id: 06571533
dt: j
an: 2016c.00478
au: Selling, Sarah Kate
ti: Learning to represent, representing to learn.
so: J. Math. Behav. 41, 191-209 (2016).
py: 2016
pu: Elsevier, New York, NY
la: EN
cc: D53 C73 C53
ut: representation; mathematical practices; collaboration; agency; algebra
ci:
li: doi:10.1016/j.jmathb.2015.10.003
ab: Summary: This study explores how students learn to create, discuss, and
reason with representations to solve problems. A summer school algebra
class for seventh and eighth graders provided opportunities for
students to create and use representations as problem-solving tools.
This case study follows the learning trajectories of three boys. Two of
the three boys had been low-achievers in their previous math classes,
and one was a high achiever. Analysis of all three boysâ€™ written work
reveals how their representations became more sophisticated over time.
Their small group interactions while problem-solving also show changes
in how they communicated and reasoned with representations. For these
boys, representation functioned as a learning practice. Through
constructing and reasoning with representations, the boys were able to
engage in generalizing and justifying claims, discuss quadratic growth,
and collaborate and persist in problem-solving. Negotiating different
student-constructed representations of a problem also gave them
opportunities to act with agency, as they made choices and judgments
about the validity of the different perspectives. These findings have
implications for the importance of giving all students access to
mathematics through representations, with representational thinking
serving as a central disciplinary practice and as a learning practice
that supports further mathematics learning.
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