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Zaslavsky, Orit; Peled, Irit – Journal for Research in Mathematics Education, 1996
Inservice (n=36) and preservice (n=67) mathematics teachers were asked for a commutative, nonassociative binary operation. Responses were analyzed for correctness, productiveness, mathematical content, and underlying difficulties. Both groups exhibited a weak concept by failing to produce an example and using a limited content search space.…
Descriptors: Cognitive Structures, Elementary Secondary Education, Mathematics Teachers, Number Concepts

Irwin, Kathryn C. – Journal for Research in Mathematics Education, 1996
Interviews with 107 children, ages 4-7, about uncounted quantities, counted quantities, and numerical equations showed that the ability to predict changes to counted quantities increased with age. Only 7-year olds were able to use covariance and compensation in the purely numerical context of derived equations. (Author/MKR)
Descriptors: Cognitive Structures, Elementary School Students, Foreign Countries, Interviews

Greeno, James G. – Journal for Research in Mathematics Education, 1991
This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…
Descriptors: Cognitive Development, Cognitive Structures, Concept Formation, Elementary Secondary Education

Jones, Graham A.; And Others – Journal for Research in Mathematics Education, 1996
Validates a framework for assessing children's thinking in multidigit number situations and uses the framework to evaluate instructional programs. Key constructs--counting, partitioning, grouping, and number relationships--appear stable within each of 5 levels across 12 case studies, suggesting a possible hierarchy of thinking. (DF)
Descriptors: Case Studies, Cognitive Structures, Elementary School Students, Grade 1