Combinatorics and Reasoning

Maher, Carolyn A. (EDT)/ Powell, Arthur B. (EDT)/ Uptegrove, Elizabeth B. (EDT)

Editore: Springer Verlag, 2011
ISBN 10: 9400706146 / ISBN 13: 9789400706149
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Riassunto: 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.

Contenuti:

Introduction.- The Longitudinal Study.- Methodology.- Representations as a Tool for Building Arguments.- Building Towers: Justifications Leading to Proof Making.- Making Pizzas: Reasoning by Cases and recursion.- Responding to Ankur's Challenge: Co-construction of Argument Leading to Proof.- Co-construction of Proof.- The Case of Stephanie.- Representations and Connections.- Pizzas, Block Towers, and Binomials.- Generalizing from Pizzas, Towers, Binomial Expansion, and Pascal's Triangle.- Extending and Generalizing the Isomorphism: Towers, Pizzas, Pascal's Triangle, and the Taxicab Problem.- College Students Building Towers and Making Pizzas.- Comparing the Problem Solving of College Students with Longitudinal Study Students.- Conclusions and Suggestions for Practice.

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Dati bibliografici

Titolo: Combinatorics and Reasoning
Casa editrice: Springer Verlag
Data di pubblicazione: 2011
Legatura: Hardcover
Condizione libro: New

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Leo, Heinrich,
Editore: Halle, Anton, 1854-67. (1854)
ISBN 10: 9400706146 ISBN 13: 9789400706149
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Descrizione libro Halle, Anton, 1854-67., 1854. Mit losem und unbeschnittenem Register zum I. u. II Bande und Stammtafeln. Bd. 1: XVI, 607 S.; Bd. 2: X, 761 S.; Bd. 3: XVI, 742 S.; Bd. 4: VIII, 1089 S.; Bd. 5: 1391 S. OPp. mit reich vergold. Rückentitel und Rotschnitt. Sehr selten. Wenige Seiten leicht stockfleckig, Einband etwas berieben, Ecken bestoßen, ansonsten gut erhalten. Der erkonservative Historiker Heinrich Leo 1799-1878) erhielt dank Hegels Empfehlung 1828 eine Professur an der Universität Halle, der er auch von 1854-1856 als Rektor vorstand. Die hier vorliegenden Vorlesungen sind sämtlich aus eklektischem Quellen- und Literaturstudium hervorgegangen, wobei die Fehler der Vorlagen zumeist mitübernommen wurden. Leo trat für ständische Ordnungen und für die Rechte der Krone ein, nicht ohne die preußischen Konservativen gelegentlich zu kritisieren. Mit F. J. Stahl verbanden ihn der "christliche Staat" und die "evangelische Katholizität". Seinen Kampf gegen den Linkhegelianismus krönte er mit dem auf sein Drängen hin erfolgten Verbot der "Hallischen Jahrbücher" 1841. Vgl. NDB 14, S. 244. Codice articolo 490BB

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Carolyn A. Maher (Editor), Arthur B. Powell (Editor), Elizabeth B. Uptegrove (Editor)
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Descrizione libro Springer, 2011. Hardcover. Condizione: New. 2011. Codice articolo DADAX9400706146

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Descrizione libro Springer, Netherlands, 2011. Hardback. Condizione: New. 2011 ed.. Language: English . Brand New 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. Codice articolo LIB9789400706149

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Editore: Springer, Netherlands (2011)
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Descrizione libro Springer, Netherlands, 2011. Hardback. Condizione: New. 2011 ed.. Language: English . Brand New 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. Codice articolo LIB9789400706149

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Carolyn A. Maher (editor), Arthur B. Powell (editor), Elizabeth B. Uptegrove (editor)
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Descrizione libro Springer Netherlands 2011-01-14, Dordrecht, 2011. hardback. Condizione: New. Codice articolo 9789400706149

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Carolyn A. Maher
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Descrizione libro Springer, 2011. HRD. Condizione: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice articolo IP-9789400706149

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Carolyn A. Maher
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Descrizione libro Springer-Verlag Gmbh Apr 2011, 2011. Buch. Condizione: Neu. Neuware - 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. 226 pp. Englisch. Codice articolo 9789400706149

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Carolyn A. Maher
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Descrizione libro Springer-Verlag Gmbh Apr 2011, 2011. Buch. Condizione: Neu. Neuware - 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. 226 pp. Englisch. Codice articolo 9789400706149

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Carolyn A. Maher
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Descrizione libro Springer-Verlag Gmbh Apr 2011, 2011. Buch. Condizione: Neu. Neuware - 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. 226 pp. Englisch. Codice articolo 9789400706149

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Carolyn A. Maher
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Descrizione libro Springer-Verlag Gmbh Jan 2011, 2011. Buch. Condizione: Neu. Neuware - 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. 226 pp. Englisch. Codice articolo 9789400706149

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