An Analysis of Calculus Students’ Errors When Using and Interpreting Variables in
Expressions and Equations
Susan S. Gray
sgray@une.edu
University of New England, Biddeford, ME
Barbara J. Loud
Regis College, Weston, MA
barbara.loud@regiscollege.edu
Carole P. Sokolowski
Merrimack College, No. Andover, MA
carole.sokolowski@merrimack.edu
This study documents and analyzes common errors undergraduates made as they
constructed and interpreted algebraic expressions or equations in the context of word
problems. An adaptation of Küchemann’s (1981) algebra test was administered to 170
students on the first day of Calculus I. A large percentage of these students performed
poorly on word problems requiring either interpretation of variables or construction of
algebraic expressions or equations. Frequently observed errors included evaluating
variables incorrectly, using variables as labels, and making strictly literal interpretations
of variable expressions. These errors reflect uses of variables that are well below
expectation for beginning calculus students.