Combinatorics and Reasoning

Representing, Justifying and Building Isomorphisms

Inbunden, Engelska, 2010

AvCarolyn A. Maher,Arthur B. Powell,Elizabeth B. Uptegrove

1 379 kr

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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.

Produktinformation

Utgivningsdatum2010-09-17
Mått155 x 235 x 25 mm
Vikt508 g
FormatInbunden
SpråkEngelska
Antal sidor224
FörlagSpringer-Verlag New York Inc.
ISBN9780387981314

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Kombinatorik och grafteori inom Naturvetenskap och teknik

Introduction, background, and methodology.- The Longitudinal Study.- Methodology.- Foundations of proof building (1989-1996).- Representations as Tools for Building Arguments.- Towers: Schemes, Strategies, and Arguments.- Building an Inductive Argument.- Making Pizzas: Reasoning by Cases and by Recursion.- Block Towers: From Concrete Objects to Conceptual Imagination.- Making connections, extending, and generalizing (1997-2000).- Responding to Ankur’s Challenge: Co-construction of Argument Leading to Proof.- Block Towers: Co-construction of Proof.- Representations and Connections.- Pizzas, Towers, and Binomials.- Representations and Standard Notation.- So Let’s Prove It!.- Extending the study, conclusions, and implications.- “Doing Mathematics” from the Learners’ Perspectives.- Adults Reasoning Combinatorially.- Comparing the Problem Solving of College Students with Longitudinal Study Students.- Closing Observations.- Erratum.