Abstract
This study examined the relationships among parental involvement, learning engagement, self-efficacy, and mathematics achievement to identify actionable factors for improving student performance. A data-driven quantitative design was employed using secondary data from 354 respondents, analyzed through nonparametric methods, mediation modeling, association rule mining, and exploratory predictive modeling with classification and regression trees. Reliability analysis confirmed strong internal consistency for all scales, and descriptive statistics indicated generally high levels of parental involvement, engagement, and self-efficacy among participants. Correlation and mediation analyses revealed that parental involvement significantly influenced mathematics achievement both directly and indirectly through learning engagement and self-efficacy, with combined mediators accounting for more than half of the total effect. Prescriptive analytics highlighted engagement and self-efficacy as multidimensional levers (behavioral, emotional, and cognitive) for improvement, while predictive models demonstrated good classification performance and meaningful reductions in error for continuous achievement scores. These findings underscore the importance of integrated strategies that strengthen family-school partnerships while simultaneously fostering engagement and confidence to optimize mathematics outcomes. The study concludes that parental involvement, learning engagement, and self-efficacy are critical, interrelated factors in mathematics achievement and recommends multilevel interventions while acknowledging limitations of cross-sectional secondary data. Future research should employ longitudinal and experimental designs to establish causality and validate these findings across diverse contexts.