The focus of NCTM's 2001 Yearbook is one aspect of how students learn mathematics in particular, how they learn to form abstractions and build mathematical representations of phenomena. It explains how students come to develop mathematical habits of mind, and even how they develop misunderstandings about mathematics. Discussions on the nature and roles of representation, the use of representation tools for gaining insights, various symbol systems used in mathematics, and the role of context in the interplay between modeling and representation make this an excellent resource for teachers who want to make smart decisions about content and pedagogy.
Author(s): Albert A. Cuoco, Frances R. Curcio
Year: 2001
Language: English
Pages: 282
Contents......Page 2
Preface......Page 6
1. Systems of Representations and the Development of
Mathematical Concepts......Page 11
2. Representation and Abstraction in Young Children’s
Numerical Reasoning......Page 34
3. Algebra: What Are We Teaching?.......Page 45
4. Attending to Transparent Features of Opaque Representations
of Natural Numbers......Page 54
5. The Influence of Language on Mathematical Representations......Page 63
6. The Role of Tools in Supporting Students’ Development of
Measuring Conceptions......Page 73
7. Promoting the Use of Diagrams as Tools for Thinking......Page 87
8. Constructing a Foundation for the Fundamental Theorem
of Calculus......Page 100
9. Mapping Diagrams: Another View of Functions......Page 113
10. A Multirepresentational Journey through the Law of Cosines......Page 127
11. Representations of Reversal: An Exploration of
Simpson’s Paradox......Page 139
12. Presenting and Representing: From Fractions to
Rational Numbers......Page 156
13. Representations of Patterns and Functions: Tools
for Learning......Page 176
14. Promoting Multiple Representations in Algebra......Page 183
15. From Fibonacci Numbers to Fractals: Recursive Patterns and
Subscript Notation......Page 196
16. Tracing the Origins and Extensions of Michael’s
Representation......Page 211
17. Listen to Their Pictures: An Investigation of Children’s
Mathematical Drawings......Page 225
18. Using Literature to Invite Mathematical Representations......Page 238
19. Representation in Realistic Mathematics Education......Page 248
20. Charting a Visual Course to the Concept of Function......Page 261
21. Teaching Mathematical Modeling and the Skills of
Representation......Page 279
