Structural Differences Between Two-Step Word Problems.

ABSTRACT .A logical analysis of word problems pro.4ides an hypothepis about' the kinds of knowledge that may be necessary for solving multi -step word problems. This hypothesis is that knowledge of the overall pattern of relations in a problem may functionin problem solving, apart from.knowledge of the particular entities and the local relations in which they participate. This overall pattern or structure determines equivalence classes of problems, problems whose solutions differ in the specific mathematical operations utilized 'mit which are.cif similar diffictilty. To illustrate this analysis, a notation system for one-step word probledls is introduced and aIlescription-of two-step word problems according to this . notation is provided. Experimental results (using third-, fourth-, and fifth-grade students as subjects) are.then presented that verify the psychological validity of the analysis, namely, that for all grade levels the problem structure (the overall pattern of relations between the quantities in the problem) has an effect on problem-solving success. Speculation on the representation of knowledge,thSt could account for these results is included. (Author/JN)