
05881882
a
2011d.00640
Subramaniam, K.
Banerjee, Rakhi
The arithmeticalgebra connection: A historicalpedagogical perspective.
Cai, Jinfa (ed.) et al., Early algebraization. A global dialogue from multiple perspectives. Berlin: Springer (ISBN 9783642177347/hbk; 9783642177354/ebook). Advances in Mathematics Education, 87107 (2011).
2011
Berlin: Springer
EN
H23
F13
C33
A33
arithmetic and algebra in the Indian mathematical tradition
building on students' understanding of arithmetic
history of mathematics
curriculum
grade 6
lower secondary
doi:10.1007/9783642177354_6
Summary: The problem of designing a teaching learning approach to symbolic algebra in the middle school that uses students' 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 arithmeticalgebra connection from a teachinglearning 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.