Cognitive models underlying algebraic and non- algebraic solutions to unequal partition problems

Abstract

The structure of certain word-problems can be perceived in different ways, depending on the grammatical form of presentation of the problem and the student's expectation of how it will be solved. The results of our study involving 268 school students aged 14-16 show that, for a certain class of problems, different problem presentations promote the construction of different cognitive models of the situation described. Our data provide support for the hypothesis of Nathan et al. (1992) that in the solution of algebra word-problems there are three components of interpretation and modelling: a propositional text base, a cognitive model of the situation, and a formal model of the mathematical rel..