Abstract
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.
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Subramaniam, K., Banerjee, R. (2011). The Arithmetic-Algebra Connection: A Historical-Pedagogical Perspective. In: Cai, J., Knuth, E. (eds) Early Algebraization. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_6
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