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 : Imprint: Springer, 2010.
• 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, 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.