First, strengthen the teaching of thinking methods, teach students to guess and cultivate innovative ability.
Mathematical thinking method is the soul, essence and core of mathematics. It is a means for students to acquire knowledge, a link connecting all kinds of knowledge and a bridge from knowledge to ability. It is more general and abstract than knowledge. When students master mathematical thinking methods, they can acquire knowledge faster, understand knowledge more thoroughly and benefit for life. The thinking methods involved in middle school mathematics can be roughly divided into three types: technical (such as special, general, elimination, substitution, reduction, formula, undetermined coefficient method, etc. ), logical type (such as analogy, induction, analysis, synthesis, deduction, reduction to absurdity, etc. ), macro type (such as function and equation, classification discussion, combination of numbers and shapes, induction and conjecture, integration and reduction).
Modern educational scientific research theory points out that education should raise practical experience to a theoretical level, further guide practice, and make students consciously and actively use thinking methods to solve mathematical problems. The content of the college entrance examination reform also emphasizes: paying more attention to the examination of ability, on this basis, examining the innovative ability and practical ability that are suitable for the high school level. Teachers should fully explore the mathematical thinking methods contained in textbooks, highlight the teaching of mathematical thinking methods, and cultivate students' innovative ability. If conjecture is a very important mathematical thinking method, then scientific breakthroughs, technological innovations and other inventions often start with conjecture. Teachers should teach students to guess through observation and experiment; Through the analysis of special cases, the general (* * *) law is summarized and a guess is made; Through comparison and generalization, we get a guess; To make a macro estimate, there must be a guess first, and then a strict mathematical proof. In this way, "guessing and proving are both taught", which stimulates students' desire to guess and makes them realize that mathematics is also a lively, passionate and philosophical subject.
Second, strengthen language training, promote information exchange and improve comprehensive ability.
Mathematical language level is an important factor to reflect a student's mathematical quality and ability. Mathematical language includes three forms: written language, graphic language and symbolic language. Written language is the daily language of mathematical logic, science and standardization, graphic language is intuitive and vivid, and symbolic language is simple, abstract, accurate and generalized. "Mathematical language is the carrier of mathematical thinking and a tool to solve problems". Without language, it is impossible to learn and communicate.
In mathematics teaching, we should strengthen concept teaching, enrich students' language vocabulary and improve students' comprehensive ability to solve problems. Students should not only remember mathematical concepts and symbols, but more importantly, master the specific contents revealed by them. Whether a student can solve problems smoothly depends on whether he can accurately understand and translate various languages. In recent years, problems such as language translation, reading comprehension and small-scale integration within disciplines have occurred frequently in senior high school entrance examination and college entrance examination, and the student turnover rate is high. It can be seen that strengthening the training of mathematical language and improving students' comprehensive ability to use knowledge play an important role in cultivating students' mathematical quality. With the continuous improvement of social mathematicization and scientific mathematicization, mathematical language will become an important means of human communication and information storage, enabling students to master mathematical language, which is a tool for students to work and survive better in the future.
Third, attach importance to the application of mathematics, actively carry out mathematical modeling, and cultivate the ability to solve practical problems.
First of all, let teachers carry out training and research on applied mathematics. Secondly, actively carry out social practice, in-depth investigation, and carry out mathematical modeling activities. The practical application problems in the college entrance examination are all artificially transformed and abstracted, which are different from mathematical modeling activities. Mathematical modeling needs to ask questions and summarize them abstractly, which is more complicated and creative than solving application problems. In the activity, students should be the main body, fully arouse their enthusiasm, obtain rich first-hand information, arrange students to write small modeling papers, stimulate their enthusiasm for participating in modeling, and cultivate their innovative ability and interest in learning. Our mathematics education should not only let students learn the basic knowledge and skills of mathematics necessary for further study, but more importantly, let students look at the world from a mathematical perspective, observe and analyze the real society with a mathematical way of thinking and solve problems in real life. Therefore, actively carrying out mathematical modeling activities can greatly improve the ability to solve application problems and cultivate more innovative talents for the country. Thirdly, the content of applied mathematics should be added to the new textbooks, and the number of applied mathematics problems should be appropriately increased in the examinations at all levels, so that everyone can fully understand the great power of mathematics.
Fourth, pay attention to psychological counseling, create a good environment and strictly cultivate education.
Senior high school mathematics psychological education can be implemented from two aspects: psychological process and personality quality. In the process of psychological cognition, it is an effective way to strengthen students' metacognitive training, that is, to experience, observe, monitor and adjust their cognitive activities, which is conducive to improving students' conscious initiative in learning, developing students' autonomous learning ability, developing students' intelligence and solving the problem of "teaching students how to learn". For example, middle school students' memory, observation, generalization, imagination and thinking. How to cultivate and acquire them, what are their goals, plans and actions, and why they should do so are all under monitoring and adjustment. This kind of monitoring and adjustment is often more important than intelligence. Some very smart students have a low level of study, but they just can't monitor and adjust themselves. In the process of emotional will, mainly on the basis of cognitive process, combined with specific teaching content, students are given patriotic education, dialectical materialism education, mathematical aesthetic education and the role of mathematical education in socialist modernization, so that students have the need, motivation and initiative to learn, and then experience the joy of success and inspire their tenacious will to climb. In terms of personality quality, we should conscientiously implement the cultivation of personality quality in the syllabus, closely focus on cultivating interest and good study habits, and teach students in accordance with their aptitude, so that students can establish correct beliefs, ideals and world outlook, and form and develop their own abilities and personalities. The main channel of mathematics psychological education in middle schools is classroom teaching. Teachers should fully tap the factors of psychological education when preparing lessons, have the consciousness of psychological education, and conduct psychological education in a timely and appropriate manner in the form of infiltration and small lectures.