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Download full textWilliams, Gaye – International Group for the Psychology of Mathematics Education, 2003
The impact of prior learning on new learning is highlighted by the case of Dean, a Year 8 student who developed his own method to find the sum of the interior angles of a polygon without knowing why his method worked. Enriched transcripts and visual displays of the cognitive, social (Dreyfus, Hershkowitz, & Schwarz, 2001) and affective elements…
Descriptors: Prior Learning, Generalization, Geometry, Concept Formation
Mitchelmore, Michael C. – 2002
Although mathematics deals with generalizations relating abstract ideas, very little attention has been given in the mathematics education literature to the role of abstraction and generalization in the development of mathematical knowledge. In this paper, the meanings of "abstraction" and "generalization" are first explored by…
Descriptors: Abstract Reasoning, Cognitive Processes, Concept Formation, Elementary Secondary Education
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
Pateman, Neil A., Ed; Dougherty, Barbara J., Ed.; Zilliox, Joseph T., Ed. – International Group for the Psychology of Mathematics Education, 2003
This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) Improving Decimal Number Conception by Transfer from Fractions to Decimals (Irita Peled and Juhaina Awawdy Shahbari); (2) The Development of Student Teachers' Efficacy Beliefs in Mathematics during…
Descriptors: Student Teachers, Mathematics Education, Teacher Effectiveness, Metalinguistics
