Combinatorics and Reasoning Representing, Justifying and Building Isomorphisms /

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Maher, Carolyn A. (Επιμελητής έκδοσης), Powell, Arthur B. (Επιμελητής έκδοσης), Uptegrove, Elizabeth B. (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Dordrecht : Springer Netherlands, 2011.
• Έκδοση: 1.
• Σειρά: Mathematics Education Library ; 47
• Θέματα: Education.; Combinatorics.; Mathematics > Study and teaching.; Mathematics Education.

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...

Πίνακας περιεχομένων:

• 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.