Abstract
In previous chapters, we looked at the development of various forms of reasoning in students working in a classroom in small group settings. In this chapter, we focus on an individual student – we examine Stephanie’s development of combinatorial reasoning. In previous chapters, we saw how Stephanie, working with others and on her own, made sense of the towers and pizza problems. In this chapter we see how Stephanie extended that work. In her examination of patterns and symbolic representations of the coefficients in the binomial expansion, using ideas from earlier explorations with towers in grades 3–5, she examined several fundamental recursive processes, including the addition rule in Pascal’s Triangle.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Davis, R. B., Maher, C. A., & Martino, A. M. (1992). Using videotapes to study the construction of mathematical knowledge by individual children working in groups. Journal of Science, Education and Technology, 1(3), 177–189.
Maher, C. A., & Martino, A. (1991). The construction of mathematical knowledge by individual children working in groups. In P. Boero (Ed.), Proceedings of the 15th conference of the International Group for the Psychology of Mathematics Education (vol. 2, pp. 365–372). Assisi, Italy.
Maher, C. A., & Martino, A. M. (1992a). Teachers building on students’ thinking. The Arithmetic Teacher, 39, 32–37.
Maher, C. A., & Martino, A. M. (1992b). Individual thinking and the integration of the ideas of others in problem solving situations. In W. Geeslin, J. Ferrini-Mundy, & K. Graham (Eds.), Proceedings of the sixteenth annual conference of the International Group for the Psychology of Mathematics Education (pp. 72–79). Durham, NH: University of New Hampshire.
Maher, C. A., & Martino, A. M. (1996a). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 27(2), 194–214.
Maher, C. A., & Martino, A. M. (1996b). Young children inventing methods of proof: The gang of four. In L. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of mathematical learning. Hillsdale, NJ: Erlbaum.
Maher, C. A., & Speiser, R. (1997b). How far can you go with block towers? Stephanie’s intellectual development. Journal of Mathematical Behavior, 16(2), 125–132.
Weil, A. (1984). Number theory, an approach through history. Boston, MA: Birkhauser.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Speiser, R. (2011). Block Towers: From Concrete Objects to Conceptual Imagination. 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_7
Download citation
DOI: https://doi.org/10.1007/978-94-007-0615-6_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0614-9
Online ISBN: 978-94-007-0615-6
eBook Packages: Humanities, Social Sciences and LawEducation (R0)