Exploring Problem-Based Learning to Improve Higher Secondary Students’ Mathematics Skills: A Mixed-Methods Approach

Abstract

This study aimed to determine how effectively Problem-Based Learning (PBL) enhances eleventh-grade students’ mathematical problem-solving abilities, motivation, engagement, and attitudes toward mathematics. The purpose was to compare the outcomes of students taught through PBL with those who received traditional instruction and to understand whether PBL supports stronger learning performance and more positive experiences in upper secondary mathematics classrooms. A mixed-methods, quasi-experimental design was used to provide a comprehensive understanding of PBL’s impact. The quantitative component involved a pretest-posttest non-equivalent control group design in which higher secondary school students were placed into a PBL intervention group and a traditional instruction control group. Students’ mathematical problem-solving skills were assessed through five essay-based tests. The qualitative component complemented the experiment through focus group discussions, student reflection journals, and classroom observations, which helped capture students’ motivation, engagement, and attitudes toward mathematics. Quantitative data were analyzed through t-tests to determine whether the difference between pre- and post-test performance for the PBL and traditional groups was statistically significant. The qualitative data were examined using thematic analysis, where responses from focus groups, reflections, and observations were coded to identify recurring patterns related to students’ motivation, engagement, confidence, and perspectives on mathematical learning under PBL. The results showed that students in the PBL group performed better than those taught through traditional instruction, with statistically significant improvements in post-test scores (p < 0.05), indicating that PBL strengthens higher-order mathematical problem-solving abilities. Qualitative findings revealed that PBL fostered greater motivation, deeper engagement, and more positive attitudes toward mathematics. Students reported improved confidence, stronger collaboration, higher participation, and greater enjoyment when solving complex mathematical problems under PBL. The study concludes that Problem-Based Learning is an effective teaching approach for upper secondary mathematics, as it enhances problem-solving skills while simultaneously improving motivation, engagement, and attitudes toward the subject. These results highlight PBL’s potential to support holistic student development and align with modern educational priorities, providing valuable evidence for educators and policymakers seeking to integrate active, student-centred learning strategies into mathematics classrooms.