In teaching practice, mathematics is the foundation of science and technology. In the information society, mathematics contributes to business, finance, health and national defense, opens the door to students' career and enables people to make wise decisions. We need mathematical thinking more than ever before. The cultivation of mathematical ability focuses on mathematical education. From the new mathematical movement to problem solving, from popular mathematics to the sudden emergence of mathematics curriculum reform in many countries, people have been committed to better cultivating students' mathematical ability. However, the existing school reform movement ignores the obvious point that what teachers know and what they can do is very important for students to learn. In addition to advanced ideas as a guide, the key to the reform of mathematics curriculum lies in teachers. Teachers are concrete executors. If teachers do not actively participate in curriculum reform, or just appreciate new ideas without taking practical actions, reform will only be a beautiful light ring. Therefore, building a team of high-quality mathematics teachers is the key to the reform of mathematics education and the key to revitalizing mathematics education and cultivating mathematics talents. The specialization of mathematics teachers is the common trend of the development of mathematics teachers in all countries. 1980 The World Education Yearbook with the theme of teachers' professional development points out that teachers' professionalization has two goals. One is to regard teachers as a stratum in social stratification. Therefore, the goal of teacher professionalization is to strive for professional status and rights, and strive for collective upward mobility. The second goal is to improve teachers' teaching level and expand the development direction of personal knowledge and skills. From the second goal, the specialization of mathematics teachers can be regarded as the professional development of mathematics teachers. There are many articles in this field, but most of them focus on the teaching reform in normal universities. But on the whole, math teachers (young or old) think that their pre-service training is not the most important source of their teaching and knowledge, and their teaching knowledge mainly comes from their own work experience or reflection and daily communication with colleagues. This not only shows the importance of the reform of normal universities, but also shows that we should pay more attention to the professional development of teachers after leaving their posts. In addition, the specialization of a profession is not only an understanding, but also a process of struggle, that is, the recognition of professional qualifications, and a conscious pursuit of lifelong learning and continuous renewal. From this aspect, we should pay more attention to the professional development of math teachers after leaving their posts. Second, the professional knowledge and ability of math teachers. Obviously, the professional development of mathematics teachers must first determine what knowledge and ability a professional mathematics teacher needs. At the international conference on mathematics education held in 1992, Lapan and West Lubinschy emphasized that mathematics teachers need at least three kinds of knowledge, namely mathematics, mathematics pedagogy and students, in order to carry out effective teaching, and pointed out that it is the interaction of different aspects of thinking that makes mathematics teachers form rational teaching reasoning. Today, mathematics education has become a relatively independent subject to a certain extent, and quite a few people are engaged in mathematics education research. We think it is necessary to discuss the intersection of these three kinds of knowledge more clearly. Specifically, we believe that a professional math teacher should have at least the following knowledge. 2 Mathematical knowledge as a discipline. How much math knowledge a professional math teacher needs is a difficult question to answer. But obviously, professional math teachers should need a well-supplied and well-organized math knowledge warehouse, in which good organization is more important than math knowledge. He should be able to examine the mathematics knowledge he teaches from a high angle, know the essential connection and context between them, and have the ability to transform mathematics knowledge into educational mathematics knowledge, and impart mathematics knowledge to students in the form that is most convenient for students to understand without losing rigor. Academician Zhang Jingzhong believes that it is not only a problem of education, but also a problem of mathematics to transform mathematical knowledge into educational mathematics. Mathematics pedagogy and mathematics educational psychology. Mathematics teachers master not only general pedagogy and psychology, but also their integration with mathematics. From the initial mathematics teaching method to the present mathematics education research, mathematics pedagogy has become a relatively mature subject in China. Mathematics educational psychology is a relatively new subject. In the past, I only cared about teaching and ignored students' learning psychology. Although we have summarized some experiences, the research on students' learning psychology has not risen to the theoretical level and has not been better developed and applied. More and more research shows that only by clearly understanding students' psychology of learning mathematics can students better master mathematical knowledge and develop mathematical ability. 