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.

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.

This research endeavors to assess the legal requirements for the operation of mediation and conciliation centers in the UAE based on Federal Law No. 17 of 2016 and its amendment in 2021 No. 5. It is structured into three main sections: the first establishes and defines these centers, the second defines conciliation procedures and the third considers the preceding. The aim is to identify the legal procedures associated with mediation and conciliation centers within the UAE judicial systems and their function in providing solutions for civil and business litigations with the most efficiency and minor financial investments. It also calls for using other forms of conflict adjudication before adopting the legal approach. The conclusions and recommendations indicate the necessity of further improving the Mediation and Conciliation Centers Law due to the necessity of legislative shifts, which would contribute to the UAE’s leading position in legislation related to centers for mediation and conciliation.

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.

Objective: To explore the influencing factors of mental health and the mediating role of self-compassion between family cohesion and mental health. Method: Family Cohesion Scale, Symptom Checklist, and Self-compassion Scale were used to investigate 593 college students in Zhejiang Province. Result: Family Cohesion was negatively correlated with mental health and positively correlated with Self-compass- ion among college students; Self-compassion was negatively correlated with mental health. Self-compassion fully mediates the relationship between the two. Conclusion: The path of family cohesion is indirect, and strengthening Self-compassion education can improve the mental health level of college students.

The article emphasizes the dynamism of social processes in the world aimed at humanizing modern society. Social work in the third millennium became one of the priority topics in Europe and acquired the status of an independent field of science and research in terms of science and education. The possibility of extrapolation of innovative foreign technologies into the practice of social work in Ukraine was investigated. It was found that the process of implementation of innovative foreign technologies into the practice of social work in Ukraine has already begun and is ongoing. In the improvement of the domestic system of professional training of social workers, the authors of the article see an appeal to the experience of applying European innovative technologies and practices of social work, in particular in the Republic of Poland. The leading determinants of social technologies, which determine their specificity, are singled out: multidisciplinarity, hierarchy, multidirectionality, flexibility, standardization. The need for effective and timely implementation of the integration of three groups of social support technologies in the conditions of the martial law in which Ukraine is today has been updated. The perspective of further scientific research is defined in the substantiation of the organizational and pedagogical conditions of their application in the process of informal and informal education.