Mathematics has a high degree of abstraction, strict logic and wide application, which determines that mathematics is a subject with high difficulty in teaching and learning in all disciplines. Mathematics teaching method is a comprehensive marginal science, which requires that the basic principles of related disciplines must be used in the teaching process, especially some new ideas and methods in philosophy, psychology, teaching theory and logic. Tan Jilun, an American mathematics educator, wrote in his book:> In this book, the research object of mathematics education is regarded as the three vertices of a triangle, that is, mathematics education has three research aspects: curriculum, teaching and learning. The center of the triangle is called the "center of interest", which refers to the learners' interest in learning mathematics. The midpoint of the triangle "teaching-curriculum" is the role of teachers, which means that teachers should not only have in-depth research and understanding of the curriculum, but also have excellent teaching methods to form an optimized teaching plan. The midpoint of the "learning-course" side is the point of students' action, that is, students should not only process and store the acquired knowledge information to form a new knowledge structure, but also conduct creative learning to make their cognitive structure more orderly. The midpoint of "teaching-learning" is knowledge point, that is to say, the transmission of knowledge information depends not only on the order of teachers' output information (teaching method), but also on students' information absorption and processing ability (learning method). The cooperation between these elements is centered on students' interest in learning. In teaching, I made a survey on the learning of mathematics in two liberal arts classes: 1. Do you like math? A. I like B. I don't like C. Generalization (sometimes I like it, sometimes I don't like it very much), in which A accounts for 32.8%, B accounts for 12.5%, and C accounts for 56.25%. 2. The reasons why you like math are () A. You are interested in math, B. Teachers teach it well, C. You are forced to go to school, D. Other reasons, among which A accounts for 28.9. At the same time, psychology tells us that the most successful side of people must be what they are most interested in and love. When a student has a strong interest in a certain subject and a positive psychological motivation, his psychological essence will sprout a driving force for learning, so as to obtain the desired purpose and effect. As a mathematics teacher, how to induce students' psychological level of learning mathematics and make positive transfer of thinking and reasoning is particularly important for improving teaching efficiency. So, how can we cultivate and mobilize students' interest and passion in learning mathematics? First of all, we must fully understand the situation of our students. Through the investigation, communication and analysis of students, I find that some poor students I teach are not interested in learning, and there are many psychological obstacles to mathematics learning: negative, tired of learning, self-pity, laziness, natural fear and dependence. The following are the main psychological barriers: 1. Both negativity and fatigue are in the statistics. People with this psychological obstacle mainly want to learn math well, but they can't learn it well. This is mainly because students' high-intensity and long-term continuous learning activities also lead to the decline of learning ability, low learning efficiency, increased error rate and decreased interest. Moreover, they have great learning pressure and high expectations, and over time they have a negative psychology of learning-weariness. 2. Fear of mathematics leads to inferiority. According to statistics, 33.6% people have this kind of psychological obstacle, and most of them are students with poor mathematics learning. Mainly due to poor intelligence or improper learning methods, or lack of hard work, leading to repeated failures in the exam, resulting in a serious sense of loss, such as decadence, fear, sadness, anxiety, confusion and so on. This has long formed a conditioned reflex that "learning mathematics is painful" in their hearts, and anxiety and fear naturally rise in their hearts. In the summary of learning failure, we can always find that they have a natural "phobia" about mathematics in the exam. Even if you can do it well at ordinary times, you will eventually fail because of lack of self-confidence and tension, which will eventually lead to serious self-blame and inferiority. 3. Inertia psychology accounts for about 57.8% of the population. Most of these students are weak-willed and a little hot at best, but they will not last long and return to their original state. Some students are afraid of hard mental work and lack perseverance because of their long-term sloppy and lazy habits. When encountering insurmountable difficulties, most people will retreat, lose the courage and confidence to advance, and have psychological imbalance, thus creating psychological barriers. Then the main reasons why the students in this class form the above psychological obstacles are as follows: ① The students' psychological quality is poor and they lose confidence and interest in mathematics learning. (2) Teachers' sense of responsibility is not strong, their learning attitude is not correct, the classroom air is inactive because of the randomness of teaching, and the teaching methods are dull, which does not touch the excitement of students. (3) Poor learning environment (that is, improper study style and class style) leads to students' dislike of mathematics. 