Instructional Practices and Problem- solving Skills Competence in Calculus among BSED Mathematics Students: A Mixed- methods Study

This study aimed to examine the relationship between instructional practices and problem-solving competence in calculus among the BSED Mathematics students in college. It aimed to explore how the various instructional techniques exert an effect on the ability of the students to solve calculus problems in an effective manner. Using a convergent parallel mixed-methods design, it combined the quantitative data from the survey answers by 284 students with the qualitative revelations acquired through interviews and focus group discussions with a purposive sample. The results showed a clear linkage between successful instruction and improved problem-solving, which was measured in terms of dimensions of creative thinking, analysis, decision-making, emotional intelligence, research, and collaboration. Cognitive, intrapersonal, and interpersonal instructional strategies were the main instructional strategies that were identified. Qualitative findings also endorsed the difficulties encountered by students, including abstraction, metacognitive processes, and instruction limitations. The alignment of both data sets highlighted the significance of structured learning, scaffolding methods, and group work in the acquisition of calculus competence. The research concludes that successful instructional strategies play a significant role in students' problem-solving skills in calculus, with the suggestion that teachers incorporate novel and student-oriented teaching methods. Additional research is called for to investigate additional instructional interventions that facilitate the acquisition of these key skills