Undergraduates' Errors in Using and Interpreting Algebraic Variables: A Comparative Study

Document Type

Conference Proceeding


Gwendolyn M. Lloyd, Melvin Wilson, Jesse L. M. Wilkins, Stephanie L. Behm

Publication Title

Proceedings of the 27th Annual Meeting of PME-NA North American Chapter of the International Group for the Psychology of Mathematics Education: Frameworks that Support Research and Learning


Psychology of Mathematics Education- North American Chapter

Publication Date


Publisher location

Roanoke, VA

Abstract/ Summary

This study examined undergraduate basic algebra, college algebra, and calculus students’ abilities to use and interpret algebraic variables. Participants completed an algebra test to identify four hierarchical levels of variable use, from the most basic, such as ignoring or evaluating variables, to the more complex uses of variables as generalized numbers or varying quantities. Students’ levels of variable use were determined, and types of common errors were tabulated and compared across the three courses. Results showed that levels of variable use generally increased with course difficulty. The levels were related to the mean course grades for college algebra and calculus students. Considerable numbers of students in all three courses exhibited high error rates on test items requiring the interpretation and use of variables as generalized numbers or functionally related quantities to represent word problems. Common errors included using variables as labels, making strictly literal translations, and failing to extract meaning from variable expressions.