Against the backdrop of education reform driven by artificial intelligence (AI), higher vocational mathematics teaching presents new characteristics such as digitalization, intellectualization, integration, and practicalization. However, the improvement of teachers’ corresponding teaching competence faces bottlenecks, including the lag in updating teaching concepts, superficial application of AI technology, insufficient curriculum adaptability, lack of ethical literacy, and weak support for teaching environments. To address these bottlenecks, this paper proposes breakthrough strategies: combining external support with internal incentives, integrating AI throughout the teaching process with precise teaching empowerment, combining competence-oriented development with literacy cultivation, combining risk identification with ethical construction, and combining technical support with teacher development. These strategies provide references for improving the teaching competence of mathematics teachers in higher vocational colleges and support for cultivating high-quality technical and skilled talents in the intelligent era.