China is currently at a critical juncture in implementing the rural revitalization strategy, with urbanization and tourism development as crucial components. This study investigates 41 counties (cities) in the Wuling Mountain area of central China, constructing an evaluation system for the coordinated development of these two sectors. The coupling coordination degree is calculated using a combination weighting method and the coupling coordination degree model. Spatio-temporal evolution characteristics are analyzed through spatial autocorrelation, while the geographic detector explores the driving factors of spatial variation. The findings reveal a significant increase in coupling coordination between urbanization and tourism, transitioning towards a coordinated phase. Spatially, urbanization and tourism exhibit positive correlations, with high-value clusters in the southeast and northwest and low-value clusters in the south. The geographical detector identifies industrial factors as the most critical drivers of spatial variation. This study offers novel insights into the dynamics of urbanization and tourism, contributing to the broader literature by providing practical implications for regional planning and sustainable development. The results are relevant to the Wuling Mountain area and serve as a reference for similar regions globally. However, the study has certain limitations, such as regional specificity and data availability, which should be considered in the context of this research.

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.

With the rapid development of the Internet, it has penetrated into various fields, including music performance teaching. This paper aims to explore the application strategies of the "Internet Plus" teaching mode in the music performance major. Firstly, the problems of traditional music performance teaching and the advantages of Internet technology are analyzed. Then, the basic principles and application strategies of the "Internet Plus" teaching mode are proposed, including the construction of online teaching resources, interaction between teachers and students, and innovation of teaching evaluation. Finally, through case analysis, the application effect of the "Internet Plus" teaching mode in the music performance major is verified. The research results of this paper have certain reference value for the teaching reform and innovation of the music performance major.

Since the 20th National Congress, with the emphasis on innovation and entrepreneurship on country, innovation and entrepreneurship education has become an important part of talent training in universities. The constructivist learning concept advocates that students' learning should respect their own meaning construction, and social mutual assistance and situational construction to acquire knowledge. Based on the current issue of students' innovation and entrepreneurship, this article takes the constructivist learning perspective as a guide to explore strategies to enhance their innovation and entrepreneurship abilities, and is committed to promoting the improvement of their abilities.