Combinatorics and Reasoning
Springer (Verlag)
978-94-007-0614-9 (ISBN)
This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
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.
Erscheint lt. Verlag | 14.1.2011 |
---|---|
Reihe/Serie | Mathematics Education Library ; 47 |
Zusatzinfo | XVIII, 226 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Schulbuch / Wörterbuch |
Mathematik / Informatik ► Mathematik ► Graphentheorie | |
Sozialwissenschaften ► Pädagogik ► Erwachsenenbildung | |
Sozialwissenschaften ► Pädagogik ► Schulpädagogik / Grundschule | |
ISBN-10 | 94-007-0614-6 / 9400706146 |
ISBN-13 | 978-94-007-0614-9 / 9789400706149 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
aus dem Bereich