In the Basic College Mathematics Course (BCMC) teaching, the contents are generally based on two-valued logic; however, fuzziness is commonly presented in real life. This leads to the insufficient cultivation of students’ innovative abilities, which constrains the expansion of students’ scientific thinking boundaries and, furthermore, the sustainability of course teaching. First, from the perspective of continuous effectiveness of course content in students’ subsequent learning and research, the connotation of sustainability of BCMC teaching was discussed. Then, based on the analysis of the basic methods of fuzzy sets, their role in cultivating students’ innovative abilities was explored. Next, focused on the three common BCMCs, namely, advanced mathematics, probability theory and mathematical statistics, and linear algebra, the specific teaching concepts and ideas were designed by integrating the fuzzy set methods. Finally, the exploratory teaching mode and approaches of integrating fuzzy set ideas into BCMCs were proposed. The proposed teaching approach helps to extend learners’ thinking boundaries, thereby providing support for cultivating students’ innovation ability and enhancing the sustained effects of course teaching. This study can also provide references for other course teaching.

Under the dual carbon strategy and the sweeping tide of digital transformation in education, higher education confronts an urgent imperative: cultivating talent equipped with interdisciplinary skills and sustainable decision-making capabilities. To meet this critical challenge, this study pioneers the PAMD (Patient Capital–Accounting–Matrix–Development) interdisciplinary teaching framework. Rooted firmly in Education for Sustainable Development (ESD) principles, PAMD uniquely weaves together patient capital, carbon asset accounting, and linear algebra matrix modeling. Utilizing a quasi-experimental design with undergraduate business students, we implemented “Carbon Asset Accounting and Low-Carbon Transition Investment Analysis” as a case study. We rigorously evaluated teaching effectiveness across academic performance, competency, and cognitive attitude dimensions using Welch’s t-test, Hedges’ g, and ANCOVA. After controlling for baseline scores, the experimental group significantly surpassed the control group in comprehensive decision-making (81.22 vs. 72.41, g = 0.71) and matrix modeling competency (3.74 vs. 3.22, g = 0.77). The experimental cohort also demonstrated consistent gains in carbon accounting reporting precision and data representation clarity. Cognitive assessments revealed moderate effect sizes for both low-carbon investment literacy and interdisciplinary learning interest. These compelling results demonstrate that embedding a long-term value orientation into accounting representation and matrix modeling powerfully cultivates students’ ability to transfer interdisciplinary knowledge and make sound sustainable decisions within complex contexts. This study offers a robust, evidence-based, and replicable pathway for driving sustainability-oriented interdisciplinary reform within business education.

Interdisciplinary teaching is a pivotal strategy for deepening disciplinary theory and broadening students’ cognitive boundaries, crucial for the sustainability of education. By considering scientific knowledge’s humanistic background and technological evolution, this study proposes a novel interdisciplinary teaching framework based on the Source–Knowledge–Use (SKU) paradigm. Then, taking fuzzy mathematics as a case, the Humanities–Science–Technology Model (HSTM), based on a tripartite progression from humanistic foundations to scientific principles and then to technological applications, was established. This study systematically expounds the HSTM’s framework, contents, and implementation design, while critically examining potential challenges and corresponding mitigation strategies. The proposed SKU-based interdisciplinary teaching framework not only provides methodological guidance for interdisciplinary instruction in fuzzy mathematics but also offers transferable insights for cognate disciplines seeking to implement sustainable educational practices.