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Davis, Robert B. – 1984
There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…
Descriptors: Cognitive Processes, Cognitive Structures, Elementary Secondary Education, Learning Strategies
Cuneo, Diane O. – 1988
An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…
Descriptors: Addition, Basic Skills, Cognitive Development, Cognitive Structures
Behr, Merlyn; Harel, Guershon – Focus on Learning Problems in Mathematics, 1990
Discussed are some situations students face that result in cognitive conflict, possible sources of these conflicts, and strategies which students use to resolve, remove, or circumvent them. A global account for observed systematic errors is offered based on a general problem-solving rule called the "Matching Rule." (KR)
Descriptors: Abstract Reasoning, Cognitive Development, Cognitive Dissonance, Cognitive Structures
Manitoba Dept. of Education, Winnipeg. – 1983
This handbook has been structured to provide teachers (K-2) with the most recent research on problem solving. It contains information and practical applications which deal with the key concepts of problem solving in mathematics. The handbook consists of four sections. The first section establishes the background and gives the purposes of the…
Descriptors: Cognitive Development, Cognitive Structures, Curriculum Design, Decision Making
Hutchinson, Nancy L. – 1985
This paper begins with a summary and analysis of Robert Glaser's arguments, presented in his paper "Education and Thinking: The Role of Knowledge," which contend there are strong interactions between structures of knowledge and cognitive processes, and that problem solving and reasoning are taught best in the context of the acquisition…
Descriptors: Cognitive Development, Cognitive Processes, Cognitive Structures, Elementary Secondary Education