id: 06664714
dt: j
an: 2016f.01394
au: Loong, Esther Yook Kin
ti: Fostering mathematical understanding through physical and virtual
manipulatives.
so: Aust. Math. Teach. 70, No. 4, 3-10 (2014).
py: 2014
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: U60 U70 D40
ut: virtual manipulatives; concrete manipulatives; problem solving;
understanding; learning
ci:
li:
ab: Summary: When solving mathematical problems, many students know the
procedure to get to the answer but cannot explain why they are doing it
in that way. According to Skemp these students have instrumental
understanding but not relational understanding of the problem. They
have accepted the rules to arriving at the answer without questioning
or understanding the underlying reasons for why a certain procedure is
carried out. To help students grasp abstract mathematical concepts and
form relational understanding of these concepts, research has found
that it is often necessary to make use of physical or virtual materials
to help scaffold their understanding and/or simplify the abstract idea.
This paper presents some ways in which fundamental concepts such as
subtraction with regrouping, equivalent fractions, dividing and
multiplying fractions, and measurement topics such as area and
perimeter, can be explored and clarified. A range of physical and
virtual manipulatives are suggested to help foster and consolidate the
relational understanding needed to grasp these concepts. A number of
examples are provided which are suitable for teachers from primary
through to middle years. Even though some of these concepts seem basic
and related to primary mathematics, they are addressed here because
they underpin the efficient working out of the more abstract concepts
associated with middle school mathematics. Having a strong relational
understanding and subsequent mastery of these concepts help prevent
misconceptions and errors, and position students better in their
mathematics learning. Additionally, these activities and strategies
have the potential to help struggling middle school students grasp
these basic concepts. (ERIC)
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