4 mathematics education technology. Mathematics education technology is listed as a separate item because previous researchers rarely mention teachers' technical knowledge. More importantly, the rising information technology has directly affected what to teach and how to teach. According to the survey of mathematics teachers in China, only 27. 2% teachers often use computer-assisted teaching. A professional mathematics teacher can not only skillfully use information technology in teaching, but also integrate information technology with mathematics well, and can teach students to discover and create mathematics by using technology. In addition to the above professional knowledge, math teachers should also have general cultural knowledge. In addition, the teacher's ability is more important for knowledge. Because teachers face active people. Educational practice and educational situation are innate, and there is no fixed model and skill to apply. Teachers must creatively make their own judgments and choices about flexible teaching situations according to their professional knowledge. This requires the comprehensive ability of mathematics teachers. For a long time, researchers have been committed to the research of teachers' professional development paradigm. Different professional paradigms reflect different directions and goals of teachers' professional development. Specifically, there are three paradigms: technical proficiency paradigm, research practitioner paradigm and reflection practitioner paradigm. The skill technician paradigm holds that teaching is close to medicine and engineering, and its professional attribute lies in the maturity and experience effect of scientific knowledge and technology in its practical field. It believes that the characteristics of expert teachers can be passed on to ordinary teachers, so that they can get professional development and become excellent teachers. And advocate a unified teaching standard, which teachers can only follow and have no right to develop their own courses. At present, the technical proficiency paradigm plays a leading role in the professional development of mathematics teachers in China. However, relevant research at home and abroad shows that teachers' own teaching experience and reflection are the most important sources of teachers' professional development, rather than the guidance and training of experts and excellent teachers. The knowledge of expert teachers is mostly personal and tacit knowledge, which cannot be formally and well passed on to others. This kind of silence can only be formed by the subject in dealing with complex and uncertain educational situations. On the other hand, teachers are always in a generative and temporary state. The educational scene is complex and changeable, full of uncertainty and chaos. Although a math teacher must have some necessary skills, the teacher's educational ability is more important. Therefore, the professional development of mathematics teachers must undergo a paradigm shift. Specifically, we should pay attention to the following points: (1) Mathematics teachers should become researchers. Because of the uncertainty of teaching situation, mathematics teachers should be not only practitioners, but also researchers. Thought should precede action, and action should promote thought. Realize professional development in research practice. Steinhaus believes that the teacher is the person in charge of the classroom, and from the experimentalist's point of view, the classroom is only an ideal laboratory to test the teaching theory. No matter what angle we understand educational research, we have to admit that teachers are full of rich research opportunities. Professional mathematics teachers should not regard the classroom as a low-level exercise, but should organize their own classroom into a big exploration, independently carry out some mathematics education reform experiments, and strive to explore new, efficient and low-consumption mathematics teaching methods aimed at quality education. Qingpu teaching experience, MM teaching method and so on are all good teaching methods summarized by front-line teachers. In addition, math teachers should also carry out math research. The best teachers are those who are a bit like those who are engaged in mathematical research. By studying the process of experience discovery, we can deepen our understanding of mathematical thinking methods, establish a better mathematical knowledge system, discover some common connections behind mathematical knowledge, give new answers to some famous questions, discover and prove some new propositions, and put forward some new conjectures and propositions. Elementary mathematics should be a good research direction for middle school mathematics teachers. Academician Zhang Jingzhong, when teaching in middle school, put forward a new idea of solving geometric problems with area method by studying plane geometry, and applied it to machine proof, which achieved great success. (2) Mathematics teachers should be practitioners of reflection. Mathematics teachers should be not only researchers, but also practitioners of reflection. Dewey believes that teachers should question teaching appropriately, instead of jumping from one teaching method to another uncritically, and teachers should reflect on practice. He criticized that education is just teaching students to adapt to the status quo. We believe that as a professional mathematics teacher, we should not only have classroom teaching knowledge, skills and techniques, but also reflect on our own belief system, teaching methods, teaching content, mathematics knowledge system and background factors, so as to keep ourselves under more rational control and always maintain a dynamic, open and sustainable development