id: 06248019
dt: j
an: 2014a.00660
au: Moon, Kyunghee; Brenner, Mary E.; Jacob, Bill; Okamoto, Yukari
ti: Prospective secondary mathematics teachersâ€™ understanding and cognitive
difficulties in making connections among representations.
so: Math. Think. Learn. 15, No. 3, 201-227 (2013).
py: 2013
pu: Taylor \& Francis (Routledge), Philadelphia, PA
la: EN
cc: G79 H39 I29 D79 C39
ut: representations; connecting; understanding; cognitive difficulties;
mathematical ideas; conic curves; variation; Cartesian connection;
graph as a locus of points
ci:
li: doi:10.1080/10986065.2013.794322
ab: Summary: This study investigates prospective secondary teachersâ€™
cognitive difficulties and mathematical ideas involved in making
connections among representations. We implemented a three-week teaching
unit to help prospective secondary mathematics teachers develop
understanding of big ideas that are critical to formulating connections
among representations, in the context of conic curves. Qualitative
analysis of data showed that most undergraduate mathematics majors and
minors in this study struggled with variation, the Cartesian
connection, and other affiliated ideas such as graph as a locus of
points. Furthermore, they were unable to identify basic metric
relations encoded in algebraic expressions such as the distance between
points, which further compounded their difficulties in making
connections among representations. We argue that mathematics teacher
education needs more focus on these ideas so that their graduates can
successfully teach these big ideas in their future instruction.
rv: