Semantic Features of Similarity and Children's Strategies for Identifying Relevant Information in Mathematical Story Problems

Abstract

Many children have difficulty solving story problems in mathematics, especially when the problems contain irrelevant information. The present studies offer a contextual analysis of the difficulty added by irrelevant information that focuses on the relation of the irrelevant to the relevant problem information. A model of discrimination performance was devised hypothesizing that students analyze the problem text (i.e., identify semantic categories such as the agent, action, and unit of measure) and search through the problem text for values of the semantic categories that match those requested in the question. Two experiments assessed the validity of the performance model across variations in problems and students and identified and compared the specific discrimination strategies used by more and less successful mathematics students. Results indicated that the model was an accurate predictor of discrimination performance for both successful and less successful students, as well as for a variety of problem types. More and less successful students differed reliably in the type of discrimination strategy used, with successful students using strategies based on an analysis of the problems' semantic features and less successful students basing strategies on information position. Although a predominant strategy could be identified for most students, both the more successful and the less successful students seemed to use multiple strategies. Implications of the results for both classroom instruction and theoretical understanding of mathematical problem solving are discussed, as well as the generality of the model and the strategies identified.