Block Towers: From Concrete Objects to Conceptual Imagination
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.
KeywordsMathematical Idea Addition Rule Concrete Object Previous Chapter Conceptual Imagination
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