id: 06664331
dt: j
an: 2016f.00620
au: Szydlik, Jennifer Earles; Parrott, Amy; Belnap, Jason Knight
ti: Conversations to transform geometry class.
so: Math. Teach. (Reston) 109, No. 7, 507-513 (2016).
py: 2016
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: D43 C53 C73 G43
ut: geometry; discussion; definitions; teaching methods; concept formation;
geometric concepts
ci:
li: http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol109/Issue7/Conversations-to-Transform-Geometry-Class/
ab: Summary: Classroom culture is negotiated and established through both
conversations and practices. Traditionally, teachers and researchers
have focused primarily on the individual and social construction of
mathematical content ‒ that is, students’ conceptual understanding
and procedural skills ‒ through mathematical actions and practices.
This article shares three explicit discussions about the nature of
mathematics: (1) Mathematical Objects Exist Only in Our Minds: The
authors put this question to their geometry students on the first day
of class; (2) Definitions Matter to Mathematicians. They Matter a Lot!:
Definitions are crucial to mathematicians. They provide a means of
conveying ideal mental objects, and they give precise conditions for
classifying objects and making arguments about those objects. The
authors have found that students learn to value and understand
definitions better if they regularly engage in cultural conversations
in which they are asked to use a definition to classify a set of
objects and then have the opportunity to discuss the very nature of
definitions; and (3) Examples ‒ Unless You Can Examine Them All ‒
Do Not Make A Mathematical Proof: During the first weeks of geometry
classes, the authors discuss the Euclidean geometry theorem that the
sum of the angles in a triangle is a straight angle. They typically
first spend ten to fifteen minutes exploring representations of various
triangles. In small groups, students may cut out triangles and then
fold the triangle so that the vertices of the triangles meet at a
single point, or they may tear off the angles containing the vertices
and arrange them so that the three angles are adjacent to one another.
They may also draw several triangle representations and measure the
angles with protractors. (ERIC)
rv: