Teachers' Beliefs and Instructional Implementation of Mathematical Problem Solving Within Project-Based Learning

In China's latest mathematics curriculum, project-based learning (PBL) foregrounds mathematical problem solving (MPS) as student-led inquiry in authentic contexts. This study examines teachers' beliefs about MPS within PBL, and how such beliefs are enacted in planning and teaching. Using a constant comparative approach, we drew on interviews, lesson plans, and reflective accounts from 14 mathematics teachers. Most teachers emphasised application and creativity, positioning themselves as guides/supporters who facilitate students' exploration. Consistent with these beliefs, lesson plans commonly drew on personally and socially grounded contexts and featured challenging, open-ended tasks attending to cognitive breadth and depth. While espoused beliefs largely aligned with described implementation, a minority endorsed procedure-focused instruction, revealing tensions between exploration- and content-oriented approaches. Examining teachers' beliefs can inform understanding of progress in curriculum reform. Sustained, long-term professional learning-supported by institutional resources and professional autonomy-is needed to help teachers navigate these tensions.