[en] arithmetical problems ; empirical study ; pupil profile ; top-down vs. bottom-up type approaches ; use of symbolism
[en] This article relates to an empirical study based on the use of mathematical symbolism in problem solving. Twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a "top-down" approach (an approach that is still applied within the French Community of Belgium): conventional symbols are presented to the pupils immediately with an explanation of what they represent and how they should be used. Teaching then focuses on calculation techniques (considered as a pre-requisite for solving problems). The results presented here show the abilities (and difficulties) demonstrated by the children in making connections between the conventional symbolism taught in class and the informal approaches they develop when faced with the problems that arc, put to them. The limits of the "top-down" approach are then discussed as opposed to the more innovative "bottom-up" type approaches, such as those developed by supporters of Realistic Mathematics Educations in particular.