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Combinatorics and Reasoning

Combinatorics and Reasoning PDF Author: Carolyn A. Maher
Publisher: Springer Science & Business Media
ISBN: 9400706154
Category : Education
Languages : en
Pages : 226

Book Description
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.

Combinatorics and Reasoning

Combinatorics and Reasoning PDF Author: Carolyn A. Maher
Publisher: Springer Science & Business Media
ISBN: 9400706154
Category : Education
Languages : en
Pages : 226

Book Description
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.

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ISBN: 0743930843
Category : Art
Languages : en
Pages : 306

Book Description


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Code of Federal Regulations, Title 33, Navigation and Navigable Waters, PT. 1-124, Revised as of July 1, 2011

Code of Federal Regulations, Title 33, Navigation and Navigable Waters, PT. 1-124, Revised as of July 1, 2011 PDF Author:
Publisher: Government Printing Office
ISBN: 9780160888885
Category : Law
Languages : en
Pages : 740

Book Description


2018 CFR Annual Print Title 33 Navigation and Navigable Waters Parts 1 to 124

2018 CFR Annual Print Title 33 Navigation and Navigable Waters Parts 1 to 124 PDF Author: Office of The Federal Register
Publisher: IntraWEB, LLC and Claitor's Law Publishing
ISBN: 1640243763
Category : Law
Languages : en
Pages : 757

Book Description


The Code of Federal Regulations of the United States of America

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ISBN:
Category : Administrative law
Languages : en
Pages : 596

Book Description
The Code of Federal Regulations is the codification of the general and permanent rules published in the Federal Register by the executive departments and agencies of the Federal Government.

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Category : Current events
Languages : en
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2017 CFR Annual Print Title 33 Navigation and Navigable Waters Parts 1 to 124

2017 CFR Annual Print Title 33 Navigation and Navigable Waters Parts 1 to 124 PDF Author: Office of The Federal Register
Publisher: IntraWEB, LLC and Claitor's Law Publishing
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