Assessing Formal Knowledge of Math Equivalence among Algebra and Pre-Algebra Students.

A central understanding in mathematics is knowledge of math equivalence, the relation indicating that 2 quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7 to 11) children's (mis) understanding of math equivalence, and recent work has developed a construct map and comprehensive assessments of this understanding. The goal of the current research was to extend this work by assessing whether the construct map of math equivalence knowledge was applicable to middle school students and to document differences in formal math equivalence knowledge between students in pre-algebra and algebra. We also examined whether knowledge of math equivalence was related to students' reasoning about an algebraic expression. In the study, 229 middle school students (ages 12 to 16) completed 2 forms of the math equivalence assessment. The results suggested that the construct map and associated assessments were appropriate for charting middle school students' knowledge and provided additional empirical support for the link between understanding of math equivalence and formal algebraic reasoning.