id: 06388194
dt: j
an: 2015a.00475
au: Fernández, Ceneida; De Bock, Dirk; Verschaffel, Lieven; Van Dooren, Wim
ti: Do students confuse dimensionality and “directionality"?
so: J. Math. Behav. 36, 166-176 (2014).
py: 2014
pu: Elsevier, New York, NY
la: EN
cc: E53 D73 G33
ut: dimensionality; linear reasoning; area; perimeter; secondary level
ci:
li: doi:10.1016/j.jmathb.2014.07.001
ab: Summary: The aim of this research is to understand the way in which
students struggle with the distinction between dimensionality and
“directionality" and if this type of potential confusion could be a
factor affecting students’ tendency toward improper linear reasoning
in the context of the relations between length and area of geometrical
figures. 131 9th grade students were confronted with a multiple-choice
test consisting of six problems related to the perimeter or the area of
an enlarged geometrical figure, then some interviews were carried out
to obtain qualitative data in relation to students’ reasoning.
Results indicate that more than one fifth of the students’ answers
could be characterized as based on directional thinking, suggesting
that students struggled with the distinction between dimensionality and
“directionality". A single arrow showing one direction (image
provided to the students) seemed to strengthen the tendency toward
improper linear reasoning for the area problems. Two arrows showing two
directions helped students to see a quadratic relation for the area
problems.
rv: