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.

Vocational colleges should not only cultivate highly skilled talents, but also improve the comprehensive quality of students. The cultivation of students' comprehensive qualities cannot be separated from the efforts of schools, counselors, and every course teacher. Vocational education is different from undergraduate education, and finding a teaching model suitable for students in vocational colleges is particularly important. The integrated teaching model proposed in this article integrates theory and practice, and the entire teaching process is integrated into curriculum ideological and political education. In order to ensure teaching effectiveness, teachers participate and supervise the entire process, aiming to cultivate students' ability to unite and assist, solve problems, and express language skills, self-learning abilities, etc., so that students can truly become a comprehensive and high-quality talent.

This study applies the multiple streams theory. It will further analyze the internal factors of the confluence of multiple sources, in order to explain why the “Joint Recruitment of Four Universities in Macao” policy has become the agenda of the Macao government. The entrance examination requirements from Macau universities are various. They increase local students’ pressure and consume their energy, thus serving as the source of the Problem Stream. The Policy Stream is represented by the Macau government’s intention to reduce students’ educational burden through establishing a unified assessment system. The Political Stream includes the Macau government’s commitment to improving the Macau education system, such as strengthening the multi-assessment system and the “The Fundamental Law of Non-tertiary Education System”. The convergence of these three sources has opened a policy window for the “Joint Recruitment of Four Universities in Macao” system, leading to a new student evaluation system. This policy not only addresses Macau’s social challenges and improves education governance while also highlighting the city’s educational diversity endeavors. Additionally, the strategies for implementing the “Four-University Joint Examination” policy include reducing the number of exams for students, implementing multi-education and multi-enrollment in higher education institutions, analyzing and improving the examination system based on educational big data, and understanding the basic elements and integration paths of big data in higher education. The Macau government can adjust major settings and enrollment quota allocation in the future, draw in more students from the Community of Portuguese-Speaking Countries and the “Belt and Road” regions, and integrate the joint admission method into the Greater Bay Area education cooperation in order to meet the needs of the growing Macao education industry.

It is possible to provide green, ecological, and innovative products and services through green and sustainable public procurement. This study analyzes the opportunity offered to public contracting authorities in the Republic of Croatia (RH) in transformation from existing economy to a sustainable one through the inclusion of small and medium sized (SME) companies and inclusion of selection criteria that promote all three sustainable goals. The study employed a qualitative method and empirical analysis of public procurement procedures for eggs in the period from 2013 to 2021 in RH. The product was procured in many social institutions, hospitals, schools, student canteens and by procuring a sustainable product, added value could be created for the entire community. Data from the Electronic Public Procurement Classifieds of the Republic of Croatia (EOJN RH) and Data from the State and European Union (EU) Statistical Office were used. The research showed that sustainable procurement criteria were used for the first time in 2021, and that public contracting authorities put a stronger focus on the environmental pillar of sustainability and less or almost none on the economic and social pillar. The volume of demand and production was also calculated. The study found that the first contractor for sustainable product was SME company, producer of food, who adapted to the green conditions of public procurement in a short period of time. The paper empirically demonstrated that public procurement can be a powerful tool, but it was not used enough in the observed period for the observed products in RH.

This article explores a method for evaluating the achievement of learning effectiveness based on virtual reality technology. The research analyzed the design and construction of a virtual learning environment, data collection of learner behavior, data analysis and evaluation methods, evaluation indicators and personalized feedback, as well as a case study of a virtual learning evaluation system. By using virtual reality technology to create an immersive learning environment, learners can gain an immersive learning experience, and evaluators can accurately record learners' behavior and performance. The learning effectiveness evaluation method based on virtual reality technology can improve learning effectiveness and teaching quality, promote educational innovation and development. These research results are of great significance for the evaluation of virtual learning effectiveness and personalized teaching in the field of education.

This paper explores the influence of the concept of "moral education" on physical education, and focuses on the application of Teaching Personal and Social Responsibility (TPSR) responsibility teaching model in physical education. Physical education teaching is not only the teaching of skills, but also the indoctrination of values. Through the thought of "cultivating people by virtue", we can make physical education based on moral education and return to the essence of education. The TPSR model makes this idea concrete, emphasizes the personal process and social responsibility, and includes the cultivation of students' sense of responsibility, team spirit and self-management ability in physical education teaching. Through theoretical discussion and empirical analysis, this study revealed the practical application and effect of TPSR model in physical education teaching, proved the importance of this teaching model, and put forward the construction idea of TPSR physical education teaching model. Future research can expand more application scenarios of the TPSR model to achieve better quality and more comprehensive physical education.