A componential view of children's difficulties in learning fractions

Florence Gabriel, Frederic Coche, Denes Szucs, Vincent Carette, Bernard Rey, Alain Content

    Research output: Contribution to journalArticlepeer-review

    48 Citations (Scopus)


    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.

    Original languageEnglish
    Article numberArticle 715
    Pages (from-to)Article: 715
    Number of pages12
    JournalFrontiers in Psychology
    Issue numberOctober
    Publication statusPublished - 2013


    • Arithmetic operations
    • Equivalence
    • Fraction subcontructs
    • Fractions
    • Part-whole
    • Proportion


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