id: 05358896
dt: j
an: 2008f.00349
au: Proulx, Jérôme; Pimm, David
ti: Algebraic formulas, geometric awareness and Cavalieri\rq s principle.
so: Learn. Math. 28, No. 2, 17-24 (2008).
py: 2008
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: G40 G30 A30
ut: plane geometry; solid geometry; rectangles; parallelograms;
transformations; Cavalieri-equivalence; prisms; pyramids; cubes;
cylinders; Cavalieri transformations; arithmetisation of geometry
ci:
li:
ab: From the introduction: The starting point for this article is an
exploration of the complex set of connections between algebraic
formulas and geometric awareness, in particular the limited extent to
which the latter is either embedded in or necessary for the former. We
do so within the core school mathematical topic of area (and, to some
extent, of volume), but we wish to go beyond what is now explicit in
curriculum documents of various countries, namely that such formulas
should be motivated or even proven using geometric arguments. One
complaint in relation to this minor move (as we see it) is that it
leaves unchallenged the prominent place taken by formulas themselves as
the primary or even sole goal of teaching and learning about area and
volume. We wish to examine a possibly unfamiliar way (namely
Cavalieri\rq s principle, our mediating third of the title) of staying
with the geometry on its own terms. In doing so, we take seriously
Tahta\rq s formulation that “the geometry that can be told is not
geometry”, noting that area and volume formulas are unreservedly
about such tellings. The moment the word “measure” is uttered, the
instant that variables are deployed, geometry has vanished (despite the
etymological origins of the word itself).
rv: