In-service teachers’ perceptions of problems in mathematics instruction when using a problem-based learning model

Abstract

Although Problem-Based Learning (PBL) is mandated in Indonesian curricula to promote critical thinking and higher-order reasoning, persistent questions remain about how teachers implement it in mathematics classrooms. This study investigated in-service mathematics teachers' perceptions and enactment of problems within PBL, specifically examining what types of problems teachers design and how they facilitate them. Using a descriptive qualitative approach, 333 in-service mathematics teachers enrolled in a national certification program submitted lesson modules, which were analyzed using a validated Problem Classification Rubric assessing five dimensions: context, cognitive demand, solution process, real-life relevance, and student engagement. Classroom observations of a subset of lessons were also conducted to document facilitation practices. The analysis revealed three predominant problem categories: routine problems (recall-based), algorithmic problems (artificial contexts with procedural solutions), and constructive problems (open-ended, concept-generative). Approximately 85% of teachers designed routine or algorithmic problems, while only 15% created constructive problems. Facilitation styles varied significantly by problem type: routine and algorithmic problem lessons featured directive, answer-focused teaching, whereas constructive problem lessons exhibited facilitative discourse and student inquiry. The findings indicate that the implementation gap stems not from lack of teacher effort but from incomplete understanding of what distinguishes a genuine problem from a procedural exercise. The study recommends targeted professional development on problem design, curriculum policy support through problem exemplars, and further research on how different problem types of impact student learning outcomes.