What is the initial representation of arithmetic problems before and after schooling?

Speaker: Rémi Brissiaud (IUFM de Versailles)

Date : 15 June 2006

Problem solving is a cognitive activity that has been the object of many studies and models over the past thirty years. In the original approach, formal schemas (Kintsch et Greeno,1985), the schema was used both to interpret the problem and find a solution. This approach quickly became viewed as limited because it does not take into account how a person interprets the terms of the statement of the problem. Reusser (1989) introduced the notion of a situational model that transposes from the notion of a situational model to a problem solving model for text comprehension (van Dijk & Kintsch, 1983). This situational model is defined as the intermediary that allows us to pass from the text to the problem model. In this case, problem solving is viewed in two stages: the initial representation of the problem followed by the selection of a numeric process to solve the problem. This manner of solving problems is not used by children before they enter school. Many studies (for a review, see Verschaffel et De Corte, 1997) claim that children solve basic addition and multiplication problems by simulating the situation described in the problem statement either with objects, a counting procedure, or by using known numeric relationships. In this case, problem solving does not take place over successive stages. As noted by Verschaffel and De Corte: "the chidren’s problem representation and solution process is complex, interrelated whole."

The question we address is the following: after schooling has taken place, does the initial representation of a problem most resemble a "situational model" (interpretation of the problem statement is followed by the selection of an operational procedure) or does it remain based on a mental simulation of the situation described in the problem statement (interpretation of the problem statement has itself an operational dimension)? We will show how it is possible to answer this question by re-examining the results of a longitudinal study of solving addition and multiplication problems by year 1 pupils (Brissiaud et Sander, 2005) and that these data reveal themselves to be clearly in favour of an initial representation that continues to be based on a mental simulation of the described situation. These results mark the importance of the isolated variable in this study: concordance/discordance between the initial representation of the problem and the efficiency of its numeric solution.



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Further reading: Brissiaud (2006) Calcul et résolution de problèmes arithmétiques: il n'y a pas de paradis perdu