Educational Studies in Mathematics

, Volume 66, Issue 1, pp 3–21 | Cite as

Modelling mathematical argumentation: the importance of qualification

  • Matthew InglisEmail author
  • Juan Pablo Mejia-Ramos
  • Adrian Simpson


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.


Argumentation Informal logic Number theory Proof Reasoning Toulmin 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Matthew Inglis
    • 1
    Email author
  • Juan Pablo Mejia-Ramos
    • 2
  • Adrian Simpson
    • 3
  1. 1.Learning Sciences Research InstituteUniversity of NottinghamNottinghamUK
  2. 2.Institute of EducationUniversity of WarwickCoventryUK
  3. 3.School of EducationUniversity of DurhamDurhamUK

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