4. In the teaching of dependent psychomathematics, students generally have a sense of dependence on teachers, especially for students in liberal arts classes. According to statistics, about 38.3% people have this kind of psychological obstacle, which shows that they lack the initiative of learning and creation. I hope the teacher will sum up the math problems and speak them one by one, highlighting the key points and difficulties: it is best to "passively accept" all the problems without thinking. They are always used to imitating step by step in their homework, which may be related to their liberal arts students' habit of thinking in images rather than rational thinking and abstract thinking. I wonder if students' creative thinking and research spirit have been suppressed? After a long time, students lose their initiative and interest in learning. The only thing left is to finish the task and be forced to learn mathematics passively. Of course, the reason for this result should be attributed to the traditional indoctrination teaching method of teachers. In view of the above main psychological problems, we should always pay attention to the learning process of students with psychological problems in teaching, help them build up their confidence in learning mathematics, have the opportunity to let them vent their troubles and puzzles, and communicate and discuss face to face with them as friends, so as to achieve psychological mutual recognition, trust and perfection, and at the same time meet their needs of being understood and respected. Pay more attention to their emotions and attitudes in mathematics activities and give them positive comments in time; A word of positive encouragement is always much more effective than ten sentences of criticism. Everyone needs recognition from others psychologically and emotionally, so it is necessary to provide them with the beginning of expressing their thoughts freely, expressing their opinions bravely and realizing a leap in thinking. Suhomlinski once said in the book Believe in Children: "What affects students' inner world should not dampen their most sensitive corner-self-esteem. Therefore, teachers should become appreciators and supporters in the learning process, so as to heal their self-esteem and build their self-confidence. Only in this way can they cultivate and mobilize their interest and passion in mathematics. So, how can we cultivate and mobilize students' interest and passion in learning mathematics? Second, to create a good emotional atmosphere between teachers and students, first of all, let your students have a first impression of your teacher, and students should identify with you psychologically. Only when students like this teacher will they like the subject you teach-mathematics, and they will gradually become interested in it. In order to make students have a good first impression on themselves, they must have the following conditions: (1) high quality, including ideological quality and cultural quality, not only extensive professional and cultural knowledge, but also profound other related knowledge. Teachers have a refined and rigorous work style in business study, which exerts a subtle influence on students, making them have a strong interest in mathematics and forming a strong will and perseverance. Teachers, preach, teach and dispel doubts! Teachers are living examples for students to learn, and teachers' conduct is also very important. Teachers' good personality is the cornerstone of students' admiration. Because teachers are in direct contact with students, teachers' noble conduct has a far-reaching impact on students' outlook on life and behavior in the future. Therefore, teachers should not only learn all aspects of knowledge to improve themselves, but also pay attention to their own moral cultivation. Teachers are called the second parents of students, giving them advice and teaching them the truth of being human. (2) The language in the classroom should be vivid, and the rigid mathematical knowledge should be concretized, visualized and even humorous, so that students can understand and accept new knowledge in a relaxed and happy environment. The language in the classroom should be vivid and harmonious with body language. Body language is the most primitive language, and it is also the most vivid and charming language. It can express many abstract emotions that can't be expressed in words, and it has received very good results. Teachers can infect students with vivid, close to students and humorous language. Teachers can also arrange a rigorous and vivid teaching structure to form a warm and harmonious atmosphere, so that students can study actively and happily and fully mobilize their enthusiasm and initiative in learning. (3) Teachers should be full of passion in the classroom, and let students participate with you to achieve a * * * sound, and passion comes from teachers' own love for their jobs. If a teacher doesn't love his job, but regards it as a profession to make a living, how can you impress students to love the courses you teach? Teachers are role models in students' minds. Teachers should be willing to devote themselves to education, take training talents as a sacred duty, and integrate the sincere feelings of caring for students. (4) Be caring and selfless to students, neither lay particular stress on gifted students nor discriminate against poor students, but encourage more concern for poor students, as Gorky said: "It is a mother's business to love children, but being good at educating children is a national event, which requires talent and a deep understanding of life." Teachers should start from scratch, care for and care for students, form a real emotional integration between teachers and students, let students form a positive emotional response, imitate teachers in words and deeds and be willing to confide their ideas to teachers, and then take the initiative to receive education and guidance, resulting in the effect of "learning from others and believing in their ways". As the saying goes, people who love each other, people who respect each other, and people who respect each other will always be mutual. We only love each other. For poor students, it is particularly important to respect each student's personality, stimulate students' shallow tendency to learn mathematics from a psychological point of view, win students' love and respect, and then love mathematics. (5) The classroom should be full of active and democratic atmosphere. When explaining mathematical problems, allow others to fully express their views and different solutions, and let them show them in class. If the students' methods are better, they must be fully affirmed and praised. Communicate with teachers and students after class to enhance the trust between teachers and