Taking Xinjiang Agricultural University as an example, based on Rain Classroom and Dingding platform, the linear algebra course changes the current situation of "emphasizing theory and ignoring application" in traditional mathematics classrooms, adding applied teaching cases with the background of industry and agriculture, using online and offline The blended teaching mode, through inquiry-based and case-based teaching methods and students' autonomous learning and discussion methods, develops from a teaching mode focusing on "teaching" to focusing on "learning". The teaching mode has been comprehensively reformed, and satisfactory results have been achieved.

The epidemic has had a great impact on people and improved students' awareness of paying attention to their own health. Through the investigation of higher vocational students, the author and the research team collected 4741 questionnaires for research and analysis, and analyzed the data in four aspects: the impact of the epidemic on sports concept and psychology, the impact of intelligent equipment on physical exercise, the purpose of sports activities and the selection of online teaching content, and the impact of gender differences. This paper puts forward some suggestions on the development of online teaching of physical education courses in higher vocational colleges.

This study aimed to analyze government policies in education during the Covid-19 pandemic and how teachers exercised discretion in dealing with limitations in policy implementation. This research work used the desk review method to obtain data on government policies in the field of education during the Covid-19 pandemic. In addition, interviews were conducted to determine the discretion taken in implementing the learning-from-home policy. There were three learning models during the pandemic: face-to-face learning in turns (shifts), online learning, and home visits. Online learning policies did not work well at the pandemic’s beginning due to limited infrastructure and human resources. To overcome various limitations, the government provided internet quota assistance and curriculum adjustments and improved online learning infrastructure. The discretion taken by the teachers in implementing the learning-from-home policy was very dependent on the student’s condition and the availability of the internet network. The practical implication of this research is that street-level bureaucrats need to pay attention to discretionary standards when deciding to provide satisfaction to the people they serve.

In the process of teaching and learning at any stage, the important role of interest guidance cannot be ignored. Especially in college mathematics teaching, mathematical knowledge is very complex and abstract, and most students are unable to effectively understand and master it during the learning process. So it is even more important to fully stimulate students' interest in learning. This article analyzes the significance and current situation of stimulating students' learning interest in university mathematics teaching, and conducts effective strategy analysis. In order to effectively awaken students' desire for knowledge, guide students to change from passive learning to active learning, so that students can continue to grow and progress in this process.

The "chain length system" is a breakthrough attempt made to adapt to the needs of industrial management under the new development pattern of dual circulation and its industrial policy form. The cultivation of cross-border e-commerce talents in vocational colleges has received much attention. Currently, there are still many problems in the construction and teaching mode of cross-border e-commerce courses in vocational colleges, which are highlighted as the disconnection between course offerings and industry needs, low practical value of course content, low professional literacy of graduates, and inability of graduates to handle practical work. Therefore, it is crucial to construct and innovate a golden course for the development of cross-border e-commerce careers in the new era, focus on strengthening and supplementing the cross-border e-commerce talent chain, and open up the "last mile" of the cross-border e-commerce talent chain, so as to  improve the specifications and quality of talent cultivation. Starting from the pain points and difficulties of industry enterprise demand, curriculum teaching patterns, characteristics, and main contradictions as breakthrough points, we will carry out the construction of golden courses, using "task driven", "module teaching", "project teaching", "project incubation", "achievement recognition", and "point exchange" throughout the entire teaching process, in order to enhance the core competitiveness of cross-border e-commerce talents and serve the chain leader system in the Guangdong Hong Kong Macao Greater Bay Area.

With the continuous development of educational information technology, college English teaching is gradually transitioning to digital and informational. This article discusses and researches the application of educational information technology, the impact of educational information technology on student learning outcomes, changes and reasons in learning methods, and the construction of college English teaching staff under educational information technology. It is believed that conducting effective research on college English teaching under educational information technology will not only help improve the level of college English teaching, but also promote the development of educational informationization.