A formative assessment of students’ algebraic variable misconceptions

• A formative assessment to diagnose algebraic variable misconceptions was developed.
• The assessment items showed strong reliability, predictive validity, and construct validity.
• Variable misconceptions were found to be robust and entrenched.
• The most common misconception was a belief that a variable is a label for an object.
• High-school students harbored more misconceptions than middle-school students.

Gaining an accurate understanding of variables is one challenge many students face when learning algebra. Prior research has shown that a significant number of students hold misconceptions about variables and that misconceptions impede learning. Yet, teachers do not have access to diagnostic tools that can help them determine the misconceptions about variables that their students harbor. Therefore, a formative assessment for variable misconceptions was created and administered to 437 middle- and high-school students. Analyses from the test scores were found to exhibit strong reliability, predictive validity, and construct validity in addition to important developmental trends. Both teachers and researchers can use the test to identify students who hold misconceptions about variables.