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Peer reviewedHarel, Guershon; Tall, David – For the Learning of Mathematics, 1991
The terms generalization and abstraction are used with various shades of meaning by mathematicians and mathematics educators. Introduced is the idea of "generic abstraction" that gives the student an operative sense of a mathematical concept and provides a passage point in the process toward formal abstraction. (MDH)
Descriptors: Cognitive Processes, Concept Formation, Generalization, Learning Theories
Peer reviewedBalacheff, Nicolas – For the Learning of Mathematics, 1990
Discussed are the recognition and the relevance, in terms of teacher/student awareness and subsequent effective teacher treatment techniques, of cognitive disequilibrium as experienced by the student, when such disequilibrium is provoked by mathematical contradictions and/or counterexamples, within the classroom paradigm of constructivism. (JJK)
Descriptors: Cognitive Dissonance, Cognitive Psychology, Concept Formation, Developmental Psychology
Peer reviewedAvital, Shmuel; Barbeau, Edward J. – For the Learning of Mathematics, 1991
Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)
Descriptors: Cognitive Development, Cognitive Processes, Generalization, Geometric Concepts
