Sylvie Gamo

This research shows important differences between isomorphic problems that are resolved by two operations depending on the nature of the variables used in the problem (amounts, price, ages, durations, heights, weights). These differences concern not only performance but also resolution strategies and therefore reveal how the student represents the problem. These problems are solved in two ways: a step by step calculation using addition, substraction, or both, or, a simple subtraction operation chosen because the problem contains two groups with common information.

Previous research has shown that the problem chosen determines the transfer possibilities. By using experimental data, the goal of the current study is to test pedagogical choices such as identifying the relevant semantic dimensions pour students, working on the construction of the interpretation of the problem in order to improve transfer, the difficulty of a problem based on adequate interpretation... This leads us to connect the notion of learning transfer to the notion of conceptualisation: how should learning transfer be organised so that conceptualisation evolves in arithmetic problem solving in elementary school?



The results support the hypothesis:

- certain variables (amount, price, height, weight) create more of a cardinal representation (quantities that accumulate) whereas other (durations and ages) work more with an ordinal representation that uses the comparison of quantities and the calculation of the difference associated with the comparison.
The first kind of representation is resistant: even experts like the students at the teaching university (IUFM) have trouble switching between the two representations.

- the nature of the variable is not the only element influencing mental representations and the choice of problem solving strategies, the scenario is also essential (obtained by manipulating linguistic forms).

- we can help students build the more abstract representation necessary for understanding the more difficult strategy by showing them the similarities between situations.

Experiments are conducted to show the feasability of the above approach and aim to assess the direct implications in the school context. (Learning method based on the construction of problem interpretation compatible with its formal structure).

 

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