Cognitive Science and Mathematics Education by Alan H. Schoenfeld

By Alan H. Schoenfeld

This quantity is due to the mathematicians, cognitive scientists, arithmetic educators, and lecture room lecturers combining their efforts to aid deal with problems with significance to school room guideline in arithmetic. In so doing, the members supply a basic advent to primary principles in cognitive technology, plus an summary of cognitive conception and its direct implications for arithmetic schooling. a realistic, no-nonsense try to carry contemporary learn within sight for practising lecturers, this e-book additionally increases many matters for cognitive researchers to think about.

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Since the message doesn't usually take on the first try, we show them again. If we are inventive, we show them a slightly different version the second time. By the time we're done, we may have shown them the same thing five or six different ways-all in the hope that the message will eventually sink in. This approach makes good sense; it tries to reach the student in many different ways. " It may be the case, as with misconceptions in physics, that the student has indeed learned something-a consistent interpretation of the subject matter that just happens to be wrong.

Much of the research has been conducted by cognitive psychologists, who seek to develop and validate theories of human learning and problem solving, and mathematics educators, who seek to understand the nature ofthe cognitive interaction between students and the mathematical subject matter they study and the problems they solve. This paper summarizes briefly some of the most salient features of the cognitive theory and research and draws from that research a few suggestions for designing mathematics instruction that will *An earlier version of this paper was presented at the annual meeting of the American Educational Research Association, Chicago, IL, April 1985.

The work from one set of students he had examined demonstrated a consistent sequence of error patterns that differed from those he had seen previously. Not only 28 SCHOENFELD was that behavior unusual, but the theoretical analyses done by the researcher indicated that such behavior was unlikely. One of the teachers suggested that the students' behavior might have been the result of what they had been taught the previous year. A particular textbook series teaches an antecedent procedure in a nonstandard way, and misinterpretations of that procedure might have led the students to produce the kind of behavior the researcher saw in the laboratory.

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