Bernard Rey

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 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.

Faire la classe à l'école élémentaire

Comment mettre les eleves au travail ? Comment preparer la classe ? Comment ramener a la tâche les eleves distraits ou agites ? Comment mettre en place des activites qui fassent reellement apprendre ? Comment reagir a l’agressivite ou a l’insolence de tel ou tel ? Comment et quand evaluer ? Comment aider les eleves en difficulte ? A ce type de questions, ce livre donne des reponses precises et concretes, et meme ce qu’on pourrait appeler des « recettes ». Mais faire la classe n’est pas une activite ordinaire qu’on pourrait pratiquer mecaniquement. Il faut faire des choix et se donner des principes. Ce sont eux que Bernard Rey s’attache a eclairer. Il s’adresse ainsi aux enseignants debutants. Mais le livre provoquera aussi la reflexion des maitres chevronnes. Quant aux parents d’eleves, ils trouveront grâce a lui un acces aux coulisses d’une activite qui concerne, jour apres jour, leurs enfants. Date de premiere edition : 1998.