id: 05240101
dt: a
an: 2008a.00296
au: Banerjee, Rakhi; Subramaniam, K.
ti: Developing procedure and structure sense of arithmetic expressions.
so: Chick, H. L. (ed.) et al., Proceedings of the 29th annual conference of the
International Group for the Psychology of Mathematics Education, PME
29, Melbourne, Australia, July 10‒15, 2005. Vol 1-4. Melbourne:
University of Melbourne, Dep. of Science and Mathematics Education.
Part II, 121-128 (2005).
py: 2005
pu: Melbourne: University of Melbourne, Dep. of Science and Mathematics
Education
la: EN
cc: F33 H23 C33 A63
ut: arithmetic expressions; beginning symbolic algebra; procedural knowledge;
structural understanding; grade 6; lower secondary; student observation
ci:
li: emis:proceedings/PME29/PME29RRPapers/PME29Vol2BanerjeeSubramaniam.pdf
ab: Summary: This paper describes sixth grade students’ performance in tasks
related to arithmetic expressions in the context of a design experiment
aimed at developing a principled approach to beginning symbolic
algebra. This approach, which is centered on the concept of ‘term’,
is described elsewhere. In the paper, students’ performance in two
kinds of tasks over items that test procedural knowledge and items that
test structural understanding is examined. We address questions of
consistency in the use of procedures in different task items, and the
transfer of procedural knowledge to the more structure-oriented items.
The data shows that the relation between procedural knowledge and
structural understanding is complex. Developing a structural
understanding of expressions requires the consistent use of the
procedures and rules in various situations/ contexts and making sense
of the relationships between the components of the expression. We cite
some preliminary evidence in favour of the effectiveness of the
structure-oriented approach both in strengthening procedural knowledge
and structural understanding.
rv: