id: 05945694
dt: j
an: 2011e.00329
au: Tall, David
ti: Crystalline concepts in long-term mathematical invention and discovery.
so: Learn. Math. 31, No. 1, 3-8 (2011).
py: 2011
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: D20 C30
ut: geometric concepts; models of cognitive psychology; theory of mathematics
education; concept formation
ci:
li: http://flm.educ.ualberta.ca/index.php?do=details&lang=en&vol=31&num=1&pages=3-8
ab: Summary: This paper introduces the notion of "crystalline concept" as a
focal idea in long-term mathematical thinking, bringing together the
geometric development of Van Hiele, process-object encapsulation, and
formal axiomatic systems. Each of these is a strand in the framework of
"three worlds of mathematics" with its own special characteristics, but
all three have an underlying structure that has deductive relationships
constrained by the context. In mathematics we may make choices and
construct ideas for ourselves, but once a mathematical context is
established, it has a crystalline structure of relationships that we
discover as a consequence of the structure. (ERIC)
rv: