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Children's understanding and misunderstanding of the inverse relation in division
Author(s) -
Squire Sarah,
Bryant Peter
Publication year - 2003
Publication title -
british journal of developmental psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.062
H-Index - 75
eISSN - 2044-835X
pISSN - 0261-510X
DOI - 10.1348/026151003322535192
Subject(s) - quotient , psychology , relation (database) , matching (statistics) , contrast (vision) , divisor (algebraic geometry) , representation (politics) , inverse , developmental psychology , cognitive psychology , mathematics , statistics , computer science , artificial intelligence , pure mathematics , political science , geometry , database , politics , law
Two studies are presented on 5–8‐year‐olds' understanding of the inverse relation between divisor and quotient in division problems. The problems concerned sharing carrots between rabbits invited to two parties, with the same total number of carrots allocated to each party. Children had to reason that the greater the number of rabbits invited to each party, the less food each would receive. Possible effects of the size contrast between the two different divisors (large vs. small), the representation that children were given (full‐pictures vs. numbers) and the response mode (verbal vs. matching task) were investigated. The results of both studies demonstrated that most children tended to be consistently correct or incorrect, regardless of the variations in the tasks. A substantial proportion of 5‐year‐olds had great difficulty in understanding the inverse relation between the divisor and quotient and may even have had a misconception about it. There was developmental improvement in this understanding by 7–8 years.