id: 06664330
dt: j
an: 2016f.01045
au: Meagher, Michael S.; Edwards, Michael Todd; Özgün-Koca, S. Asli
ti: What’s your answer? Searching for triangles.
so: Math. Teach. (Reston) 109, No. 7, 500-506 (2016).
py: 2016
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G43 U73
ut: geometry; use of technology; teaching methods; problem solving;
manipulative materials; triangles
ci:
li: http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol109/Issue7/What_s-Your-Answer_-Searching-for-Triangles/
ab: Summary: The article opens with a Geoboard Triangle Quest in this form:
“How many noncongruent triangles can be constructed on a $4 \times 4$
geoboard? How do you know? Justify your answer with significant
supporting work.” The use of advanced digital technologies as tools
for problem solving receives much attention in the methods classes if
the authors. They anticipated that some students would use technology
to solve the task. The authors looked forward to the interplay between
those approaches and hands-on approaches mirroring those adopted by
Allen’s students. Ultimately, the students attempted the task in many
ways, using both digital and analog techniques. Interestingly,
different solution strategies yielded different numbers of triangles.
Although Allen’s students tentatively concluded that 72 triangles
were possible, they did not provide a proof, and none of the students
arrived at this answer. In this article, the authors discuss how they
came to what they consider a definitive solution and, on the way,
address a challenge that arises in many inquiry-based classrooms: When
confronted with multiple, conflicting results, how does one determine
which ‒ if any ‒ answers are correct? (ERIC)
rv: