Middle School Students' Conceptual Understanding of Equations: Evidence From Writing Story Problems. WCER Working Paper No. 2009-3

This study investigated middle school students' conceptual understanding of algebraic equations. Participants in the study--257 sixth- and seventh-grade students--were asked to solve one set of algebraic equations and to generate story problems corresponding with another set of equations. Structural aspects of the equations, including the number of operations and the position of the unknown, influenced students' performance on both tasks. On the story-writing task, students' performance on two-operator equations was poorer than would be expected based on their performance on one-operator equations. Students made a wide variety of errors on the story-writing task, including (a) providing story contexts that reflected operations different from those in the given equations, (b) failing to provide a story context for some component of the given equations, (c) failing to include mathematical content from the given equations in their stories, and (d) including mathematical content in their stories that was not present in the given equations. The nature of students' story-writing errors suggests two main gaps in students' conceptual understanding. First, students lacked a robust understanding of the operation of multiplication. Second, students demonstrated difficulty combining multiple mathematical relationships into coherent stories. (Contains 4 tables and 2 figures.) [The research reported in this paper was supported by the McDonnell Foundation (Grant No.JSMF 97-56), the Interagency Education Research Initiative (Grant No. REC 0115661), and the Wisconsin Center for Education Research, School of Education, University of Wisconsin--Madison.]