© 2011

Combinatorics and Reasoning

Representing, Justifying and Building Isomorphisms

  • Carolyn A. Maher
  • Arthur B. Powell
  • Elizabeth B. Uptegrove

Part of the Mathematics Education Library book series (MELI, volume 47)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Introduction, Background, and Methodology

    1. Front Matter
      Pages 1-1
    2. Carolyn A. Maher
      Pages 3-8
    3. Carolyn A. Maher, Elizabeth B. Uptegrove
      Pages 9-14
  3. Foundations of Proof Building (1989–1996)

    1. Front Matter
      Pages 15-15
    2. Carolyn A. Maher, Dina Yankelewitz
      Pages 17-25
    3. Carolyn A. Maher, Manjit K. Sran, Dina Yankelewitz
      Pages 27-43
    4. Carolyn A. Maher, Manjit K. Sran, Dina Yankelewitz
      Pages 45-57
    5. Carolyn A. Maher, Manjit K. Sran, Dina Yankelewitz
      Pages 59-72
  4. Making Connections, Extending, and Generalizing (1997–2000)

    1. Front Matter
      Pages 87-87
    2. Lynn D. Tarlow, Elizabeth B. Uptegrove
      Pages 97-104
    3. Ethel M. Muter, Elizabeth B. Uptegrove
      Pages 105-120
    4. Lynn D. Tarlow
      Pages 121-131
    5. Elizabeth B. Uptegrove
      Pages 133-144
    6. Arthur B. Powell
      Pages 145-154
  5. Extending the Study, Conclusions, and Implications

    1. Front Matter
      Pages 155-155
    2. Barbara Glass
      Pages 171-183

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.


College Mathematics Combinatorics Learning Isomorphism Longitudinal Studies Proof Building

Editors and affiliations

  • Carolyn A. Maher
    • 1
  • Arthur B. Powell
    • 2
  • Elizabeth B. Uptegrove
    • 3
  1. 1.Graduate School of EducationRutgers UniversityNew BrunswickUSA
  2. 2.Department of Urban EducationRutgers UniversityNewarkUSA
  3. 3.Department of Mathematical SciencesFelician CollegeRutherfordUSA

Bibliographic information

  • Book Title Combinatorics and Reasoning
  • Book Subtitle Representing, Justifying and Building Isomorphisms
  • Editors Carolyn A. Maher
    Arthur B. Powell
    Elizabeth B. Uptegrove
  • Series Title Mathematics Education Library
  • DOI
  • Copyright Information Springer Netherlands 2011
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law Education (R0)
  • Hardcover ISBN 978-94-007-0614-9
  • Softcover ISBN 978-94-007-3495-1
  • eBook ISBN 978-94-007-0615-6
  • Edition Number 1
  • Number of Pages XVIII, 226
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics Education
  • Buy this book on publisher's site