state. As a reflective math teacher, it is particularly important in today's new curriculum reform. We believe that the new curriculum reform is not a top-down expert movement, but a movement combining theory with practice and experts with teachers. Mathematics teachers should take the curriculum reform as the master and reflect on the concept of curriculum reform. In the new curriculum standard, many new ideas are put forward to overcome the shortcomings in the past mathematics teaching, such as that students' mathematics learning content should be realistic, interesting and challenging, so that students can explore independently and so on. Although these new ideas are undoubtedly a good medicine for the disadvantages of traditional teaching. However, in specific teaching, teachers must grasp a degree. If every lesson is introduced into teaching through real situations, fragmentary mathematical knowledge is submerged in a large number of life examples, or students only pay attention to the cultivation of their own guessing ability and ignore the slightly complicated proof, our mathematics class will lose the meaning of mathematics itself, and students will learn something else instead of mathematics. Only through practical reflection can mathematics teachers grasp this degree and truly develop students' mathematical ability in an all-round way. We should reflect on the newly compiled textbooks. Many teachers complain about the newly compiled textbooks. Perhaps some teachers are at a loss in the face of suddenly changed textbooks, or there are problems with the newly compiled textbooks themselves. Only through the practice and reflection of math teachers can we draw a good conclusion. Only when teachers really participate in the curriculum reform, instead of focusing on books, can they make an objective evaluation of the curriculum reform through practical reflection, the new curriculum reform can be successful, and the mathematics education in China can flourish. (3) The construction of mathematics teacher's identity comes not only from his own teaching experience and reflection, but also from his daily communication with colleagues, which is also an important source of mathematics teacher's professional knowledge. Therefore, the establishment of the same group of mathematics teachers is also a necessary condition for teachers' professionalization. The establishment of the * * * identity of mathematics teachers makes up for the lack of self-employment and helps to expand the consciousness of critical self-reflection. Mathematics teachers in a grade, a school and a region should form their own mathematics teachers, have better exchanges and cooperation, and form a good professional and technical culture. There should be more discussion about professional practice among teachers. We should create conditions for establishing isomorphism of mathematics teachers. For example, strengthen the planning of new teachers, all math teachers work in the same office, and hold regular seminars for math teachers in schools or regions. Only in this way can teachers jump out of their narrow space and achieve better professional development. (4) Pay attention to the after-service education of math teachers. Although the professional knowledge of mathematics teachers mainly comes from their own experience and reflection, the on-the-job training of mathematics teachers can not be ignored. Although China has a complete after-service education system for teachers, it obviously can't keep up with the requirements of the times. Mainly reflected in: attaching importance to academic qualifications while ignoring the cultivation of knowledge and ability, and unilaterally pursuing teachers' academic qualifications, so that the after-service education of mathematics teachers has become academic education. Most teachers think that this kind of education is only for a diploma, which has no practical significance and is a practice of putting the cart before the horse; The curriculum and teaching methods of post-service education lag behind, and the curriculum of post-service education still follows the past practice of emphasizing theory but neglecting practice. Many textbooks were actually ten years ago. There is still only a single teaching method. Today, when autonomous learning and cooperative learning are advocated, this is obviously inappropriate. Only teachers who have experienced autonomous learning and cooperative learning can make better use of it in their own classrooms; The training time is short, and the current teacher training takes up teachers' vacation time, and the training is only a few days. We believe that every teacher can study full-time for half a year after several years of teaching practice, so as to study systematically. For the training of mathematics teachers, we think we should pay attention to the following points: (1) Transforming academic education into knowledge and ability education; (2) The training of mathematics knowledge should not be the repetition of university knowledge, but should be closely related to middle school knowledge, which comes from middle school mathematics knowledge and is higher than middle school mathematics knowledge; (3) Training must be based on personal practical experience, so as to arouse teachers' enthusiasm and let trainers turn theoretical knowledge into practical experience, otherwise it can only be a flower in the mist and a moon in the water; (4) Strengthen modern technical training. In short, on-the-job training is not only the obligation of mathematics teachers, but also the right of mathematics teachers. Only by doing a good job in-service training for math teachers can we better realize professional development.