An Analysis of Teaching the Determinant Concept Using a ‘Problem Chain’ Approach Based on Problem-Based Learning

The teaching of linear algebra is challenging since its abstractness. This paper analyses the design of a "problem chain" teaching model based on problem-based learning for teaching the determinant concept in linear algebra. Through a step-by-step sequence of problems, students are guided from solving linear equation systems to understanding the definition, properties, and applications of determinants, enabling a deeper comprehension of the core concept in linear algebra from both algebraic and geometric perspectives. According to the theoretical foundation analyse, the problem chain teaching model focuses on student-centered learning, emphasizing active knowledge construction and inquiry. Using the determinant concept as an example, this paper demonstrates the design method and implementation of the problem chain model, providing theoretical and practical references for teaching reform in linear algebra and other mathematics courses.