id: 06439949
dt: a
an: 2015c.00508
au: Weber, Keith
ti: Proof as a cluster concept.
so: 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).
py: 2014
pu: [s. l.]: International Group for the Psychology of Mathematics Education
la: EN
cc: E50 D20 E20
ut: proofs; proving; conceptualization
ci:
li:
ab: 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.
rv: