Nature et rôle des inférences impliquées dans la résolution de problèmes mathématiques

Among high school mathematics teachers, it is a common conception that student have a hard time solving problems because « they don’t know how to read ». Although it seems common sense that a relation between reading abilities and problem solving abilities exists, it is nonetheless important to examine systematically this relation in order to go beyond popular belief. This thesis addresses this issue by exploring the role of reading comprehension in mathematical problem solving, focusing on inferences which are one of reading comprehension’s components.   Various reading comprehension models have been explored in order to discern the role inferences play within this process. Most researchers agree that it is important, to understand a text properly, to build a situation model, which is a particular type of mental representation of the text, in the construction of which inferences play an important part. Many authors who studied mathematical problem comprehension also consider the construction of a situation model, as opposed to a direct translation strategy (which consists in combining numbers and keywords as they appear in the problem statement to get to a solution), as very important for succeeding in problem solving, although they don’t mention inferences. Since inferences play an important role in the situation model construction, the failure to construct the latter might be explained by a weakness in inference generation. That is what this research addresses, as well as the nature of the inferences that are involved in problem solving and their role in that process.    To achieve this goal, we administered various tests to 175 secondary 4 students from the Province of Quebec: an inferential skills test, a problem solving test, a recall task about the problem statements, and, for some participants, an individual interview.  The data thus obtained allowed us to draw the following conclusions. First of all, there is a positive correlation between the inference generation score and the problem solving score; we were even able to determine which types of inferences were more closely related to successful problem solving. Since inferences take part in the situation model construction, we wanted to know if the students who did build such a situation model got a better inference generation score than the students who mostly used a direct translation strategy, which they did. General conclusions on the nature of the inferences implied in mathematical problem solving were drawn from these results, but we also wanted to see if the data could lead to a more specific understanding of this relation. Therefore, we tried to establish student profiles by combining their inference generation abilities and their preferred problem solving strategy. We identified six different profiles, each with specific characteristics. Finally, we analyzed the problem solving and the interviews to highlight six different inference functions within the problem solving process, as well as the moments when inferences were used and the types of inferences involved, which let us to better understand and define these functions.

Keyphrases: Problem solving, Reading, Mathematics, Comprehension