2 Mathematical knowledge as a discipline. How much math knowledge a professional math teacher needs is a difficult question to answer. But obviously, a professional math teacher 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 mathematical knowledge he teaches from a high angle, know the essential relationship and context between them, and have the ability to transform mathematical knowledge into educational mathematical knowledge. Teach mathematics knowledge to students in the most convenient and rigorous form. 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 education psychology. Mathematics teachers not only master general pedagogy and psychology, but also combine them with mathematics. From the initial mathematics teaching method to the current mathematics education research, mathematics pedagogy has become a relatively mature discipline in China, while mathematics educational psychology is a relatively new discipline. In the past, I only cared about teaching and ignored students' psychology. Although some experience has been summarized, the research on students' learning psychology has not yet risen to the theoretical level, so it cannot be better developed and applied. More and more studies show that only by clearly understanding students' learning psychology can students better master mathematical knowledge and develop their mathematical ability.
4. Mathematics education technology. Mathematics education technology is listed as a separate item because previous researchers rarely mentioned teachers' technical knowledge. More importantly, the rising information technology directly affects the question of 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 and mathematics well.
In addition to the above professional knowledge, math teachers should also have general cultural knowledge. Besides, as far as knowledge is concerned, teachers' ability is more important. Because teachers are faced with dynamic people, educational practice and educational scenes have the characteristics of life, and there are no fixed models and skills to apply. Teachers must make creative independent judgments and choices on flexible teaching scenarios according to their own professional knowledge, which requires the comprehensive ability of mathematics teachers.
Third, how can math teachers better realize their professional development?
For a long time, researchers have devoted themselves 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 workers, research practitioners and reflective practitioners. The "skilled worker" paradigm holds that teaching is closely related to medicine and engineering. 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. It also advocates unified teaching standards, and teachers can only follow them and have no right to develop their own courses. At present, "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 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 situation 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:
(A) Mathematics teachers should become researchers.
Because of the uncertainty of teaching situation, mathematics teachers should be not only practitioners, but also researchers. He should "think before moving" and "promote thinking with action" to realize professional development in research practice. Steinhaus believes that "the teacher is the person in charge of the classroom. From the experimentalist's point of view, the classroom is only an ideal laboratory for testing teaching theory. No matter from what angle, everyone has 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, etc. Are they all good teaching methods summarized by front-line teachers? In addition, math teachers should also do research on mathematics. The best teachers are those who have done math research. By studying the process of empirical discovery, we can deepen our understanding of mathematical thinking methods, establish a better mathematical knowledge system, discover some common connections behind mathematical knowledge, and also give new solutions to some famous problems and discover and prove some new propositions. 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, obtained a new idea of solving geometric problems by area method through studying plane geometry, and applied it to machine proof, which achieved great success.
(B) 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, teachers should reflect on practice". He criticized education simply by teaching students to follow 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 contents, 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 of theory and practice. The movement of combining experts with teachers. Mathematics teachers should take the curriculum reform as the master and reflect on the concept of curriculum reform. The new curriculum standard puts forward many new ideas in view of the disadvantages of previous mathematics teaching, such as "students' mathematics learning content should be realistic, interesting and challenging" and "let students explore independently". Although these new ideas are undoubtedly a good medicine for the disadvantages of traditional teaching, teachers must grasp a "degree" in specific teaching. If every class is introduced into teaching through real situations, fragmentary mathematics knowledge is submerged in a large number of life examples, or only students' guessing ability is cultivated, while slightly complicated proofs are ignored, our mathematics class will lose the meaning of mathematics itself, and students will learn something else instead of mathematics. Only through practical reflection can math teachers grasp this "degree". In order to truly and comprehensively develop students' mathematical ability, 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 is something wrong with the newly compiled textbooks themselves. Only through the practice and reflection of math teachers can we draw a good conclusion. Only teachers really participate in the curriculum reform, not only focusing on books, but also reflecting on the curriculum reform through practice.
(C) the construction of mathematics teachers * * * the same body
Besides my own teaching experience and reflection, daily communication with colleagues is also an important source of professional knowledge for math teachers. Therefore, it is also a necessary condition for teachers' professionalization to establish the identity of mathematics teachers. The establishment of * * * identity of mathematics teachers makes up for the shortage of "self-employment" and helps to expand the consciousness of critical self-reflection. All math teachers in a grade, a school and a region should form their own math teachers. There should be better exchanges and cooperation to form a good professional and technical culture. Teachers should have more discussions about professional practice. We should create conditions to establish the same team of math teachers. For example, we should strengthen the plan of bringing the old with the new, all math teachers work in the same office and hold seminars for math teachers in schools or regions on a regular basis. Only in this way can teachers jump out of their narrow space and achieve better professional development.
(D) 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 on-the-job education system for teachers, it obviously can't keep up with the requirements of the times. Mainly reflected in the following aspects: attaching importance to academic qualifications while ignoring the cultivation of knowledge and ability, and unilaterally pursuing teachers' high academic qualifications makes the on-the-job education of mathematics teachers 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 are actually ten years ago, and the teaching method is still a single teaching method. It is obviously inappropriate to advocate autonomous learning and cooperative learning today. 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 math teachers, we think we should pay attention to the following points:
(1) Transform 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 a word, on-the-job training is not only the obligation of math teachers, but also their right. Only by doing a good job in-service training for math teachers can their professional development be better realized.
To sum up, in order to realize the specialization of mathematics teachers and strengthen their professional development, teachers themselves must actively study, be diligent in reflection, be willing to communicate and be good at learning. Only in this way can our math teachers change from "teachers" to professional teachers. Only in this way can our current curriculum reform not become a mere formality, and only in this way can our math education make a qualitative leap.