Dmitri Pavlov - Синтаксическая математика
August 7th, 2007
10:59 pm

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Синтаксическая математика

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From:(Anonymous)
Date:August 8th, 2007 - 11:41 pm
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Навскидку пара случайных ссылкок про делей и арифметику.

Individual Differences in Arithmetic: Implications for Psychology, Neuroscience, and Education,
by Ann Dowker


Или вот пара случайных статей, одна про детей и кардиналы, впрочем, не про школьников.

Ann Dowker
Individual differences in 4-year-olds' mathematical abilities
http://www.science.mcmaster.ca/~BBCS/2005/viewabstract.php?id=95

he present study investigated individual differences in different aspects of early number concepts in 4-year-olds. 40 4-year-old children from Oxford nursery classes took part. They were tested on accuracy of counting sets of objects; the cardinal word principle; the order irrelevance principle; repeated addition and subtraction by 1 from a set of objects; number conservation; and establishing numerically equivalent sets. Most were reasonably proficient at counting. 73% understood the cardinal word principle, but only 10% passed the number conservation task. As results repeated addition and subtraction by 1, the children could be divided into three approximately equal groups: those who were already able to use an internalized counting sequence for the simplest forms of addition and subtraction; those who relied on a repeated 'counting-all' procedure for such tasks; and those who were as yet unable to cope with such tasks. Counting concepts and procedures were related to one another, and to other numerical tasks. However, when individual profiles were examined, discrepancies in both directions were found between almost any two components of numerical ability.

http://www.science.mcmaster.ca/~BBCS/2005/viewabstract.php?id=8&symposium=0
Arithmetic concepts and how they develop: A microgenetic investigation
Multiple Paper Presentation, M Robinson, J M Roy, M R Norick

Researchers are increasingly focussing on children’s conceptual knowledge of arithmetic and inversion problems (e.g., 3 + 9 - 9) are commonly used. If participants understand that addition and subtraction are reverse operations, no calculations are required (the “inversion shortcut”). Even preschoolers are able to use the inversion shortcut and use increases across development. A related inversion problem using the operations of multiplication and division (e.g., 3 x 9 ÷ 9) exists and research in my lab has found that both children and adults use the inversion shortcut less on these new problems than the former. As well, many Grade 6 and 8 students do not use the shortcut on the multiplication and division (M/D) inversion problems at all.
... The shortcut, once discovered, was not always used thereafter despite the advantages. Factors influencing the discovery and use of the inversion shortcut will be discussed.
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