
06439949
a
2015c.00508
Weber, Keith
Proof as a cluster concept.
Nicol, Cynthia (ed.) et al., Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education ``Mathematics education at the edge", PME 38 held jointly with the 36th conference of PMENA, Vancouver, Canada, July 1520, 2014, Vol. 5. [s. l.]: International Group for the Psychology of Mathematics Education (ISBN 9780864913609/set; 9780864913654/v.5). 353360 (2014).
2014
[s. l.]: International Group for the Psychology of Mathematics Education
EN
E50
D20
E20
proofs
proving
conceptualization
Summary: Proof is a central concept in mathematics education, yet mathematics educators have failed to reach a consensus on how proof should be conceptualized. I advocate defining proof as a clustered concept, in the sense of {\it G. Lakoff} [Women, fire, and dangerous things. Cambridge, UK: Cambridge University Press. (1987)]. I contend that this offers a better account of mathematicians' practice with respect to proof than previous accounts that attempted to define a proof as an argument possessing an essential property, such as being convincing or deductive. I also argue that it leads to useful pedagogical consequences.