Math self-concept through SRL components mediated with math self-efficacy: A PLS-SEM and Gaussian copula approach

With the increasing adoption of blended learning environments, understanding the psychological and self-regulatory factors that influence student learning has become increasingly important. However, the interplay among motivational beliefs, self-regulated learning (SRL) components, and self-efficacy remains insufficiently understood. This study investigates the relationship between SRL components (motivation, cognitive, and metacognitive strategies), math self-efficacy as a mediating factor, and math self-concept in a blended learning environment. We used partial least squares structural equation modeling (PLS-SEM) with robustness checks based on the Gaussian copula to analyze self-reported data from a cross-sectional survey of 938 junior high school students in Central Visayas, Philippines. PLS-SEM results showed that all paths were significant; however, robustness checks confirmed only five paths and changed two partial mediations to no mediations. The Gaussian copula analysis indicates that the newly estimated relationships are not substantially affected by endogeneity, thereby increasing confidence in the model's validity. Given the significant link between math self-efficacy and self-concept, implementing growth-mindset frameworks and mastery-level feedback can be effective ways to strengthen reciprocal relationships. Metacognitive strategies unexpectedly have a negative effect on math self-efficacy. Future research may investigate whether factors such as cognitive overload and overthinking contribute to this negative effect. Several implications aligned with existing literature, policy insights, and future research recommendations were discussed.