Combinatorics and Reasoning: Representing, Justifying and
Building Isomorphisms is based on the accomplishments of a cohort
group of learners from first grade through high school and beyond,
concentrating on their work on a set of combinatorics tasks. By
studying these students, the editors gain insight into the
foundations of proof building, the tools and environments necessary
to make connections, activities to extend and generalize
combinatoric learning, and even explore implications of this
learning on the undergraduate level.
This volume underscores the power of attending to basic ideas in
building arguments; it shows the importance of providing
opportunities for the co-construction of knowledge by groups of
learners; and it demonstrates the value of careful construction of
appropriate tasks. Moreover, it documents how reasoning that takes
the form of proof evolves with young children and discusses the
conditions for supporting student reasoning.
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