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

In advanced mathematics education, compartmentalized knowledge acquisition and inadequate development of higher-order thinking skills remain persistent challenges. This study introduces a problem-driven teaching model that incorporates knowledge graphs as a cognitive framework to facilitate inquiry-based learning. Focusing on "Multivariable Differential Calculus" and "Curve Integrals" as key units, we designed teaching cases to help undergraduate students in computer science actively build and integrate knowledge through problem-solving. A quasi-experimental comparative study was conducted over one semester with 120 second-year students (60 in the experimental class using the model and 60 in the control class using traditional lectures). Higher-order thinking skills, such as analysis, synthesis, and transfer, were measured through a unified comprehensive test, including a basic knowledge section (60 points) and a higher-order thinking section (40 points). Results showed that the experimental class significantly outperformed the control class in both structured knowledge mastery and higher-order thinking development (p < 0.05). These findings offer empirical evidence and practical guidance for reforming advanced mathematics teaching and fostering innovative talent.