The Lancaster mutual teaching model originated in late 18th century England and quickly spread to the American colonies after receiving positive responses in Europe. In the 1820s, renowned Spanish physician, educator, and publisher Manuel Codorniú Ferreras brought it to Mexico, making outstanding contributions to the newly independent nation in educational philosophy, system, and methods. In the mid-19th century, with the absence of a centralized institution for public education in Mexico, the Lancaster Company took on the significant responsibility of guiding the direction of national public education development. Although this function did not persist for too long due to political changes in Mexico, the educational system continued to play an important role in the Mexican education sector. The Lancaster Company and its teaching system exerted a positive and profound influence on the democratization and secularization of education in Mexico, laying important foundations for the modernization and reform of Mexican education.

With the rapid development of China’s economy and society, the reform of talent training mode for business administration has become the most concerned and valued issue in the current teaching work in colleges and universities. From the current situation of undergraduate education curriculum system construction in vocational colleges, the traditional teaching methods of higher English still occupy the majority. The all English bilingual course for the undergraduate major of business administration takes the basic knowledge of language and the theory of natural science as the core content. Therefore, this paper will focus on how to build a perfect talent training mode for business administration majors that meets the actual needs and employment direction of students, and put forward specific teaching strategies in order to provide more application-oriented and professional development platforms for business administration students.

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.

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 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.

The current with the rapid development of Internet and new media technology, the information openness and diversity makes ideological education is facing big challenge, in accordance with the "five a three-ring four law" teaching mode,the fundamental task of implementing ideological and political education, fostering values and cultivating talents is comprehensively carried out. We are advancing the resonance of the “three classrooms” and promoting the synchronous implementation of the “four transformations”, aiming to enhance the “five capacities” of students, according to the current construction of" big education courses "concept, change education thought and idea.