Early Fraction learning is centrally of interest to studentsand researchersin mathematics education, tackling as itdoes one of that discipline's most vexing problems: why arefractions so difficult to learn and to teach?
Early Fraction learning is centrally of interest to studentsand researchersin mathematics education, tackling as itdoes one of that discipline's most vexing problems: why arefractions so difficult to learn and to teach?Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
1. Introduction.- References.- 2. Pre-fraction Concepts of Preschoolers.- Method.- Results.- Discussion.- References.- 3. Dimensions of Young Children's Conceptions of the Fraction One Half.- Theory.- Method.- Results.- Discussion.- References.- 4. The Social Origins of Pre-fraction Knowledge in Three Year Olds.- Method.- Results.- General Discussion.- References.- 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.- References.- 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.- References.- 9. Cognitive Issues about Dealing.- Dealing and Counting.- Commentary on Tom's Responses.- Cognitive and Problem Solving Aspects of Tom's Responses.- General Discussion.- References.- 10. Sharing by Dealing as Problem Solving.- A Sharing Problem.- Children's Strategies.- Conclusions.- References.- 11. Cognitive Research on Early Fraction Learning Applied to Classrooms: Two Experiments.- I. An Experiment in Teacher-focused Curriculum Change.- II. Applyingthe Didactic Framework.- References.- 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.- References.- 13. On Clinical Methods for Studying Young Children's Mathematics.- Examples of Recent Adaptations.- Artifacts of the Clinical Interview.- References.- 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.
1. Introduction.- References.- 2. Pre-fraction Concepts of Preschoolers.- Method.- Results.- Discussion.- References.- 3. Dimensions of Young Children's Conceptions of the Fraction One Half.- Theory.- Method.- Results.- Discussion.- References.- 4. The Social Origins of Pre-fraction Knowledge in Three Year Olds.- Method.- Results.- General Discussion.- References.- 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.- References.- 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.- References.- 9. Cognitive Issues about Dealing.- Dealing and Counting.- Commentary on Tom's Responses.- Cognitive and Problem Solving Aspects of Tom's Responses.- General Discussion.- References.- 10. Sharing by Dealing as Problem Solving.- A Sharing Problem.- Children's Strategies.- Conclusions.- References.- 11. Cognitive Research on Early Fraction Learning Applied to Classrooms: Two Experiments.- I. An Experiment in Teacher-focused Curriculum Change.- II. Applyingthe Didactic Framework.- References.- 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.- References.- 13. On Clinical Methods for Studying Young Children's Mathematics.- Examples of Recent Adaptations.- Artifacts of the Clinical Interview.- References.- 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.
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