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 1,700 years after Aristotle. Some well-known examples of theological...
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References
Cobb P, Bauersfeld H (1995) The emergence of mathematical meaning. Lawrence Erlbaum and Associates, Mahwah
Fischbein E (1980) Intuition and proof. Paper presented at the 4th conference of the international group for the psychology of mathematics education, Berkeley, CA
Hersh R (2006) 18 unconventional essays on the nature of mathematics. Springer, New York
Kline M (1976) NACOME: implications for curriculum design. Math Teach 69:449–454
Lakatos I (1976) Proofs and refutations: the logic of mathematical discovery. Cambridge University Press, Cambridge
Whitehead AN, Russell B (1927) Principia mathematica. Cambridge University Press, Cambridge
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Umland, K., Sriraman, B. (2014). Argumentation in Mathematics. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_10
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