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AWARENESS OF REVERSIBILITY: ITS EFFECT ON PERFORMANCE OF CONVERSE ARITHMETICAL OPERATIONS
Author(s) -
EIFERMANN RIVKA R.,
ETZION DALIA
Publication year - 1964
Publication title -
british journal of educational psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.557
H-Index - 95
eISSN - 2044-8279
pISSN - 0007-0998
DOI - 10.1111/j.2044-8279.1964.tb00619.x
Subject(s) - converse , subtraction , arithmetic function , arithmetic , carry (investment) , mathematics , mathematics education , computer science , psychology , algebra over a field , discrete mathematics , pure mathematics , geometry , finance , economics
S ummary . Why is the operation of addition easier than that of subtraction, even to adults and even when the sums involved do not exceed 10? Addition and subtraction are converse operations and it is surprising, therefore, that adults, who undoubtedly comprehend their reversible nature, find one of the operations more difficult to carry out than the other. Our assumption was that this fact resulted largely from the way the two operations were taught at school, where addition was more thoroughly trained than was subtraction. In order to test this assumption, we created a system isomorphic to the number system of from 1 to 10, a system based on the differences between various lengths of coloured rods. We then taught the system to a group of sixteen students, in a way that did not give preference to the operation of addition over that of subtraction. The result was, that when the subjects were required to carry out the two operations on the newly learnt system, the difference in response time to addition as against subtraction problems was significantly reduced when compared with the same difference obtained in solving problems with numbers. It may thus be possible that a teaching method which emphasizes the reversible nature of arithmetical operations may enable a more comprehensive and flexible approach to arithmetic.