More Than the Same: A Substitutive Conception of the Equal Sign Predicts Algebraic Problem Solving

• In Event: Elementary Students' Mathematical Cognition: Insights Into Estimation, Relational Reasoning, and Effective Feedback in Mathematics

Abstract

Understanding of equality is critical for algebraic reasoning. Recent evidence suggests that students may hold two distinct relational conceptions of the equal sign, a sameness conception and a substitutive conception. This study investigated whether the substitutive conception is developmentally more advanced than the sameness conception and whether a substitutive conception is uniquely associated with performance on algebraic tasks. Participants (in Grade 3 and Grade 6) rated definitions of the equal sign and completed assessments of understanding of equivalence and algebra. Patterns of definition ratings revealed that the sameness conception is distinct from and precedes the substitutive conception. Further, endorsements of the substitutive conception were associated with performance on equivalence and algebraic tasks, over and above endorsements of the sameness conception.

Authors

• Lauren E. Anthony, University of Wisconsin - Madison

• Andrea M. Donovan, University of Wisconsin - Madison

• Ana C. Stephens, University of Wisconsin - Madison

• Percival Grant Matthews, University of Wisconsin - Madison

• Martha W. Alibali, University of Wisconsin - Madison