\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015c.00508}
\itemau{Weber, Keith}
\itemti{Proof as a cluster concept.}
\itemso{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 PME-NA, Vancouver, Canada, July 15--20, 2014, Vol. 5. [s. l.]: International Group for the Psychology of Mathematics Education (ISBN 978-0-86491-360-9/set; 978-0-86491-365-4/v.5). 353-360 (2014).}
\itemab
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.
\itemrv{~}
\itemcc{E50 D20 E20}
\itemut{proofs; proving; conceptualization}
\itemli{}
\end