Abstract
This chapter explores two contrasting ways of presenting algebra by looking at key differences across the presentation of simultaneous equations to students in eighth-grade. The examples are from a qualitative analysis of the 1995 TIMSS Video Study data including eighth-grade mathematics instruction in Japan and the United States covering topics on simultaneous equations. The U.S. lesson example shows a procedural approach to this topic, where students focus on getting answers through a series of routine steps. In contrast, the Japanese lesson highlights a strong focus on building generalized solution methods and understanding relationships represented in systems of equations. A discussion of key differences as they relate to important ideas in understanding algebra compared to how it was treated in the classrooms follows the examples.
This data used in this article were collected using video data from TIMSS Laboratory at the University of California, Los Angeles. I wish to thank the TIMSS Video Laboratory for access to a unique and resourceful data set. This research was supported by a grant of the American Educational Research Association which receives funds for its “AERA Grants Program” from the National Center for Education Statistics and the Office of Educational Research and Improvement (U.S. Department of Education) and the National Science Foundation under NSF Grant # RED-9452861. Opinions reflect those of the author and do not necessarily reflect those of the granting agency.
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Smith, M. (2011). A Procedural Focus and a Relationship Focus to Algebra: How U.S. Teachers and Japanese Teachers Treat Systems of Equations. 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_26
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