Optimizing Problem Format to Facilitate Children's Understanding of Math Equivalence

Mathematical equivalence is a foundational concept. Unfortunately, most children (ages 7-11) struggle to understand it and have difficulties solving math equivalence problems, which have operations on both sides of the equal sign (e.g., 3 + 4 = __ + 5). One prevailing explanation for children’s poor performance is that children encode, or internally represent, the problems inaccurately. Previous research has found that children’s encoding of math equivalence problems depends on format, with accuracy encoding right-blank problems (e.g., 3 + 4 = 5 + __) being much lower than accuracy encoding left-blank problems (e.g., 3 + 4 = __ + 5). Following the prevailing account, if poor encoding causes solving difficulties, then right-blank problems should be more difficult to solve correctly than left-blank problems. However, a second, equally plausible prediction is that the role of encoding in solving differs based on problem format. This project examined the role of encoding in (1) children’s performance solving math equivalence problems, using an integrative data analysis, and (2) children’s learning to solve math equivalence problems correctly, using a randomized experiment. Contrary to the prevailing view that encoding performance predicts solving performance, accuracy on right-blank problems was significantly higher than accuracy on left-blank problems. Additionally, overall encoding accuracy was significantly correlated with performance on right-blank problems only. Results indicate that the role of encoding in children’s solving of math equivalence problems depends on problem format, and specifically that the interpretation of what is encoded may matter more than accuracy encoding problem features. Furthermore, results from the randomized experiment suggest it may be more efficient to teach math equivalence using right-blank versus left-blank problems.