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Early Fraction Learning / edited by Robert P. Hunting, Gary Davis.
- Format:
- Book
- Series:
- Recent Research in Psychology
- Language:
- English
- Subjects (All):
- Educational psychology.
- Mathematics--Study and teaching.
- Mathematics.
- Educational Psychology.
- Mathematics Education.
- Local Subjects:
- Educational Psychology.
- Mathematics Education.
- Physical Description:
- 1 online resource (244 pages)
- Edition:
- 1st ed. 1991.
- Place of Publication:
- New York, NY : Springer New York : Imprint: Springer, 1991.
- Language Note:
- English
- Summary:
- Early Fraction learning is centrally of interest to students and researchersin mathematics education, tackling as it does one of that discipline's most vexing problems: why are fractions so difficult to learn and to teach?
- Contents:
- 1. Introduction
- References
- 2. Pre-fraction Concepts of Preschoolers
- Method
- Results
- Discussion
- 3. Dimensions of Young Children’s Conceptions of the Fraction One Half
- Theory
- 4. The Social Origins of Pre-fraction Knowledge in Three Year Olds
- General Discussion
- 5. Higher Order Thinking in Young Children’s Engagements with a Fraction Machine
- The Copy Cat Fraction Machine
- Copy Cat Performance
- Counting Performance
- Relationships Between Copy Cat Performance and Counting
- The Case of Jayme and One-third
- 6. Fractions as Operators and as Cloning Machines
- The Rational Numbers as Operators
- Fraction Algorithms and Abstract Symbolism
- A More General Construction of Fields of Fractions via Operators
- 7. Preschoolers’ Knowledge of Counting and Sharing in Discrete Quantity Settings
- Counting
- The Theory of Counting Types
- Sharing in Discrete Quantity Settings
- The Link Between Counting and Sharing
- The Counting Tasks
- The Sharing Tasks
- Classification Criteria
- Counting Tasks
- Sharing Tasks
- Observed Frequencies for Counting and Sharing
- Poor Counters but Good Sharers
- Good Counters but Weak Sharers
- 8. Preschoolers’ Spontaneous Partitioning of Discrete Items
- 9. Cognitive Issues about Dealing
- Dealing and Counting
- Commentary on Tom’s Responses
- Cognitive and Problem Solving Aspects of Tom’s Responses
- 10. Sharing by Dealing as Problem Solving
- A Sharing Problem
- Children’s Strategies
- Conclusions
- 11. Cognitive Research on Early Fraction Learning Applied to Classrooms: Two Experiments
- I. An Experiment in Teacher-focused Curriculum Change
- II. Applyingthe Didactic Framework
- Appendix: Fractions and Sharing Interview
- 12. The Interaction of Thought, Words, and Deeds in Children’s Early Fraction Learning
- The Problem
- What the Interviews Revealed
- Concluding Comments
- 13. On Clinical Methods for Studying Young Children’s Mathematics
- Examples of Recent Adaptations
- Artifacts of the Clinical Interview
- 14. A Fraction of Epistemology
- Relations and Reality
- Order and Symmetry Breaking
- Reflection, Disequilibrium, and the Transition to Order
- Information and Action
- The Idea of a Concept
- References.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references at the end of each chapters.
- ISBN:
- 1-4612-3194-9
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