id: 05913268
dt: j
an: 2011d.00449
au: Bass, Hyman
ti: Vignette of doing mathematics: A meta-cognitive tour of the production of
some elementary mathematics.
so: Mont. Math. Enthus. 8, No. 1-2, 3-34 (2011).
py: 2011
pu: Information Age Publishing (IAP), Charlotte, NC; Department of Mathematical
Sciences, The University of Montana, Missoula, MT
la: EN
cc: E20 E40 E50
ut: conjecturing; proving; foundations of mathematics; mathematical inquiries
ci:
li:
ab: Summary: My intention is to offer the reader a first hand and accessible
account of the generation of an interesting and elementary piece of new
mathematics and to give the reader a palpable and authentic, yet
accessible, image of what it means to do mathematics. The mathematics
itself, while of some modest interest, serves here mainly as context,
or backdrop. The main story is the metacognitive narrative of the
mathematical trajectory of the work. Several features of the event
recommend it for this purpose. First, the initial question grew from a
topic in the elementary mathematics curriculum, in the teaching of
fractions. The mathematical work illustrated here is launched by asking
a “natural question" that is precipitated by this elementary context.
>From that start, explorations, discoveries, and new questions
proliferate, some within easy reach of the standard repertoire of the
school curriculum, perhaps mobilized in some novel ways, and others
seeming to demand some new idea or perspective or method. But,
importantly for our present purposes, the ideas and methods invoked
never transcend the reach of a secondary learner who is prepared to
think flexibly about some less familiar ways of combining elementary
ideas.
rv: