1. Mathematical concepts and principles: Mathematical educators need to be familiar with various mathematical concepts and principles, including algebra, geometry, probability and statistics. They need to understand the definition, nature and application of these concepts so that they can be effectively taught to students.

2. Teaching methods and strategies: Mathematics educators need to master different teaching methods and strategies to meet the learning needs and ability levels of different students. They need to know how to guide students to think mathematically and solve problems, and how to design effective teaching activities and evaluation methods.

3. History and culture of mathematics: Mathematics educators need to understand the historical and cultural background of mathematics, so as to be able to link mathematics knowledge with practical application and stimulate students' interest and curiosity in mathematics.

4. Educational Psychology: Mathematics educators need to understand the basic principles of educational psychology, including learning theory, cognitive development, motivation and emotion. They need to understand students' learning characteristics and psychological needs in order to provide personalized teaching and support.

5. Technology application: With the development of science and technology, mathematics educators need to master some basic technology applications, such as using electronic whiteboards, teaching software and online resources. They need to know how to use technology to enhance the teaching effect and students' learning experience.

In short, mathematics educators need to have a solid foundation of mathematics knowledge and pedagogy, and at the same time, they need to constantly learn and update their knowledge and skills to adapt to the changing educational environment and students' needs.