Abstract
In the preceding chapters in this section, we considered how students made sense ofPascal’s Triangle and isomorphic combinatorics problems using their own increasingly sophisticated and abstract representations. In this chapter, we see how onegroup built on those ideas in order to derive, explain, and record Pascal’s Identity(the addition rule for Pascal’s Triangle) using standard mathematical notation. Thisremarkable demonstration of how students can come to make sense of complexmathematical ideas was captured during the session that came to be referred to asthe “Night Session,” since it took place on a weekday evening from 7:30 to 10:00 PM(Uptegrove, 2004).
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References
Davis, R. B., & Maher, C. A. (1990). The nature of mathematics: What do we do when we “do mathematics”? [Monograph]. Journal for Research in Mathematics Education, 4, 65–78.
Uptegrove, E. B. (2004). To symbols from meaning: Students’ investigations in counting. Unpublished doctoral dissertation, Rutgers, The State University of New Jersey, New Brunswick, NJ.
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© 2011 Springer Science+Business Media B.V.
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Uptegrove, E.B. (2011). Representations and Standard Notation. In: Maher, C.A., Powell, A.B., Uptegrove, E.B. (eds) Combinatorics and Reasoning. Mathematics Education Library, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0615-6_12
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DOI: https://doi.org/10.1007/978-94-007-0615-6_12
Publisher Name: Springer, Dordrecht
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