Modelling the relationship among calculus scholars’ beliefs, critical thinking, elaboration, and problem-solving

The aim of this research was to establish a structural relation among calculus scholars’ beliefs, self-regulated learning (SRL) strategies, and problem-solving skills related to differential equations (DEs). To identify the relationships between different variables and their impact on DE problem-solving, a correlational study design with an a priori model was established. Three questionnaires were utilized to measure the epistemological and useful mathematics beliefs and SRL of 430 higher secondary school students. Additionally, an evaluation test consisting of five DE tasks was administered. The results demonstrated that there was a strong correlation among epistemological mathematics beliefs, the perceived usefulness of the subject, SRL, and problem-solving. This study confirms (β = .29, T = 4.05, and p < 0.001) that students who perceive mathematics as useful tend to improve their problem-solving skills. Similarly, only elaborations (β = .06, T = 2.40, and p < 0.001) had shown the mediation role between beliefs and problem-solving. These findings highlight the potential use of these factors in improving students’ skills for solving the real tasks. A few important implications were also outlined to promote culture for deep and meaningful learning.