Combinatorics and Reasoning

Representing, Justifying and Building Isomorphisms

Editors: Maher, Carolyn A., Powell, Arthur B., Uptegrove, Elizabeth B. (Eds.)

  • Offers unique, longitudinal research over twenty years
  • Presents compelling evidence of the advantages to using combinatorics in mathematics education
  • Offers extensive discussion of mathematical tasks
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eBook $119.00
price for USA (gross)
  • ISBN 978-0-387-98132-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-0-387-98131-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-94-007-9293-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

Table of contents (18 chapters)

  • The Longitudinal Study

    Maher, Carolyn A.

    Pages 3-8

  • Methodology

    Maher, Carolyn A. (et al.)

    Pages 9-14

  • Representations as Tools for Building Arguments

    Maher, Carolyn A. (et al.)

    Pages 17-25

  • Towers: Schemes, Strategies, and Arguments

    Maher, Carolyn A. (et al.)

    Pages 27-43

  • Building an Inductive Argument

    Maher, Carolyn A. (et al.)

    Pages 45-57

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-0-387-98132-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-0-387-98131-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-94-007-9293-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorics and Reasoning
Book Subtitle
Representing, Justifying and Building Isomorphisms
Editors
  • Carolyn A. Maher
  • Arthur B. Powell
  • Elizabeth B. Uptegrove
Copyright
2010
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-387-98132-1
DOI
10.1007/978-0-387-98132-1
Hardcover ISBN
978-0-387-98131-4
Softcover ISBN
978-94-007-9293-7
Edition Number
1
Number of Pages
XVII, 224
Topics