An Analysis of Arithmetic Problem Posing by Middle School Students

Abstract

The mathematical problems generated by 509 middle school students, who were given a brief written “story-problem” description and asked to pose questions that could be answered using the information, were examined for solvability, linguistic and mathematical complexity, and relationships within the sets of posed problems. It was found that students generated a large number of solvable mathematical problems, many of which were syntactically and semantically complex, and that nearly half the students generated sets of related problems. Subjects also solved eight fairly complex problems, and the relationship between their problem-solving performance and their problem posing was examined to reveal that “good” problem solvers generated more mathematical problems and more complex problems than “poor” problem solvers did. The multiple-step data analysis scheme developed and used herein should be useful to teachers and other researchers interested in evaluating students' posing of arithmetic story problems.