Frequency norms and structural analysis of algebra story problems into families, categories, and templates

Abstract

The goal of this study was to develop a framework for classifying algebra story problems and to determine observed frequencies for each problem type. A total of 1097 algebra story problems were selected from ten standard algebra textbooks. These are divided into eight families based on the nature of the source formula involved; for example, nearly 300 problems were classified in the “time rate family” because they were based on the source formula, “distance = rate x time” or “output = rate x time.” Each family was divided into problem categories based on the general form of the story line; for example, the time rate family consisted of “motion,” “current,” and “work” categories. Each category was divided into templates based on the specific propositional structure of the problem; for example, there were a dozen templates for motion problems such as “overtake,” “closure,” “round trip,” etc. This article describes the procedure for generating families, categories, and templates and provides frequency counts for each observed template. Implications for fostering productive research and instruction are discussed.