Comparing analogs is a key recommendation in mathematics instruction, but successful structure-mapping may impose high demands on children’s executive functions (EF). We examine the role of individual differences in EF resources on learning from an everyday mathematics video-lesson placing a particular strain on children’s cognitive resources: comparing three analogs presented sequentially. Specifically, we examine the separate contributions of working memory (WM) and inhibitory control (IC) on successful schemaformation. Overall, WM and IC explained distinct variance for predicting improvements in procedural knowledge, procedural flexibility, and conceptual knowledge after a 1- week delay. WM & IC are less predictive at immediate posttest, suggesting that these functions are not simply correlated with mathematics skill, but may be particularly important in the process of structure-mapping for durable schemaformation. These results inform the literature on both analogy and mathematics learning, extending previous findings implicating EFs as key for successful structure-mapping to an ecologically valid learning context.

Individual differences in Executive Function (EF) are well established to be related to overall mathematics achievement, yet the mechanisms by which this occurs are not well understood. Comparing representations (problems, solutions, concepts) is central to mathematical thinking, and relational reasoning is known to rely upon EF resources. The current manuscript explored whether individual differences in EF predicted learning from a conceptually demanding mathematics lesson that required relational reasoning. Analyses revealed that variations in EF predicted learning when measured at a delay, controlling for pretest scores. Thus, EF capacity may impact students' overall mathematics achievement by constraining their resources available to learn from cognitively demanding reasoning opportunities in everyday lessons. To assess the ecological validity of this interpretation, we report follow-up interviews with mathematics teachers who raised similar concerns that cognitively demanding activities such as comparing multiple representations in mathematics may differentially benefit their high versus struggling learners. Broader implications for ensuring that all students have access to, and benefit from, conceptually rich mathematics lessons are discussed. We also highlight the utility of integrating methods in Science of Learning (SL) research.