Problem posing in university mathematics education: A study informed by deep learning theory

Abstract

Problem posing is increasingly recognized as a key instructional strategy for promoting deep learning in college mathematics education; however, its effective implementation largely depends on teachers’ pedagogical understanding and classroom practices. This study adopts a mixed-methods approach to examine university mathematics teachers’ understanding of deep learning and whether their classroom questioning aligns with deep learning principles. Quantitative data were collected through questionnaires administered to 102 mathematics teachers, while qualitative data were obtained from classroom observations of three advanced mathematics courses and semi-structured interviews with four teachers. The findings indicate that although teachers generally value positive teacher–student relationships and diversified learning forms, their understanding of deep learning remains limited, particularly with regard to critical thinking and meta-cognitive development. Classroom observations show that reasoning-based questions dominate instructional practice, whereas critical, creative, and modeling-oriented questions are relatively scarce. In addition, teachers mainly rely on direct questioning and evaluative feedback, with limited use of dialogic, inquiry-based, or scaffolded questioning to support deeper exploration. Interview data further reveal that teachers’ questioning practices are largely influenced by textbooks and examination requirements rather than being consciously guided by deep learning theories. In response, this study proposes a professional development framework integrating theoretical learning, contextualized problem design, progressive questioning sequences, student exploration support, and diversified feedback strategies. Overall, the findings reveal a gap between deep learning theory and classroom practice in college mathematics teaching and provide practical guidance for fostering students’ conceptual understanding, creativity, and reflective thinking.