
05882026
a
2011c.00720
Speiser, Robert
Block towers: from concrete objects to conceptual imagination.
Maher, Carolyn A. (ed.) et al., Combinatorics and reasoning. Representing, justifying and building isomorphisms. New York, NY: Springer (ISBN 9780387981314/hbk; 9789400706149/hbk; 9780387981321/ebook). Mathematics Education Library 47, 7386 (2010).
2010
New York, NY: Springer
EN
K23
C33
D53
combinatorics
reasoning
justification
problem solving
combinatorial thinking
grade 8
interviews
educational research
doi:10.1007/9789400706156_7
Summary: 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 35, she examined several fundamental recursive processes, including the addition rule in Pascal's Triangle.
B. RufferHenn (B\"ohlIggelheim)