Exploring the Episodic Structure of Algebra Story Problem Solving

Abstract

This article analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent undergraduates. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attempts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complementary activities, giving rise to a succession of problem-solving episodes. Although direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of model-based reasoning to identify, pursue, and verify quantitative constraints required for solution. The article concludes by discussing the implications of these finding for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction.