Combinatorics and reasoning: representing, justifying and building isomorphisms
by Maher, Carolyn Alexander Powell, Arthur B. Uptegrove, Elizabeth B.
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…
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- Full title :Combinatorics and reasoning : representing, justifying and building isomorphisms / Carolyn A. Maher, Arthur B. Powell, Elizabeth B. Uptegrove (editors).
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 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.
Read More ↓Edition Statements
- Publication Date:©2010.
Publication Statements
- Publisher(s):Springer
- Place of Publication:New York
- Language:eng
- Publication Date:©2010.
The Physical Object
- Description:xvii, 224 pages : : illustrations ; : 25 cm.
Edition Identifiers
- ISBN:9780387981314, 0387981314, 9780387981321, 0387981322
- DOI:10.1007/978-0-387-98132-1
- oclc:ocn310400895
- LC Classification:QA164
- Dewey Decimal:511.6
Table of Contents
The longitudinal study / Carolyn A. Maher -- Methodology / Carolyn A. Maher and Elizabeth B. Uptegrove -- Representations as tools for building arguments / Carolyn A. Maher and Dina Yankelewitz -- Towers : schemes, strategies, and arguments / Carolyn A. Maher, Manjit K. Sran, and Dina Yankelewitz -- Buidling an inductive argument / Carolyn A. Maher, Manjit K. Sran, and Dina Yankelewitz -- Making pizzas : reasoning by cases and by recursion / Carolyn A. Maher, Manjit K. Sran, and Dina Yandelewitz -- Block towers : from concrete objects to conceptual imagination / Robert Speiser -- Responding to Ankur's challenge : co-construction of argument leading to proof / Carolyn A. Maher and Ethel M. Muter -- Block towers : co-construction of proof / Lynn D. Tarlow and Elizabeth B. Uptegrove -- Representations and connections / Ethel M. Muter and Elizabeth B. Uptegrove -- Pizzas, towers, and binomials / Lynn D. Tarlow -- Representations and standard notation / Elizabeth B. Uptegrove -- So let's prove it! / Arthur B. Powell -- "Doing mathematics" from the learners' perspectives / John M. Francisco -- Adults reasoning combinatorially / Barbara Glass -- Comparing the problem solving of college s…
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