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Peer reviewedHope, Jack A. – Educational Studies in Mathematics, 1985
The processes and procedures used by expert mental calculators are identified from a literature review. Experts are characterized by knowledge of a variety of methods, ability to recall numerical equivalents, and ability to remember the numbers involved in various stages of calculations. (MNS)
Descriptors: Adults, Cognitive Processes, Computation, Educational Research
Peer reviewedHeege, Hans Ter – Educational Studies in Mathematics, 1985
Children use acquired knowledge as they learn basic multiplication facts. If informal thinking strategies are stressed, the border between "figuring out" and "knowing by heart" gradually disappears. Children will acquire a flexible mental structure of multiplication facts instead of a collection of rules. (MNS)
Descriptors: Basic Skills, Cognitive Processes, Computation, Educational Research
Peer reviewedHunting, Robert P. – Educational Studies in Mathematics, 1986
The behavior of one child as she constructed knowledge about fractions over a nine-month period is presented. The intent is to explain behavioral patterns for which certain mental processes, called schemes, seem responsible. (MNS)
Descriptors: Case Studies, Cognitive Processes, Educational Research, Elementary Education
Peer reviewedKilpatrick, Jeremy – Educational Studies in Mathematics, 1985
How the computer as a metaphor affects our understanding of the processes of learning and teaching is explored. After describing reflection and recursion in mathematics and their roles in thinking and learning, models of the mind and teaching effects are discussed, with self-awareness as a theme. (MNS)
Descriptors: Cognitive Processes, Cognitive Structures, Computers, Conference Papers
Peer reviewedCobb, Paul – Educational Studies in Mathematics, 1986
The relationship between arithmetical concepts and solution methods is discussed. A case study illustrates the contention that some children with relatively sophisticated concepts express those concepts with primitive methods. (MNS)
Descriptors: Arithmetic, Case Studies, Cognitive Processes, Computation
Peer reviewedStreefland, Leen – Educational Studies in Mathematics, 1984
Ideas on a teaching-learning theory of ratio are presented. Views of children and of members of an international panel are presented, and five questions and their responses are compared with real classroom experience. (MNS)
Descriptors: Cognitive Processes, Educational Research, Elementary Education, Elementary School Mathematics
Peer reviewedDenvir, B.; Brown, M. – Educational Studies in Mathematics, 1986
Three studies on the development of number concepts (counting, addition, subtraction, and place value) in seven- to nine-year-olds considered low attainers in mathematics were conducted. The search for a descriptive framework, the development of a diagnostic assessment instrument, and a longitudinal study are reported. (MNS)
Descriptors: Addition, Cognitive Processes, Diagnostic Teaching, Educational Research
Peer reviewedTall, David; Thomas, Michael – Educational Studies in Mathematics, 1991
Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…
Descriptors: Algebra, Cognitive Development, Cognitive Dissonance, Cognitive Processes
