Combinatorics and Reasoning

Combinatorics and Reasoning

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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.Students worked on the shirts and jeans problem at the end of second grade and again at the beginning of third grade ... In third grade, when the children were again presented with this problem, they did not remember how they had solved theanbsp;...

Title:Combinatorics and Reasoning
Author:Carolyn A. Maher, Arthur B. Powell, Elizabeth B. Uptegrove
Publisher:Springer Science & Business Media - 2010-06-29


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