RUME 28
2026
Alexandria, Virginia
Is Equivalence Just “Same Number”? College Students’ Numerical vs Non-Numerical Conceptions of Equivalence
Page: 459
As coursework extends beyond arithmetic, students encounter forms of equivalence beyond numerical equality. This study examines how college students characterize equivalence in mathematics generally, and specifically for equations and expressions. Responses from 198 students were analyzed and coded as numerical or non-numerical. Across questions, most responses appealed to numerical criteria, treating equivalence as equality to a single number, with higher prevalence of non-numerical criteria correlating with higher-level courses. We observed multiple variants of both numerical and non-numerical criteria, including converting algebraic expressions to numbers to justify equivalence. Findings highlight the need for educators to support students in distinguishing types of equivalence and their associated criteria.