With the rapid development of internet technology, online education has become an important trend in the education industry. Especially under the influence of the global COVID-19 epidemic, online teaching has been widely applied and promoted. However, there are also some problems with online teaching, such as a lack of realism and low student engagement. Therefore, exploring the integration of online and offline teaching models has become a hot research topic in the field of education. This article will analyze the reform strategy of integrating online and offline teaching in university mathematics courses, aiming to explore how to improve the teaching effectiveness of university mathematics courses and promote students' learning interest and ability through the integration of online and offline teaching.

The six core competencies of mathematics in vocational schools are becoming increasingly important in mathematics learning. The reverse teaching design of vocational school mathematics, which focuses on core competencies, precisely grasps the internal logic of knowledge from a holistic perspective, and designs it on a unit by unit basis. The design process is to infer the starting point from the endpoint. Therefore, how to use reverse thinking in teaching design research in vocational school mathematics teaching under the background of core competencies will be the main content of this article.