id: 06297577
dt: a
an: 2014c.00539
au: Ellis, Amy B.; Lockwood, Elise; Dogan, M. Fatih; Williams, Caroline C.;
Knuth, Eric
ti: Choosing and using examples: how example activity can support proof
insight.
so: Lindmeier, Anke M. (ed.) et al., Proceedings of the 37th conference of the
International Group for the Psychology of Mathematics Education
“Mathematics learning across the life span", PME 37, Kiel, Germany,
July 28‒August 2, 2013. Vol. 2. Kiel: IPN‒Leibniz Institute for
Science and Mathematics Education at the University of Kiel (ISBN
978-3-89088-288-8). 265-272 (2013).
py: 2013
pu: Kiel: IPN‒Leibniz Institute for Science and Mathematics Education at the
University of Kiel
la: EN
cc: E55
ut: proof; proving; role of examples
ci:
li:
ab: Summary: The results of two studies aimed at identifying the ways in which
successful provers (students and mathematicians) engage with examples
when exploring and proving conjectures. We offer a framework detailing
the participants’ actions guiding a) their example choice and b)
their example use as they attempt to prove conjectures. The framework
describes three categories for example choice (choose examples that
test boundaries, emphasize mathematical properties, and build a
progression of example types) and three categories of uses (identify
commonality, see generality, and anticipate change).
rv: