id: 06571650
dt: j
an: 2016c.00465
au: Kontorovich, Igor’; Koichu, Boris
ti: A case study of an expert problem poser for mathematics competitions.
so: Int. J. Sci. Math. Educ. 14, No. 1, 81-99 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: D50 B60
ut: experts; mathematical competitions; mathematical problem; nesting ideas;
problem posing
ci:
li: doi:10.1007/s10763-013-9467-z
ab: Summary: This paper is concerned with organizational principles of a pool
of familiar problems of expert problem posers and the ways by which
they are utilized for creating new problems. The presented case of Leo
is part of a multiple-case study with expert problem posers for
mathematics competitions. We present and inductively analyze the data
collected in a reflective interview and in a clinical task-based
interview with Leo. In the first interview, Leo was asked to share with
us the stories behind some problems posed by him in the past. In the
second interview, he was asked to pose a new competition problem in a
thinking-aloud mode. We found that Leo’s pool of familiar problems is
organized in classes according to certain nesting ideas. Furthermore,
these nesting ideas serve him in posing problems that, ideally, are
perceived by Leo as novel and surprising not only to potential solvers,
but also to himself. Because of the lack of empirical research on
experts in mathematical problem posing, the findings are discussed in
light of research on experts in problem solving and on novices in
mathematical problem posing.
rv: