Argumentation theory for mathematical argument

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

Research output: Contribution to journalArticle

Abstract

To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport’s structured proofs.
LanguageEnglish
JournalArgumentation
DOIs
StatePublished - 4 Jan 2019

Fingerprint

Argumentation Theory
Discourse
Computational
Salient
Inference
Expository Text
Mathematical Model

Bibliographical note

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Keywords

  • inference anchoring theory
  • mathematical practice
  • mathematical argument
  • structured proof

Cite this

Corneli, J., Martin, U., Murray-Rust, D., Rino Nesin, G., & Pease, A. (2019). Argumentation theory for mathematical argument.. DOI: 10.1007/s10503-018-9474-x
Corneli, Joseph ; Martin, Ursula ; Murray-Rust, Dave ; Rino Nesin, Gabriela ; Pease, Alison. / Argumentation theory for mathematical argument. 2019
@article{2ee5ef77beed4377a876778f1aa0cd2f,
title = "Argumentation theory for mathematical argument",
abstract = "To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport’s structured proofs.",
keywords = "inference anchoring theory, mathematical practice, mathematical argument, structured proof",
author = "Joseph Corneli and Ursula Martin and Dave Murray-Rust and {Rino Nesin}, Gabriela and Alison Pease",
note = "This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.",
year = "2019",
month = "1",
day = "4",
doi = "10.1007/s10503-018-9474-x",
language = "English",

}

Corneli, J, Martin, U, Murray-Rust, D, Rino Nesin, G & Pease, A 2019, 'Argumentation theory for mathematical argument'. DOI: 10.1007/s10503-018-9474-x

Argumentation theory for mathematical argument. / Corneli, Joseph; Martin, Ursula; Murray-Rust, Dave ; Rino Nesin, Gabriela; Pease, Alison.

04.01.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Argumentation theory for mathematical argument

AU - Corneli,Joseph

AU - Martin,Ursula

AU - Murray-Rust,Dave

AU - Rino Nesin,Gabriela

AU - Pease,Alison

N1 - This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

PY - 2019/1/4

Y1 - 2019/1/4

N2 - To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport’s structured proofs.

AB - To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport’s structured proofs.

KW - inference anchoring theory

KW - mathematical practice

KW - mathematical argument

KW - structured proof

U2 - 10.1007/s10503-018-9474-x

DO - 10.1007/s10503-018-9474-x

M3 - Article

ER -

Corneli J, Martin U, Murray-Rust D, Rino Nesin G, Pease A. Argumentation theory for mathematical argument. 2019 Jan 4. Available from, DOI: 10.1007/s10503-018-9474-x