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...
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| Other Authors: | , , |
| Format: | Electronic |
| Language: | English |
| Published: |
Dordrecht :
Springer Netherlands,
2010.
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| Series: | Mathematics Education Library ;
47 |
| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-98132-1 |
Table of Contents:
- 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.