students. Rogers believes that "psychological freedom" or "psychological security" is the basic condition of creative work. If a student feels that the psychological atmosphere in the classroom is free and safe, he will feel better, without spending time to protect himself or being afraid of criticism from others. He can always make progress according to the goals he chooses. In fact, most students who don't talk in class are afraid of being criticized by their classmates for saying something wrong, which makes them feel insecure and insecure. Over time, these students simply don't try to explore, don't ask, don't answer, and think slowly. Create a classroom teaching space with psychological freedom, eliminate the inhibiting factors of creative thinking, and let students dare to ask questions, express their opinions and challenge authority. Only in a good psychological state can students open their minds, think faster and imagine more, so as to better accept new knowledge and gradually develop creative learning habits of active learning and independent thinking. Third, move with emotion and create a pleasant learning situation. High school students with poor learning conditions are generally depressed, deeply feeling bleak and tired of learning. Some students are still locked in their hearts, not good at talking and unwilling to communicate. In view of this situation, teachers should take the initiative to care about them, understand them and be their bosom friends. As Bing Xin, a famous modern female writer and children's writer in China, said, "I only think that' teachers' and' students' should be friends who respect and love each other." Classroom should be full of true feelings and encourage students, such as "good answer", "thoughtful", "good question" and "will it be now". Poor students, in particular, feel inferior because of poor foundation. When the teacher asks questions but can't, the most common scene in teaching is either "obscurity" or "no". Faced with this situation, teachers must give more encouragement to ease their nervousness. Tell them: "It doesn't matter, say as much as you know", and give them adaptive praise, so that poor students can participate in the classroom again, and have a * * * sound with the teacher's thinking, forming a benign interaction between teachers and students. Don't ignore it, and don't get angry easily, which will easily weaken students' enthusiasm for participation and increase their sense of attribution to failure, and students' weariness of learning will naturally arise. Of course, questions should be targeted, not too difficult for poor students and too simple for excellent students. Eugenics should ask some difficult questions at the right time, and don't make them feel too simple, proud and disdainful. In a word, the classroom atmosphere is relaxed and pleasant, so that poor students can get rid of the "guilt" of failure, so that gifted students can advance despite difficulties, so that they can be linked with teachers' thinking, and the communication between teachers and students can form a virtuous circle. According to the theory of emotional education, good emotions can promote people to achieve their learning goals: to stimulate imagination and give full play to creative thinking; On the contrary, it will suppress people's initiative and creativity in learning. Emotional injection is the key to open students' hearts, make students like teachers more, produce unusual feelings, and even give teachers advice. The teacher will say that students are mathematical geniuses, and they are talented, brilliant, incisive and creative in learning mathematics, so that the whole class will applaud me. This emotional injection is reflected in the teaching strategies for gifted and underachievers. However, Rogers, an anthropological educational psychologist, believes that true emotions, well-designed mathematical problems and appropriate teaching situations are easy to infect students' emotions, play a guiding role in students' cognitive learning, drive and induce students' learning motivation, and produce a psychological tendency to study urgently to achieve their goals. Fourthly, to cultivate students' creative and innovative ability, we should pay attention to the development of students' personality in mathematics class, gradually let students have the spirit of daring to take risks and not being afraid of failure, and encourage students to think independently, ask questions boldly and participate enthusiastically. In teaching, students are guided to discover, analogize and guess, and their creative consciousness, strong creative motivation and creative potential are stimulated. Using the wrong trap from time to time and the sharp contrast in the process of solving problems can often make students consciously innovate, and at the same time let students understand that learning should not be satisfied with the ready-made answers in books, let alone superstitious teachers. Be critical and aggressive about the teacher's solution. To dare to challenge the teacher's teaching, the teacher's answer is only a reference, not an imperial edict. Every student should have his own opinion, not to be a slave under the guidance of a teacher, but to be the master of his own thoughts. The cultivation of innovative consciousness should not only cultivate the logical and conventional thinking ability that traditional education pays attention to, but also pay attention to those unconventional or even unconventional thinking methods. In middle school mathematics teaching, lateral thinking and reverse thinking are particularly important. Lateral thinking can find solutions to problems from many possibilities, while reverse thinking is more used in mathematics, such as reverse analysis, reduction to absurdity, reverse formula and so on. To train and master these thinking methods, we should reflect and summarize them purposefully and systematically after solving problems, and teach them to use their knowledge to "guess before proving" some unknown problems. Especially in senior high school & gt In this chapter, the method of "guess-induction-verification" will play an unexpected role in solving the general term of series and proving the problems that are difficult to be