Bridging Abstract Theory and Digital Reality: A Collaborative Filtering Teaching Case for Linear Algebra Instruction

This paper presents a linear algebra teaching case built around collaborative filtering recommendation systems, using familiar digital platforms such as Netflix, TikTok, and Taobao as motivating examples. The case is designed to help students connect abstract concepts in linear algebra, including user–item matrices, vector spaces, singular value decomposition, and matrix factorization, with a recognizable real-world application. The instructional design follows a sequence of phenomenon introduction, model construction, algorithm implementation, and reflection, intending to support students’ mathematical modeling and application abilities. The case was piloted with 120 students in four classes at the University of Science and Technology Liaoning, where an experimental group received case-based instruction and a control group received traditional lecture-based instruction. Post-course survey responses and post-test results suggested more positive learning outcomes in the experimental group, including higher mean post-test scores (86.7 vs. 78.2, p < 0.01). However, these findings should be interpreted cautiously because the evaluation was conducted at a single institution using a quasi-experimental design without random assignment or a pre-test. Overall, the study offers a practice-oriented example of how contemporary recommendation scenarios may be used to make foundational linear algebra content more accessible and relevant to students.