Modelling mathematical argumentation: the importance of qualification

By Matthew Inglis, Juan Pablo Mejía-Ramos, Adrian P. Simpson. 2007

261 citations recorded by the source corpus.

In recent years several mathematics education researchers have attempted to analyse students’ arguments using a restricted form of Toulmin’s [The Uses of Argument, Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role in mathematical argumentation, and that one of the goals of instruction should be to develop students’ abilities to appropriately match up warrant-types with modal qualifiers.

Subfields: Developmental and Educational Psychology, Education

View Paper: https://www.semanticscholar.org/paper/96ddb6bde53932f48104dbbea60e6d864aa9d2f2

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In Developmental and Educational Psychology

In Education

Citations in the corpus

Why and how mathematicians read proofs: an exploratory study (2011, methodology): “In this paper we expand the typology of warrant-types described by Inglis, Mejia-Ramos, and Simpson (2007) by distinguishing four types of arguments that an individual may use when reading a proof.”
ADAPTING A METHODOLOGY FROM MATHEMATICS EDUCATION RESEARCH TO CHEMISTRY EDUCATION RESEARCH: DOCUMENTING COLLECTIVE ACTIVITY (2012, methodology): “The Toulmin model of argumentation has been adapted by many in the fields of mathematics and science education as a tool to assess the quality or structure of a specific mathematical or scientific argument and to analyze students’ evolving conceptions by documenting their collective argumentation (E”
The role of abduction in proving processes (2011, result): “As has been highlighted by other researchers (e.g., Inglis, Mejia-Ramos, Simpson, 2007 ) these elements are very important.”
Can slope be negative in 3-space? Studying concept image of slope through collective definition construction (2011, background): “Inglis, Mejia-Ramos and Simpson (2007) describe arguments by graduate students in mathematics who frequently used both qualifiers and rebuttals in individually constructed mathematical arguments, which”
Learning opportunities from group discussions: warrants become the objects of debate (2008, background): “Inglis, Mejia-Ramos, and Simpson (2007) argue that although these components generally are not used by mathematics educators when analyzing argumentation, considering these qualifications can provide a more comprehensive description of individuals’ argumentation and reasoning processes.”
Semiotic and theoretic control in argumentation and proof activities (2011, methodology): “Following other researchers (see for instance Pedemonte, 2007; Inglis, Mejia-Ramos & Simpson, 2007; Jahnke, 2008), we shall adopt Toulmin's (complete) model to study argumentation and proof not only as products but also as processes.”
‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation (2012, methodology): “Our proposed approach follows suit from the work of Inglis and colleagues (Inglis et al, 2007) who also proposed a classification of warrants (though with reference to their analysis of purely mathematical arguments) and emphasised the need to deploy the complete version of Toulmin’s model.”
Identifying Kinds of Reasoning in Collective Argumentation (2014, background): “As Krummheuer (1995) and others have pointed out, it is often difficult to determine precisely how students are using particular information as either data or warrants.”
Proofs as bearers of mathematical knowledge (2008, background): “... proof (Reiss and Renkl 2002); the emphasis on the logical structures of proofs in teaching at the tertiary level (Selden and Selden 1995); proof as explanation and justification (Hanna 1990, 2000; Sowder and Harel 2003); proof and hypotheses (Jahnke 2007); curricular issues (Hoyles 1997); proof ”
Doctoral students’ use of examples in evaluating and proving conjectures (2008, background): “Previous reports of this study have focused on the importance of qualification in mathematicians’ descriptions of their own certainty about mathematical inferences (Inglis et al. 2007).”