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Combinatorics and reasoning : representing, justifying and building isomorphisms

Author: Carolyn Alexander Maher; Arthur B Powell; Elizabeth B Uptegrove
Publisher: Dordrecht : Springer, ©2011.
Series: Mathematics education library, v. 47.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Combinatorics and reasoning
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Carolyn Alexander Maher; Arthur B Powell; Elizabeth B Uptegrove
ISBN: 9789400706156 9400706154 9781282973541 1282973541 9780387981321 0387981322
OCLC Number: 695386993
Description: 1 online resource (xvii, 224 pages).
Contents: Machine generated contents note: 1. Longitudinal Study --
2. Methodology / Carolyn A. Maher --
3. Representations as Tools for Building Arguments / Elizabeth B. Uptegrove / Carolyn A. Maher --
4. Towers: Schemes, Strategies, and Arguments / Carolyn A. Maher / Dina Yankelewitz --
5. Building an Inductive Argument / Dina Yankelewitz / Manjit K. Sran / Carolyn A. Maher --
6. Making Pizzas: Reasoning by Cases and by Recursion / Carolyn A. Maher / Dina Yankelewitz / Manjit K. Sran --
7. Block Towers: From Concrete Objects to Conceptual Imagination / Dina Yankelewitz / Carolyn A. Maher / Manjit K. Sran --
8. Responding to Ankur's Challenge: Co-construction of Argument Leading to Proof / Robert Speiser --
9. Block Towers: Co-construction of Proof / Ethel M. Muter / Carolyn A. Maher --
10. Representations and Connections / Elizabeth B. Uptegrove / Lynn D. Tarlow --
11. Pizzas, Towers, and Binomials / Elizabeth B. Uptegrove / Ethel M. Muter --
12. Representations and Standard Notation / Lynn D. Tarlow --
13. So Let's Prove It' / Elizabeth B. Uptegrove --
14. "Doing Mathematics" from the Learners' Perspectives / Arthur B. Powell --
15. Adults Reasoning Combinatorially / John M. Francisco --
16. Comparing the Problem Solving of College Students with Longitudinal Study Students / Barbara Glass --
17. Closing Observations / Barbara Glass.
Series Title: Mathematics education library, v. 47.
Responsibility: Carolyn A. Maher, Arthur B. Powell, Elizabeth B. Uptegrove (Editors).

Abstract:

Using long-term data gathered on a group of learners focusing their work on a set of combinatorics tasks, this book offers valuable insights into a number of aspects of combinatorics, such as the  Read more...

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