Fostering Higher-order Thinking in Advanced Mathematics: A Problem-driven Approach Using Knowledge Graphs

This study explores the integration of knowledge graphs as pedagogical tools in advanced mathematics courses at the university level. Through a quasi-experimental design involving 247 undergraduate students across two academic terms, we investigated whether a problem-driven approach complemented by knowledge graph construction improves higher-order thinking skills. Results indicate statistically significant improvements in analysis (d = 0.82), evaluation (d = 0.67), and creation (d = 0.74) dimensions of Bloom's taxonomy. Students in the intervention group demonstrated superior performance in complex problem-solving tasks and showed greater ability to draw connections across mathematical concepts. Qualitative analysis of student reflections and knowledge graphs revealed deeper conceptual understanding and enhanced metacognitive awareness. These findings suggest that knowledge graph-supported instruction offers a promising framework for developing mathematical thinking beyond procedural fluency.