E-raamat: Early Fraction Learning

1. Introduction.- References.-
2. Pre-fraction Concepts of
Preschoolers.- Method.- Results.- Discussion.- References.-
3. Dimensions of
Young Childrens 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 Childrens 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 Toms
Responses.- Cognitive and Problem Solving Aspects of Toms Responses.-
General Discussion.- References.-
10. Sharing by Dealing as Problem Solving.-
A Sharing Problem.- Childrens 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 Childrens
Early Fraction Learning.- The Problem.- What the Interviews Revealed.-
Concluding Comments.- References.-
13. On Clinical Methods for Studying Young
Childrens 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.