title: A componential view of children's difficulties in learning fractions.
abstract: 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.
authors.affiliation: Department of Experimental Psychology, Centre for Neuroscience in Education University of Cambridge, UK ; Laboratoire Cognition, Langage et Développement, Centre de Recherche Cognition et Neurosciences, Université Libre de Bruxelles (ULB) Bruxelles, Belgium.
authors.forename: Florence
authors.initials: F
authors.lastname: Gabriel
authors.forename: Frédéric
authors.initials: F
authors.lastname: Coché
authors.forename: Dénes
authors.initials: D
authors.lastname: Szucs
authors.forename: Vincent
authors.initials: V
authors.lastname: Carette
authors.forename: Bernard
authors.initials: B
authors.lastname: Rey
authors.forename: Alain
authors.initials: A
authors.lastname: Content
keywords: arithmetic operations; equivalence; fraction subcontructs; fractions; part-whole; proportion