Combinatorics and Reasoning Representing, Justifying and Building Isomorphisms
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 ins...
| Other Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2010, 2010
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| Edition: | 1st ed. 2010 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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