Predicting students’ performance on geometric problem-solving tasks: the roles of cognitive reflection, fluid intelligence, and mathematical beliefs

Introduction: Recent perspectives in mathematics education highlight the importance of integrating cognitive and affective dimensions in understanding students' reasoning. Accordingly, the present study investigates the interrelations of performance on geometric problem-solving and general cognitive skills, fluid intelligence, cognitive reflection, and mathematics-related beliefs. Methods: The study explored differences in geometric problem-solving performance by gender and academic year, as well as the predictive contribution of cognitive, mathematics-belief, and mathematics achievement variables. A total of 303 secondary school students (years 8-11) completed several measures assessing geometric problem-solving, cognitive reflection, fluid intelligence, and mathematics-related beliefs; prior mathematics achievement was obtained from official school grades. Correlational and hierarchical regression analyses were conducted to examine predictive relationships, while moderation and mediation analyses were performed to test interaction effects and indirect effects, respectively. Results: Results indicated significant differences in geometric problem-solving performance across academic years, with no significant gender differences. Cognitive reflection, fluid intelligence, and mathematics achievement emerged as significant predictors of performance on the geometric problem-solving task, while mathematics-related beliefs were significantly correlated with geometry performance but did not explain additional variance once cognitive and achievement variables were considered. Mediation analyses did not support significant indirect effects through mathematics-related beliefs, and moderation analyses did not show significant gender- or grade-level differences in the associations between cognitive predictors and geometry performance. Discussion: These findings highlight the relevance of reasoning processes in adolescents' geometric problem-solving and provide further evidence of the role of cognitive and belief-related factors in its development.