solved by ordinary methods. Stimulate students' interest in learning with the unique beauty of mathematics. Confucius Day: "Those who know are not as good as those who are good, and those who are good are not as happy as those who are happy". Many middle school students are interested in mathematics, not because they know much about the importance of mathematics, but because they think mathematics is profound and beautiful, geometric proofs are wonderful and mathematical operations are interesting. Whenever a difficult problem is solved, the joy in my heart will arise spontaneously. It goes without saying that learning mathematics should follow a benign interactive model: the edification of mathematical beauty-the generation and maintenance of interest-excellent learning effect. Mathematics is a beautiful art, and whenever a clever solution is encountered, a mathematical aesthetic feeling naturally arises. The beauty of mathematics comes from the organic combination of mathematical thought and practical truth, but it is higher than life. Mathematical beauty includes simplicity, symmetry, diversity and unity, harmony, singularity, logic and mathematical content. Therefore, if we want to get twice the result with half the effort, we must put the beauty of mathematics throughout the whole teaching process. Excavate aesthetic education factors in mathematics, and let students be influenced by aesthetic education. "Everyone has a love for beauty" is particularly prominent among teenagers, and beauty is the characteristic of mathematics. For example, when finding the range (y=+) of a function, it is difficult for students to think, and students only think from algebra. However, if students are guided to put (

) as the distance between A(x, 0) and B(0, 2), (

) as the distance of (x, 0), c (- 1, -3), it is easy to solve (y=|AB|+|AC|≤|BC|= with the knowledge of analytic geometry.

)。 Through this cognitive process, students immediately feel that this solution is beautiful, which embodies the beauty of the organic combination of algebra and geometry, and it is difficult to solve such a problem: (y =-); The range of (y=+) has aroused great interest. The whole mathematical system is an unparalleled harmonious and beautiful unity. Therefore, teachers must be good at feeling and refining beauty from textbooks, and integrate aesthetic education factors in textbooks into teaching plans to create the best teaching realm, so that students can appreciate the unique beauty in mathematics and stimulate their endless fun and desire to learn. 6. Stimulate interest in learning from the joy of success. Everyone is eager for success, and success will inject new vitality into people. Success will make students have a strong psychological motivation to seek knowledge when learning mathematics. In mathematics teaching, we should create more opportunities for each student to express himself, make full use of the method of "low, small, complete and fast", and start students' cascade thinking in stages. Start with simple questions, explore students' psychological bottom line, increase the channels of mathematical analysis, and guide students to make correct answers to exercises. Through their unique insights or creative thinking, students have achieved good results again and again, and gradually feel happy and proud of their success. Even if students occasionally fail to answer correctly, the answers are not perfect, and teachers should not blame them at all. But to find their bright spots, encourage them and let them feel the joy of success. Finally, let students understand that as long as they open their hearts, there is hope and success. Students who are motivated by achievements will persist in learning for longer. Even if you encounter setbacks, you often blame yourself for not working hard enough. They are bent on success, and if they fail, they will redouble their efforts until they succeed. Therefore, students with strong achievement motivation in school will generally get better grades. On the other hand, students who have never experienced success often lose their motivation in this area and turn their motivation to other things they are interested in. Psychologists have found that students may achieve their goals in two ways, trying to succeed and trying to avoid failure. After encountering setbacks, successful people's motivation is enhanced, and they often work harder to succeed, while trying to prevent losers from lowering their motivation level after encountering setbacks. In a word, proper success or failure can enhance the motivation of follow-up learning, but successful experiences have a greater stimulating effect on motivation than failed experiences. Especially for poor students, further failure will lead to the decline of learning motivation, and one or more successes will become the "activator" of learning motivation. Therefore, when designing questions, writing on the blackboard and homework, teachers should put forward different requirements for different students at different levels, so that each student can have the hope of success, thus gaining a successful experience and improving their learning motivation and interest. Einstein said, "Interests and hobbies are the best teachers." Therefore, in order to achieve good results in mathematics, teachers are required to have profound knowledge, combine the characteristics of mathematics, carefully design each class, guide learning with interest, and fully mobilize students' enthusiasm for learning mathematics. Mathematics teaching psychology believes that teachers should try to make students "hungry" for knowledge before learning mathematics, thus stimulating students' interest, motivation and enthusiasm in learning. Most students are sensitive and curious about new things, and have strong self-expression and competitive psychology. Therefore, in mathematics teaching, we should change the traditional teaching methods, use humorous language, vivid metaphors, interesting examples and unique classroom situations, and turn boring mathematics knowledge into a stimulus to stimulate students' desire for knowledge, so as to arouse students' initiative and interest in learning, and finally achieve the goal of improving mathematics teaching efficiency.