A componential view of children's difficulties in learning fractions

Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articula...

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Published inFrontiers in psychology Vol. 4; p. 715
Main Authors Gabriel, Florence, Coché, Frédéric, Szucs, Dénes, Carette, Vincent, Rey, Bernard, Content, Alain
Format Journal Article
LanguageEnglish
Published Switzerland Frontiers Media S.A 2013
Subjects
Arithmetic Operations
equivalence
Fraction Subcontructs
fractions
Part-Whole
Proportion
Psychology
equivalence
fraction subcontructs
fractions
proportion
arithmetic operations
part-whole
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Summary:Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions.
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This article was submitted to Developmental Psychology, a section of the journal Frontiers in Psychology.
Edited by: Korbinian Moeller, Knowledge Media Research Center, Germany
Reviewed by: David Geary, University of Missouri, USA; Thomas J. Faulkenberry, Tarleton State University, USA
ISSN:1664-1078
1664-1078
DOI:10.3389/fpsyg.2013.00715