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Encyclopedia of Mathematics Education pp 1–3Cite as

Argumentation in Mathematics

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Definition

Argumentation refers to the process of making an argument, that is, drawing conclusions based on a chain of reasoning. Götz Krummheuer suggests that argumentation can be thought of as a social process in which the cooperating individuals “adjust their intentions and interpretations by verbally presenting the rationales for their actions” (Cobb and Bauersfeld 1995, p. 13). In mathematics, unlike any empirically based discipline, the validity of an argument in its final form is judged solely on whether it is logically consistent.

Characteristics of Argumentation

The origins of logic, a key component of mathematical argumentation, can be traced back to Aristotelian logic and his use of syllogisms, with thinkers making improvements to this method over time as they were confronted with paradoxes. Argumentation was primarily the domain of theologians and medieval and postmedieval scholastics for over 1700 years after Aristotle. Some well-known examples of theological argumentation...

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References

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  • Whitehead AN, Russell B (1927) Principia mathematica. Cambridge University Press, Cambridge

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Author information

Authors and Affiliations

  1. The University of New Mexico, Albuquerque, NM, USA

    Kristin Umland

  2. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

  3. Content Development, Illustrative Mathematics, Oro Valley, AZ, USA

    Kristin Umland

Authors
  1. Kristin Umland
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  2. Bharath Sriraman
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Corresponding author

Correspondence to Kristin Umland .

Editor information

Editors and Affiliations

  1. South Bank University Centre for Mathematics Education, London, UK

    Steve Lerman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

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Umland, K., Sriraman, B. (2018). Argumentation in Mathematics. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_10-4

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  • DOI: https://doi.org/10.1007/978-3-319-77487-9_10-4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77487-9

  • Online ISBN: 978-3-319-77487-9

  • eBook Packages: Springer Reference EducationReference Module Humanities and Social SciencesReference Module Education

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