Childrenʹs development in solving a certain class of additive problems in mathematics: A didactic intervention based on action

Several studies have brought to light the difficulties which children experience in the representation and solution of change problems in mathematics. Analysis of these difficulties has uncovered certain implicit models used by children. These models actually interfere with the very process of number construction. A teaching experiment involving 30 third grade students (8- to 9-yr-olds) was developed on the basis of this analysis. According to research carried out in the Piagetian tradition, our didactic choice, within the form of a group sociomotor game, places the action of the subjects at the heart of the transformation of their concept of number. Observation of the notations and problem-solving procedures used throughout the experiment by the children in mathematical situations derived from a game enabled us to account for the childrenʹs development, which went from a focus on states to a type of reasoning in which changes become quantifiable “objects of awareness”.