How far can you go with block towers?

Abstract

This report focuses on the development of combinatorial reasoning of a 14-year-old child, Stephanie, who is investigating binomial coefficients and combinations in relationship to the binomial expansion and the mapping of the binomial expansion to Pascal's triangle. This research reports on Stephanie's examination of patterns and symbolic representations of the coefficients in the binomial expansion using ideas from earlier explorations with towers in grades 3–5 to examine recursive processes and to explain the addition rule in Pascal's triangle. This early work enabled her to build particular organization and classification schemes that she draws upon to explain her more abstract ideas.