Effectiveness of a cognitively grounded mathematics intervention in a high school blended learning environment: achievement gains, implementation fidelity, and demographic variability.

Introduction: This randomized pilot study evaluated the effectiveness of a cognitively grounded mathematics intervention implemented in a high school blended learning environment. The intervention was designed to support durable mathematical learning through mastery-based progression, retrieval-oriented practice, adaptive sequencing, structured feedback, and instructional supports. Grounded in principles from cognitive load theory, retrieval-based learning, mastery learning, adaptive instruction, and growth mindset research, the study examined whether this instructional model improved secondary mathematics achievement compared with business-as-usual mathematics instruction. Methods: Participants were 255 eleventh-grade students from a large urban public high school. Students were randomly assigned to either a Treatment group, which received the cognitively grounded blended mathematics intervention for one academic year, or a Control group, which continued with business-as-usual mathematics instruction. Mathematics achievement was measured using statewide high-stakes examinations administered before and after the intervention. Baseline equivalence between groups was examined across overall mathematics achievement and related mathematics subdomains. Outcome analyses compared posttest achievement while controlling for pretest performance, and gain-score analyses were conducted to examine growth from pretest to posttest. Additional analyses examined mathematics performance subdomains, implementation fidelity within the Treatment group, demographic sensitivity patterns, and the association between growth mindset and mathematics gains among Treatment students. Results: Baseline analyses confirmed that the Treatment and Control groups were equivalent before the intervention across overall mathematics achievement and related mathematics subdomains. After controlling for pretest performance, students in the Treatment group achieved significantly higher posttest mathematics scores than students in the Control group, with an adjusted mean advantage of approximately 5 points. Gain-score analyses supported these findings, showing greater mathematics growth and reduced outcome variability among Treatment students. Subdomain analyses indicated significant Treatment advantages in retrieval, procedural processing, conceptual application, data interpretation, and mathematics items of low, medium, and high complexity. Within the Treatment group, implementation fidelity was positively associated with mathematics achievement gains, suggesting that stronger enactment of the intervention corresponded to larger student gains. Exploratory demographic sensitivity analyses suggested that the intervention effect was broadly consistent across gender, race/ethnicity, parental education, lunch status, and living arrangement, although these findings should be interpreted cautiously because of the pilot design and unequal subgroup sizes. Growth mindset, measured only within the Treatment group, was moderately associated with mathematics gains, indicating that motivational beliefs may help explain individual differences in responsiveness to cognitively structured instruction. Discussion: Overall, the findings provide outcome-level evidence that a cognitively grounded, mastery-oriented mathematics intervention was associated with meaningful improvements in secondary mathematics achievement in the blended learning context examined. The results are consistent with theoretical expectations from cognitive load theory, retrieval-based learning, mastery learning, adaptive instruction, and growth mindset research. However, the study measured achievement outcomes and mathematics performance subdomains rather than directly measuring the cognitive and motivational mechanisms presumed to support learning. Therefore, causal claims about the mechanisms underlying the observed achievement gains should be made cautiously. Future multisite and longitudinal studies should incorporate process measures, delayed assessments, and broader samples to examine how cognitive and motivational factors contribute to learning, retention, and transfer across educational contexts.