id: 06454508
dt: j
an: 2015d.00496
au: Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta; Koike, Norio
ti: Proof problems with diagrams: an opportunity for experiencing proofs and
refutations.
so: Learn. Math. 34, No. 1, 36-42 (2014).
py: 2014
pu: FLM Publishing Association, c/o University of New Brunswick, Faculty of
Education, Fredericton, NB; Canadian mathematics education study group
- CMESG (Groupe Canadien d’étude en didactique des mathématiques -
GCEDM), [s. l.]
la: EN
cc: E50 G40 D70
ut: proving; proofs; geometry; refutations; diagrams; difficulties
ci: ME 2015d.00503
li: http://flm-journal.org/index.php?do=details&lang=en&vol=34&num=1&pages=36-42
ab: Summary: It has become gradually accepted that proof and proving are
essential at all grades of mathematical learning. Among the various
aspects of proof and proving, this study addresses proofs and
refutations described by {\it I. Lakatos} [Proofs and refutations. The
logic of mathematical discovery. Cambridge: Cambridge University Press
(1976; ME 2015d.00503)], in particular a part of increasing content by
deductive guessing, to introduce an authentic process into mathematics
classrooms. This paper analyzes proof problems with diagrams as an
appropriate task for this mathematical action, and illustrates, with a
sequence of three lessons in the eighth grade, that a certain type of
such problems can provide students with an opportunity to engage in
this action.
rv: