\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2011d.00640}
\itemau{Subramaniam, K.; Banerjee, Rakhi}
\itemti{The arithmetic-algebra connection: A historical-pedagogical perspective.}
\itemso{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).}
\itemab
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 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.
\itemrv{~}
\itemcc{H23 F13 C33 A33}
\itemut{arithmetic and algebra in the Indian mathematical tradition; building on students' understanding of arithmetic; history of mathematics; curriculum; grade 6; lower secondary}
\itemli{doi:10.1007/978-3-642-17735-4\_6}
\end