Definition
“Argumentation in mathematics education” can mean two things:
- 1.
The mathematical arguments that students and teachers produce in mathematics classrooms
- 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...
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References
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, Reston
Lakatos I (1976) Proofs and refutations: the logic of mathematical discovery. Cambridge University Press, Cambridge
Polya G (1954) Patterns of plausible inference. Princeton University Press, Princeton
Schoenfeld AH (1985) Mathematical problem solving. Academic, Orlando
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):2–6
Sriraman B (2006) An Ode to Imre Lakatos: bridging the ideal and actual mathematics classrooms. Interchange Q Rev Educ 37(1&2):155–180
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 369–378
Sriraman B (2017) Humanizing mathematics and its philosophy: essays celebrating the 90th birthday of Reuben Hersh. Birkhauser Basel. Springer
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Sriraman, B., Umland, K. (2018). Argumentation in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_11-4
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DOI: https://doi.org/10.1007/978-3-319-77487-9_11-4
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