This paper aims to explore the practice and effect of integrating ideological and politics in higher vocational mathematics education. Through the review of relevant literature and the analysis of practical cases, this study analyzes the necessity and feasibility of integrating ideological and political education into higher vocational mathematics teaching, as well as the promoting effect of students' ideological and political education. At the same time, it also discusses how to effectively combine the curriculum thinking and politics with higher vocational mathematics teaching, as well as the strategies and methods to achieve positive results, in order to provide some reference for the majority of higher vocational mathematics teachers.

With the development of globalization, the importance of multiculturalism in university English education is becoming more and more prominent. This paper discusses the problems related to the teaching innovation of university English education from the perspective of multiculturalism. Firstly, it introduces the concept and significance of multicultural education and emphasizes its importance to university English education. Secondly, it analyzes the problems existing in the current university English teaching, such as cultural prejudice and language barrier. Then, innovative strategies for multicultural teaching are proposed, including teacher training, textbook design, teaching activities and so on. Finally, the evaluation and future development of multicultural education are prospected.

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.