The Arithmetic-Algebra Connection: A Historical-Pedagogical Perspective

  • K. SubramaniamEmail author
  • Rakhi Banerjee
Part of the Advances in Mathematics Education book series (AME)


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.


Operational Composition Algebraic Expression Symbolic Expression Mathematics Textbook Primary Grade 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Homi Bhabha Centre for Science EducationTata Institute of Fundamental ResearchMumbaiIndia
  2. 2.School of Social ScienceTata Institute of Social SciencesMumbaiIndia

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