Journal of Higher Education Research

Linear Algebra is a foundational course for science, engineering, economics, computer science, and data-related majors. However, in many classrooms it is still taught mainly through definitions, theorems, and mechanical calculation, which may weaken students’ understanding of its social value and humanistic significance. In the context of China’s curriculum-based ideological and political education, this paper explores how ideological and political elements can be naturally integrated into Linear Algebra through case-based teaching design. Based on constructive alignment, situated learning, and active learning theory, the study proposes a teaching case design framework consisting of “mathematical knowledge, application scenario, value implication, learning activity, and assessment evidence.” Three sample cases are discussed: matrix representation and national infrastructure planning, linear systems and scientific decision-making, and eigenvalues/eigenvectors and technological innovation. The paper argues that ideological and political education in Linear Algebra should not be added mechanically, but should arise from the internal logic of mathematical knowledge, the history of scientific development, and real social applications. Such design can improve students’ mathematical competence, social responsibility, scientific spirit, and confidence in applying mathematics to national and human development.