id: 05881882
dt: a
an: 2011d.00640
au: Subramaniam, K.; Banerjee, Rakhi
ti: The arithmetic-algebra connection: A historical-pedagogical perspective.
so: Cai, Jinfa (ed.) et al., Early algebraization. A global dialogue from
multiple perspectives. Berlin: Springer (ISBN 978-3-642-17734-7/hbk;
978-3-642-17735-4/ebook). Advances in Mathematics Education, 87-107
(2011).
py: 2011
pu: Berlin: Springer
la: EN
cc: H23 F13 C33 A33
ut: arithmetic and algebra in the Indian mathematical tradition; building on
studentsâ€™ understanding of arithmetic; history of mathematics;
curriculum; grade 6; lower secondary
ci:
li: doi:10.1007/978-3-642-17735-4_6
ab: Summary: The problem of designing a teaching learning approach to symbolic
algebra in the middle school that uses studentsâ€™ knowledge of
arithmetic as a starting point has not been adequately addressed in the
recent revisions of the mathematics curriculum in India. India has a
long historical tradition of mathematics with strong achievements in
arithmetic and algebra. We review an explicit discussion of the
relation between arithmetic and algebra in a historical text from the
twelfth century, emphasizing that algebra is more a matter of insight
and understanding than of using symbols. Algebra is seen as
foundational to arithmetic rather than as a generalization of
arithmetic. We draw implications from these remarks and present a
framework that illuminates the arithmetic-algebra connection from a
teaching-learning point of view. Finally, we offer brief sketches of an
instructional approach developed through a design experiment with
students of grade 6 that is informed by this framework, and discuss
some student responses.
rv: