Search

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

Author(s)

Yan Liang*

Affiliation(s)

School of Science, Guangdong University of Petrochemical Technology, Maoming, Guangdong, China *Corresponding Author.

Abstract

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.

Keywords

Problem-Based Learning; Linear Algebra; Concept of Determinant; Problem Chain; Teaching Design

References

[1] Yan L, Simin W. Teaching Principle and Instrutional Design Analyze in Linear Algebra Course Based on Problem-Based Learning. Curriculum and Teaching Methodology, 2020, 3(1): 53-60. [2] Chagwiza C, Mutambara L H N, Sunzuma G. Exploring Zimbabwean a-level Mathematics Learners’ Understanding of the Determinant Concept. European Journal of Mathematics and Science Education, 2021, 2(2): 85-100. [3] Dorier J L, Robert A, Robinet J, et al． The Obstacle of Formalism in Linear Algebra. On the Teaching of Linear Algebra. Springer Netherlands, 2000: 85-124． [4] Kuang J C. Mathematics Teaching Should Focus on the in-depth Understanding of Fundamental Concepts. Mathematical Bulletin, 2008(9): 17-20. [5] Yalin W, Xiaofeng F, Zhihui Z. Some Thoughts on Teaching of Matrix Rank. Studies in College Mathematics, 2024, 27(05): 44-47+63. [6] Halmos P R. The Heart of Mathematics. The American Mathematical Monthly, 1980, 87(7): 519-524. [7] Huibin Z. Problem-Driven Approach is One of the Effective Teaching Methods in Linear Algebra. Higher Mathematics Research, 2008(4): 91-94. [8] Efgivia M G, Rinanda R Y A, Hidayat A, et al. Analysis of Constructivism Learning Theory. 1st UMGESHIC International Seminar on Health, Social Science and Humanities (UMGESHIC-ISHSSH 2020). Atlantis Press, 2021: 208-212. [9] Eun B. The Zone of Proximal Development as an Overarching Concept: A Framework for Synthesizing Vygotsky’s Theories. Educational Philosophy and Theory, 2019, 51(1): 18-30. [10] Daulay K R, Ruhaimah I. Polya Theory to Improve Problem-Solving Skills. Journal of Physics: Conference Series. IOP Publishing, 2019, 1188(1): 012070. [11] Yan L. Research on the Four-Step Teaching Model of Objective-Problem-Oriented Teaching Method in Linear Algebra under the Context of "Four New Trends". Proceedings of the Seminar on Reform and Innovation in University Mathematics Teaching in the New Era, Beijing: Higher Education Press, May 2024: 61-66.