Argumentation Theory for Mathematical Argument

Corneli, Joseph; Martin, Ursula; Murray-Rust, Dave; Nesin, Gabriela Rino; Pease, Alison

doi:10.1007/s10503-018-9474-x

Cited by 10 publications

(4 citation statements)

References 58 publications

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“…These activities have been studied by Ursula Martin and Alison Pease who connect the activities undertaken to the method of proofs and refutations (Martin and Pease, 2013a,b). Building on these data sets, in later work with Joseph Corneli and other colleagues, they model mathematical arguments by analyzing how the discourse unfolds (Corneli et al, 2019). They use what they call Inference Anchoring Theory + Content to further understand how these dialogues introduce and track salient features of mathematical progress.…”

Section: Mathematical Communities As Argumentativementioning

confidence: 99%

An interview with Anthony Brown, Ohio State University, Columbus, OH, USA

2022

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Formal logic has often been seen as uniquely placed to analyse mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of mathematical reasoning closely resemble patterns of reasoning in non-mathematical domains. Hence the tools developed to understand informal reasoning, collectively known as argumentation theory, are also applicable to much mathematical argumentation. This chapter investigates some of the details of that application. Consideration is given to the many contrasting meanings of the word 'argument'; to some of the specific argumentation-theoretic tools that have been applied to mathematics, notably Toulmin layouts and argumentation schemes; to some of the different ways that argumentation is implicated in mathematical practices; and to the social aspects of mathematical argumentation.If you are present at a game of chess, it will not suffice, for the understanding of the game, to know the rules for moving the pieces. That will only enable you to recognize that each move

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Section: Mathematical Communities As Argumentativementioning

confidence: 99%

An interview with Anthony Brown, Ohio State University, Columbus, OH, USA

2022

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“…In earlier work (Corneli et al 2019), we 5 explored the application of recent argumentation research to crowdsourced mathematics. We asked: How can we represent mathematical argument using Inference Anchoring Theory (IAT)?…”

Section: Argumentationmentioning

confidence: 99%

Using crowdsourced mathematics to understand mathematical practice

Pease

Martin

Tanswell

et al. 2020

ZDM Mathematics Education

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Records of online collaborative mathematical activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (comparing individual and collaborative proofs); social psychology (on the prospects for a measure of collective intelligence); human-computer interaction (on the factors that led to the success of one such project); network analysis (on the differences between collaborations on open research problems and known-but-hard problems); and argumentation theory (on modelling the argument structures of online collaborations). We also give an overview of qualitative approaches, reviewing work from empirical philosophy (on explanation in crowdsourced mathematics); sociology of scientific knowledge (on conventions and conversations in online mathematics); and ethnography (on contrasting conceptions of collaboration). We suggest how these diverse methods can be applied to crowdsourced mathematics and when each might be appropriate.

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“…In recent years, a growing number of software tools of increasing sophistication have been designed for the analysis and evaluation of argument. These tools represent a potentially invaluable resource for the study of mathematical argument, but their application to mathematics has only just begun (Pease et al, 2017;Corneli et al, 2019). Again, I am unaware of any application of these resources in mathematics education: there is a growing body of work applying digital tools to mathematics education (for example, Modeste, 2016;Durand-Guerrier et al, 2019), but not the tools specific to argumentation.…”

Section: Conclusion For Educationmentioning

confidence: 99%

Evidence, proofs, and derivations

Aberdein

2019

ZDM Mathematics Education

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The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning.

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Argumentation Theory for Mathematical Argument

Cited by 10 publications

References 58 publications

An interview with Anthony Brown, Ohio State University, Columbus, OH, USA

An interview with Anthony Brown, Ohio State University, Columbus, OH, USA

Using crowdsourced mathematics to understand mathematical practice

Evidence, proofs, and derivations

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