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.

Prefabricated decoration is an efficient construction mode in the current construction field, with the main purpose of quickly improving the efficiency and quality of decoration through the effective application of modular decoration technology. Therefore, there is a high demand for efficient prefabricated technical talents in various construction units or enterprises in the construction industry. How to cultivate efficient prefabricated technical talents is a problem that relevant professional teachers in universities must pay attention to at present. This paper mainly analyzes the research and practice of the training mode of prefabricated technical talents, summarizes the connotation of prefabricated building and the importance of prefabricated building talent training, analyzes the key points and requirements of prefabricated building teaching, summarizes the problems existing in the training process of prefabricated building talents and puts forward corresponding optimization countermeasures, so as to lay a solid foundation for the optimization of the training mode of prefabricated talents in the next stage and the promotion of talent training level.

Before the formal construction of a building, it is necessary to conduct an effective survey of the engineering geology, hydrogeology, and other contents within the construction area. The survey work is not only an important part of the early stage of engineering construction for engineering management personnel, but also an important factor in ensuring safety and stability during the construction process. Therefore, in order to effectively avoid various geological risks during the construction process or after the completion of the building, the preliminary engineering geological survey work is of great significance. In the process of engineering geological exploration, hydrogeological issues are also important exploration projects. This article will explore and study hydrogeological issues, analyze the water physical properties of rock and soil, and the impact of hydrogeological issues on the project, and then propose effective measures to do well in engineering geological exploration.

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.

As an important component of socialist culture with Chinese characteristics, excellent traditional culture is not only the "cradle" of cultural origin, but also the foundation of advanced socialist culture and ideological and political guidance for students. It is an indispensable part of socialist education. With the advent of the Internet era, it not only poses challenges to the ideological and political education of college students, but also provides opportunities for development. In the new era, by means of new ideas and new methods, integrating fine traditional culture into the course of "Chinese Traditional Flower Arrangement Art" can not only promote the effectiveness and attractiveness of the Chinese traditional flower arrangement art course, but also promote the students' ideological level and recognition of excellent traditional culture, and help students improve their cultural awareness and national self-confidence. Based on this, this article explores the strategy research of integrating cultural confidence into the course of "Traditional Chinese Flower Arrangement Art".

With the development of teaching reform, how to optimize funding and education activities from the perspective of "Great Ideological and Political Education" and improve accuracy has become a focus. From the analysis of the current teaching development situation, the guiding role of ideological and political education in funding precision education activities has been very obvious. To better enhance the effectiveness of funding education, actively optimize the precision of funding education, and innovate the way related activities are carried out, which is an inevitable choice for better education work. Based on this, this article mainly studies the precise methods of funding education under the perspective of "Great Ideological and Political Education", for reference only.