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Can children construct inverse relations in arithmetic? Evidence for individual differences in the development of conceptual understanding and computational skill
Author(s) -
Gilmore Camilla K.,
Bryant Peter
Publication year - 2008
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 - 10.1348/026151007x236007
Subject(s) - construct (python library) , subtraction , psychology , inverse , concept learning , arithmetic , development (topology) , cognitive psychology , computer science , mathematics , mathematical analysis , geometry , programming language
Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8‐ to 9‐year‐old children's use of a computational shortcut based on the inverse relationship between addition and subtraction, in problems where it was transparently applicable (e.g. 17+11−11=□) and where it was not (e.g. 15+11−8−3=□). Most children were able to construct inverse transformations and apply the shortcut in at least some situations, although they used the shortcut more for problems where it was transparently applicable. There were individual differences in the relationship between children's understanding of the inverse relationship and computational skill that have implications for theories of mathematical development.