Overview
- Unique longitudinal research over 20 years
- Presents compelling evidence of the advantages to using combinatorics in mathematics education
- Extensive discussion of mathematical tasks
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Table of contents (18 chapters)
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Introduction, Background, and Methodology
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Foundations of Proof Building (1989–1996)
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Making Connections, Extending, and Generalizing (1997–2000)
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Extending the Study, Conclusions, and Implications
Keywords
About this book
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.
Editors and Affiliations
Bibliographic Information
Book Title: Combinatorics and Reasoning
Book Subtitle: Representing, Justifying and Building Isomorphisms
Editors: Carolyn A. Maher, Arthur B. Powell, Elizabeth B. Uptegrove
DOI: https://doi.org/10.1007/978-0-387-98132-1
Publisher: Springer Dordrecht
eBook Packages: Humanities, Social Sciences and Law, Education (R0)
Copyright Information: Springer Science+Business Media, LLC 2010
Hardcover ISBN: 978-0-387-98131-4Published: 17 September 2010
Softcover ISBN: 978-94-007-9293-7Published: 23 November 2014
eBook ISBN: 978-0-387-98132-1Published: 29 June 2010
Edition Number: 1
Number of Pages: XVII, 224
Topics: Mathematics Education, Combinatorics