id: 06035698
dt: j
an: 2012c.00420
au: Ellis, Amy B.
ti: Informing practice: The proof is in the practice.
so: Math. Teach. Middle Sch. 16, No. 9, 522-527 (2011).
py: 2011
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: E53
ut: proving; justifying; generalizing; foundations of mathematics; growing
rectangles; perimeter; area; polygons; angles
ci:
li:
ab: From the introduction: Imagine an eighth-grade classroom where students are
exploring relationships between the heights and areas of rectangles.
They are investigating a special set of rectangles that grow in a
particular way by iterating the height and length values so that the
rectangles remain similar. The students create tables, comparing the
rectangles\rq heights and areas, and notice something interesting: The
second differences for the area are always constant, no matter what
type of rectangle the students use. One student, Sara, makes the
conjecture that this will be the case for any rectangle. This situation
is ideal for giving students the opportunity to develop proofs.
rv: