 publications

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“…Nonetheless, because a narrative model is a living thing, this model of MR will surely evolve and grow in the hands of its users. Lastly, in the spirit of Balacheff (2008), the explicit formulation of the epistemological underpinnings of this model of MR can also be seen as a first step in eventually creating bridges between different epistemologies.…”

Section: A Model Of Mathematical Reasoning For School Mathematicsmentioning

confidence: 99%

A conceptual model of mathematical reasoning for school mathematics

2017

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The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR, this research project aimed to qualify it from a theoretical perspective, with an elaboration that would not only indicate its ways of being thought about and espoused but also serve as a tool for reflection and thereby contribute to the further evolution of the cultures of the teaching and research communities in mathematics education. To achieve such an elaboration, a literature search based on anasynthesis (Legendre, 2005) was undertaken. From the analysis of the mathematics education research literature on MR and taking a commognitive perspective (Sfard, 2008), the synthesis that was carried out led to conceptualizing a model of mathematical reasoning. This model, which is herein described, is constituted of two main aspects: a structural aspect and a process aspect, both of which are needed to capture the central characteristics of MR.

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Section: A Model Of Mathematical Reasoning For School Mathematicsmentioning

confidence: 99%

A conceptual model of mathematical reasoning for school mathematics

2017

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“…One recommendation is the need for more explicit teaching of proof, both in school and university (Balacheff 2008;Hanna and de Villiers 2008;Hemmi 2008), with some (e.g., Stylianides and Stylianides 2007;Hanna and Barbeau 2008) arguing for it to be made a central topic in both institutions. A possible introduction to proof, suggested by Harel (2008) and Palla et al (2012) is proof by mathematical induction.…”

Section: Proof and Provingmentioning

confidence: 99%

Key Mathematical Concepts in the Transition from Secondary School to University

Thomas

Druck

Huillet

et al. 2015

The Proceedings of the 12th International Congress on Mathematical Education

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This report1 from the ICME12 Survey Team 4 examines issues in the transition from secondary school to university mathematics with a particular focus on mathematical concepts and aspects of mathematical thinking. It comprises a survey of the recent research related to: calculus and analysis; the algebra of generalised arithmetic and abstract algebra; linear algebra; reasoning, argumentation and proof; and modelling, applications and applied mathematics. This revealed a multi-faceted web of cognitive, curricular and pedagogical issues both within and across the mathematical topics above. In addition we conducted an international survey of those engaged in teaching in university mathematics departments. Specifically, we aimed to elicit perspectives on: what topics are taught, and how, in the early parts of university-level mathematical studies; whether the transition should be smooth; student preparedness for university mathematics studies; and, what university departments do to assist those with limited preparedness. We present a summary of the survey results from 79 respondents from 21 countries.

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“…They indicate one factor which influences which conception students adopt at any given time. Balacheff (2008) suggested that proof has several different meanings in the mathematics education literature, and pointed out that this could be a hindrance for research progress. The same point may be true for individual students and their mathematical progress.…”

Section: Discussionmentioning

confidence: 99%

Semantic contamination and mathematical proof: Can a non-proof prove?

Mejía-Ramos

Inglis

2011

The Journal of Mathematical Behavior

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The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of "proof" and "prove" in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove.

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The role of the researcher’s epistemology in mathematics education: an essay on the case of proof

Cited by 43 publications

References 7 publications

A conceptual model of mathematical reasoning for school mathematics

A conceptual model of mathematical reasoning for school mathematics

Key Mathematical Concepts in the Transition from Secondary School to University

Semantic contamination and mathematical proof: Can a non-proof prove?

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