Opportunities for perceptual learning influence problem solving in mathematics.

Relational reasoning-including the ability to recognize relationships, or patterns, among two or more cases and to abstract structure to accommodate novel cases-is essential in mathematics. One promising route to enhancing relational reasoning is to provide opportunities to notice perceptual invariances and dissimilarities via a perceptual learning intervention. Across two studies, we investigated the effectiveness of a perceptual learning intervention that involved experience with patterns on equation solving and relational reasoning. In Study 1, adult participants (i.e., university students in the United States) completed either a pattern extension task (pattern experience group) or received a worked example followed by a set of nonpattern-focused tasks (explicit instruction group). In an initial sample, participants in the pattern experience group were faster than those in the explicit instruction group; in a replication sample, participants in the pattern experience group were more accurate but not faster. To investigate these mixed results, Study 2 included an active control group and a modified version of the pattern extension task that made using the pattern a more efficient strategy (compared to a more computationally intensive strategy). In Study 2, the pattern experience group outperformed both the explicit instruction and control groups in accuracy on near transfer items. Both interventions led participants to shift away from using computational strategies and toward using a strategy that involved focusing on the multiplicative relations within equations. Taken together, these results suggest that perceptual learning interventions may be an effective path to enhance problem solving in mathematics and may offer advantages beyond traditional instruction. (PsycInfo Database Record (c) 2026 APA, all rights reserved).