(2) Teaching method is a basic method widely used in middle school mathematics teaching in various countries. Regardless of China or the United States, or other developed countries in the west, the teaching of mathematics knowledge is basically based on the teaching method, supplemented by other methods.
(3) generally attach importance to heuristic teaching. After the Second World War, all countries have carried out different degrees of teaching method reform, and middle school teaching is no exception. Through educational reform, all countries attach importance to how to improve students' quality and cultivate their ability, especially to the application of heuristic teaching thought in subject teaching. ①
From the reality of mathematics teaching in middle schools, there are differences between the teaching methods in China and those in western developed countries, mainly in the following aspects:
(1) Teachers and students have different relations and functions in the teaching process. Most of the teaching methods in China are teacher-centered, with a tendency of "emphasizing teaching over learning", and indoctrination teaching methods are often used in the teaching process. This is mainly caused by the long-term exam-oriented education in China. Although China's educational reform efforts are developing in the direction of quality education, due to the great influence of senior high school entrance examination and college entrance examination on students, most schools' education has consciously or unconsciously slipped into the tactics of asking questions and exam-oriented education. Although this teaching method is helpful for students to remember mathematical concepts and formulas, it has mastered deeper and more difficult mathematical knowledge to some extent. However, the disadvantages are obvious. It can't stimulate students' interest well, which restricts their learning initiative. The teaching methods in foreign countries, especially in developed countries, pay attention to the cultivation of students' self-study ability and explore students' curiosity; More heuristic teaching methods are adopted, and applied education is emphasized to encourage students' development. In the teaching process, students pay attention to voluntariness, enjoy full freedom of study, and learn more easily and happily.
The difference in the relationship between teachers and students in mathematics teaching also causes obvious differences in the teaching atmosphere. In developed countries, teachers and students are basically friends and can communicate freely. Teachers play an advisory and prompting role in the teaching process. In class, the teacher lets the students discuss purposefully, and students can come in and out freely. Sometimes teachers can even move their textbooks to the wild and study happily with the students in the bright sunshine and gentle breeze. This teaching method can promote students to use their brains actively, increase their happiness in learning mathematics, reduce their pressure and create a pleasant teaching atmosphere. However, China students have been in strict classroom management for a long time, emphasizing the classroom and their own seats, and teachers dare not let go. They are afraid that excessive relaxation will lead to chaotic scenes in the classroom, full of excitement and serious lack of freedom, because learning is not entertainment after all. At the same time, due to China's different traditional thinking and habits, there is an insurmountable "gap" between teachers and students under the influence of the serious thought of "respecting teachers and attaching importance to teaching". In the process of teaching, teachers are often too serious and students are too nervous. In addition, mathematics is different from liberal arts, and the story content is less, which makes students lose interest in learning, and students easily feel tired and slack, causing some students, especially poor students, to regard learning mathematics as a kind of "service".
(2) Pay attention to ability training and personality development. In developed countries, the cultivation of personality is emphasized and students are encouraged to develop freely, so the layered individual teaching method is adopted more. For example, they put forward non-school teaching method and computer program teaching method in the teaching reform (programming what they want to learn, so that students can face computer self-study). These methods emphasize self-study and teach students in accordance with their aptitude, which can better cultivate students' self-study ability and meet the learning needs of different students. However, this teaching method also has some disadvantages, such as making students seldom listen to the teacher's active explanation, and it is difficult to help and influence each other with their classmates; In addition, students seldom touch mathematics knowledge outside textbooks, which affects students' socialization. Most of the commonly used teaching methods in China are centralized teaching of "eating the same pot". Although this teaching method helps students to master knowledge systematically, it also helps teachers to make overall consideration and arrangement, and teachers can easily grasp the rhythm. However, it is easy to cause serious differentiation between top students and poor students, and the teaching is not targeted, which is not conducive to teaching students in accordance with their aptitude, and actually ignores the differences in personality.
In teaching mathematics as a foreign language, we should pay attention to students' understanding and communication. For example, some schools in the United States adopt the teaching diary method, in which students record their thinking process and psychological state in teaching, so that students and teachers can often talk through diaries. Teachers can easily understand the individual differences of students' cognitive level, knowledge and experience, hobbies, personal way of thinking and other non-intellectual factors. Teachers can synthesize the achievement ambition level, anxiety level and will level of various students from these materials, so as to design teaching plans and improve teaching level. In China, however, teachers attach too much importance to intellectual factors and relatively ignore non-intellectual factors. There is little communication between teachers and students, which naturally forms a gap. Teachers can't understand students' psychology, emotions, motives and interests, and they can't get feedback. Students' anxiety and communication needs can not be met in time. As a result, students' learning enthusiasm is not high. The teacher's teaching is blind ②
(3) There is a difference between cultivating students' mathematical consciousness and the concept of applied mathematics education. Foreign teaching methods generally focus on cultivating students' mathematical consciousness. Attaching importance to applied mathematics education is reflected in attaching importance to the connection between mathematics and daily life, and the examples used in mathematics come from real life as far as possible. For example, in Japanese crm teaching method (compound reality mathematics teaching method), some familiar things are selected in the teaching process, and the mathematical knowledge contained in them is discussed and explored, and finally a conclusion is drawn. This teaching method deepens students' understanding of mathematical knowledge, helps to cultivate their awareness of looking at problems and building mathematical models from a mathematical perspective, and cultivates their ability to solve practical problems by mathematical methods. After graduation, students can better adapt to the needs of society. Of course, too much contact will inevitably be far-fetched. Although China's educational goal theory attaches importance to applied education, there is no corresponding teaching method so far. In fact, it has become an armchair strategist, and it is still only based on the structure of mathematics itself to cultivate students' mathematical quality, resulting in a situation of high quality and low quality. On the other hand, the current education mode in China is very effective in cultivating students' problem-solving ability. Being good at solving problems is a prominent feature of China's teaching methods, which can be seen from the excellent achievements made in the Mathematical Olympics.
(4) There are differences between teaching tools and teaching media. Due to the development of foreign economy and technology, intuitive teaching methods have been greatly improved, and computer-aided teaching and various teaching media have been widely used. With the educational reform in China, China is also trying to improve its teaching methods, such as multimedia teaching. However, due to economic, scientific and technical reasons, the popularity of multimedia is far from being realized in the near future. ③