On the Approaches to Enhance the Sustainability of Basic College Mathematics Course Teaching via Innovative Ability Training: A Fuzzy Set Perspective

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.