Integrating Critical Thinking and Mathematical Inquiry: A Framework for Instruction in Ordinary Differential Equations

Abstract

Critical thinking is widely recognised as a core educational objective in higher education. This study examined how undergraduate students’ critical thinking can be enhanced through mathematics by proposing a teaching framework that integrates critical thinking with mathematical inquiry in the context of ordinary differential equations (ODEs). A quasi-experimental mixed-methods design was employed with 98 students from one university, combining quantitative and qualitative data to investigate the effects of different instructional approaches on students’ critical thinking development and ODE learning. The findings showed that inquiry-based instruction supported students’ conceptual understanding of ODEs and significantly improved their critical thinking skills. However, instructional approaches that explicitly infused critical thinking into inquiry-based instruction were more effective than implicit inquiry approaches in improving students’ overall critical thinking and ODE achievement. In addition, students’ critical thinking performance was strongly positively correlated with their ODE achievement. Qualitative findings further suggested that explicit critical thinking instruction may help students transfer critical thinking to real-world problem solving and foster their critical thinking disposition.