SITUATION MODEL, TEXT BASE AND WHAT ELSE? FACTORS AFFECTING PROBLEM SOLVING

ABSTRACT. Our aim in this paper is to identify factors affecting problem solving strate-gies in the case of a multiplicative comparative situation, involving three unknown quant-ities whose sum is known, and in which comparison relations between two pairs of the quantities are given. We propose a model of the complexity of a word problem about such situation. The model has several variables, namely, 1) the ratio of the number of quantities that are being compared to the number of reference quantities (the ‘reference ratio’); 2) the scheme of the situation, i.e. the type of relation between the two given elementary comparison relations; 3) the order of presenting the elementary comparison relations; 4) the words used to describe the multiplicative comparison relations (so many times ‘more’ Vs so many times ‘less’). The choice of the values of these variables in the formulation of a problem is assumed to affect the solver’s solution strategy. The most important construct of the model is what we have called the ‘complexity level ’ of a solution, namely, the number of operations (theoretically) needed to go from the text of the problem to an algebraic representation of this solution. An analysis, in terms of the model, of word problems that can be formulated about this kind of situation makes it clear that, while there are severa