The strategic use of alternative mental representations in the solving of arithmetic word problems

Solving word problems first requires the mental construction of the situation described in the statement of the problem. The strategies used by children and adults help us to infer the structure and characteristics of this mental representation. With the help of an original paradigm that does not require verbalisations from the individual, we have been able to show that the built representation is isomorphic to the structure of the problem statement. In other words, the order of calculations performed to solve the problem corresponds to the order of the underlying goals explicitly mentioned in the problem. This is the case even when other more efficient strategies for working memory are available. However, we have demonstrated that it is possible to lead individuals to construct an alternative representation from their initial strategy, especially by making the necessary calculations more complicated. The results of our work point to a predictive model of alternative mental representation in the area of arithmetic word problem solving: The probability that a mental representation will be constructed depends on its cognitive cost as well as the relative amount of resources made available in working memory.

Bibliography:

Thevenot, C., & Oakhill, J. (2006). Representations and strategies for solving dynamic and static arithmetic word problems: The role of working memory capacities. European Journal of Cognitive Psychology, 18(5), 756-775.

Thevenot, C., & Oakhill, J. (2005). The strategic use of alternative representations in arithmetic word problem solving. Quarterly Journal of Experimental Psychology-A, 58 (7),1311-1323.


Thevenot, C. Barrouillet, P. & Fayol, M. (2004). Mental representation and procedures in arithmetic word problems: The effect of the position of the question. L’Année Psychologique, 104 (4), 683-699.