Encyclopedia of Mathematics Education

Living Edition
| Editors: Steve Lerman

Argumentation in Mathematics Education

  • Bharath SriramanEmail author
  • Kristin Umland
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-77487-9_11-4


“Argumentation in mathematics education” can mean two things:
  1. 1.

    The mathematical arguments that students and teachers produce in mathematics classrooms

  2. 2.

    The arguments that mathematics education researchers produce regarding the nature of mathematics learning and the efficacy of mathematics teaching in various contexts.


This entry is about the first of these two interpretations.

Mathematics Classrooms and Argumentation

In the context of a mathematics classroom, we will take a “mathematical argument” to be a line of reasoning that intends to show or explain why a mathematical result is true. The mathematical result might be a general statement about some class of mathematical objects or it might simply be the solution to a mathematical problem that has been posed. Taken in this sense, a mathematical argument might be a formal or informal proof, an explanation of how a student or teacher came to make a particular conjecture, how a student or teacher reasoned through a...


Argumentation Beliefs Heuristics Lakatos Proof 
This is a preview of subscription content, log in to check access.


  1. Fawcett HP (1938) The nature of proof: a description and evaluation of certain procedures used in senior high school to develop an understanding of the nature of proof. National Council of Teachers of Mathematics, RestonGoogle Scholar
  2. Lakatos I (1976) Proofs and refutations: the logic of mathematical discovery. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  3. Polya G (1954) Patterns of plausible inference. Princeton University Press, PrincetonGoogle Scholar
  4. Schoenfeld AH (1985) Mathematical problem solving. Academic, OrlandoGoogle Scholar
  5. Sriraman B (2003) Can mathematical discovery fill the existential void? The use of conjecture, proof and refutation in a high school classroom. Math Sch 32(2):2–6Google Scholar
  6. Sriraman B (2006) An Ode to Imre Lakatos: bridging the ideal and actual mathematics classrooms. Interchange Q Rev Educ 37(1&2):155–180Google Scholar
  7. Sriraman B, Vanspronsen H, Haverhals N (2010) Commentary on DNR based instruction in mathematics as a conceptual framework. In: Sriraman B, English L (eds) Theories of mathematics education: seeking new frontiers. Springer, Berlin, pp 369–378CrossRefGoogle Scholar
  8. Sriraman B (2017) Humanizing mathematics and its philosophy: essays celebrating the 90th birthday of Reuben Hersh. Birkhauser Basel. SpringerGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA
  2. 2.Content DevelopmentIllustrative MathematicsOro ValleyUSA

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA