Education is an effective means of quality education. Examining mathematics education under the background of quality education is not only the central task of building a mathematics education system with China characteristics, but also of global epoch-making significance for truly implementing the education policy of all-round development. Therefore, the key of mathematics education is to face every student, so that students can develop harmoniously and fully on the basis of their original quality, and have modern adaptability and viability. Therefore, it is the requirement of quality education to strengthen the teaching of basic knowledge so that students can form a solid mathematical foundation. In mathematics teaching, students are encouraged to discover new discoveries, new ideas and new methods in the field of mathematics through their own educational influence. Taking mathematics teaching as an example, this paper expounds some experiences in senior high school teaching.
The Prime Minister said at Tongji University: "Only those who pay attention to the sky can have hope. ..... learn to be a man, learn to think, learn knowledge and skills, and be a person who cares about the fate of the world and the country. Nowadays, college students, the younger generation and even the whole nation are indifferent to grand and abstract propositions: whether it is the progress of the country or the trend of world peace; Whether it is the mystery of nature or the depths of human heart, it is considered to have nothing to do with itself and is not worthy of attention. " Today's society is in a stage of rapid development, and all walks of life need high-quality people. The purpose of education is to cultivate high-quality talents for the society. High school students are the hope of the motherland, the pillars of the future, the successors of China's characteristic cause and the new force for building a well-off society in an all-round way. Contemporary senior high school students are a truly cross-century generation, and they also grow up with the reform and opening up.
Three years in high school is a moment in the long river of life, but it is extremely precious in personal life. This is an extraordinary period in which a person's world outlook is initially formed; It is an important stage of physical development and ability training; It is a critical moment to consolidate the basic knowledge and sprint the college entrance examination. Therefore, students should not only pay attention to the cultivation of ideological and moral character, but also pay attention to the improvement of ability, pay attention to the efficiency in unit time and improve their academic performance.
Mathematics education is an effective means of quality education. Examining mathematics education under the background of quality education is not only the central task of building a mathematics education system with China characteristics, but also of overall epoch-making significance for truly implementing the policy of quality education. Therefore, the key of mathematics education is to face every student, so that students can develop harmoniously and fully on the basis of their original quality, and have the adaptability and viability of modern society. In the implementation of mathematics education, according to the characteristics of mathematics itself, we should actively explore the best combination of mathematics knowledge and quality education while imparting basic mathematics knowledge and skills, so as to promote the all-round improvement of students' quality. Mathematical activities are not only mathematical cognitive activities, but also sensory activities with emotional mentality. Successful math activities are often accompanied by the best mentality.
Mathematics is an important part of modern times, and its application is paid more and more attention by the society. The new curriculum standard points out that students' teaching and learning activities should not be limited to acceptance, memory, imitation and practice. Therefore, high school mathematics curriculum should also advocate independent exploration, hands-on practice, cooperative communication and other mathematics learning methods, and at the same time pay attention to the cultivation of students' emotions, attitudes and values, change the former "teacher-centered" to "student-centered", fully reflect students' subjectivity and initiative, and should reflect three levels of goals: knowledge and skills-process and method-emotions, attitudes and values. Teachers should always have students in their hearts, design problems from the students' point of view, choose examples, become students' collaborators, promoters and learners, create a good classroom atmosphere and humanistic spirit, cultivate students' positive emotions and attitudes in learning mathematics, and form correct and healthy values and world outlook.
The process of learning mathematics is essentially a process of solving the contradiction between cognitive subject and cognitive object. The learning characteristic of students is to develop the ability to recognize and innovate knowledge on the basis of learning knowledge under the guidance of teachers. In the teaching process, if students, as the main body of development and change, have a negative attitude, don't want to learn, don't give full play to their subjective initiative, don't use their eyes, ears, mouth and body properly, especially can't or don't want to use their brains to understand what the teacher teaches, then even if the teacher "teaches" well, it can't promote the development of students' own knowledge and ability. In the process of teachers' teaching and students' learning, the author believes that the following points should be achieved:
First, review and consolidate in time.
The ancients said, "Learn from time to time". This is the way to learn mathematics. If you don't finish your homework carefully and practice the theory you have learned, you won't learn. Not to mention good grades. Homework after class can be carefully selected and completed with high quality. First of all, it is to show respect for teachers. One of the duties of teachers is to impart knowledge to students accurately. "Teachers are people who preach, teach and dispel doubts", while students are the monument of teachers' profession. If you can't apply what you have learned to practice, you are actually condemning the teacher for not teaching you well. Secondly, it shows a student's intelligence and ability level. "A slave who doesn't do exercises should be a master at doing exercises." This requires students to classify exercises. Especially in senior two and senior three, the thinking of solving problems is clear, and only complex problems need to be done less or not; To solve problems with unclear ideas, we should study and understand them; Wrong questions should be filed in different categories. These wrong questions must be reviewed before each exam. Third, it reflects a student's "honest" quality. Honesty is the foundation of being a man. Is it possible to have integrity? "Sowing vows, harvesting actions, sowing actions, and harvesting individuality; Sow personality and harvest fate. " Every student wants to study hard and get high marks. Every student may make up his mind to study hard more than once. But when he needed a job, he forgot his oath. As the saying goes, "where there is a will, there is a way;" People who have no ambition are always determined to win! "
Second, cultivate students' thinking ability.
Pedagogical theory holds that thinking is an indirect reflection of the human brain's generalization of the nature of things and the regular relationship between things. Thinking is the core component of cognition, and the development level of thinking determines the structure and function of the whole knowledge system. Therefore, it is of great significance to develop the thinking potential of senior high school students and improve their thinking quality.
The flexibility of students' thinking is mainly manifested in the following aspects: (1) the flexibility of the starting point of thinking: the direction of thinking can be quickly determined from different angles, levels and methods according to new conditions. (2) Flexibility of thinking process: being able to use all kinds of laws, axioms, theorems, laws and formulas flexibly. Switch from one solution to another. (3) Flexibility of thinking transfer: You can draw inferences from others or draw inferences from others.
Third, think independently.
Teachers should not explain in detail, leaving room for students to think, explore and develop themselves. Otherwise, it seems difficult to internalize the students' point of view, students' independent thinking ability cannot be formed, and students cannot be left room to stimulate their independent learning and thinking. Independent thinking ability is a comprehensive ability, which shows that individuals can face different situations and use different ways of thinking, methods and skills to solve the problems they face. To cultivate this ability, we should first let students participate in specific activities and improve their participation as much as possible. Secondly, it is necessary to help students gradually master the methods of thinking and analyzing problems. Finally, we should pay attention to cultivating students' thinking quality and form the habit and ability of independent thinking.
Independent thinking is not whimsical thinking, but must follow correct laws and methods. The scientific thinking method is not divorced from the process of acquiring and using knowledge, but permeates and permeates in this process. In the process. Teachers should not only tell students the conclusion, but also let students know the process and method of drawing the conclusion, and know the ins and outs of knowledge and their relationship. Through the process of learning knowledge, learn to think correctly at the same time, and gradually build a systematic thinking method to prepare for independent thinking in the true sense. Taking the teaching process of "complex related concepts" as an example, with the deepening of students' classroom discussion, teachers and students have jointly constructed the knowledge structure of complex concepts, and in the process of solving this problem, some thinking methods have been refined.
Fourth, strengthen the organization of students' memory.
The organization of memory is the foundation of quick thinking. The agility of thinking requires an accurate grasp of what you have learned, so that you can quickly and correctly find the knowledge you need when dealing with problems, so as to achieve concise and fast thinking. Therefore, only by organizing the memory can we realize the principle in the process of thinking and achieve the agility of thinking. On the other hand, if the memory is chaotic, it is bound to be unable to reproduce the needs of thinking in time, and it is difficult to achieve the agility of thinking. Strengthening the organization of students' memory is to guide students to transfer, summarize and sort out what they have learned, to achieve conciseness and systematization, and to summarize the laws, methods and experiences of solving problems. In this way, when dealing with problems, we can search, think and transform quickly, so as to make a quick response.
Strengthening the organization of students' memory in teaching can be guided from the following two aspects: (1) guiding students to organize a "vertical" knowledge structure. Even if students systematically string together all the parts of knowledge they have learned according to the relationship, it is beneficial to the understanding and consolidation of knowledge and to the popularization and application of knowledge; (2) Guide students to organize horizontal knowledge structure. That is, all kinds of knowledge and methods scattered in various chapters but solving the same kind of problems are systematically summarized to form a complete knowledge system, which can be flexibly used in solving problems. For example, guide students to summarize the methods of finding the limit.
Fifth, summarize and accumulate effective problem-solving ideas.
The thinking of solving problems occupies a strategic position in the process of solving problems. If a problem has a correct solution idea, it can be said that most problems are solved. The agility of thinking is also manifested in shortening the calculation link and reasoning process, and directly and quickly obtaining the solution idea and result. In order to make students' thinking agile, it is required to cultivate students' agile consciousness in dealing with problems in teaching and guide students to be good at summing up and accumulating effective problem-solving ideas. The specific methods are: (1) directional thinking training. That is to say, when encountering new problems, we are good at attributing them to a certain model, and through the analysis of known conditions and conclusions, we can form clear solutions as soon as possible, so that there are "laws" to follow, "roads" to be feasible and agile; (2) Reverse thinking training. That is, from cause to cause, from source to source, to cultivate students to think in the opposite direction of the original problem, to use what they have learned flexibly in reverse, and to win by surprise; (3) Divergent thinking training. That is to train students to be good at thinking from all angles, that is, starting from a certain point, using all information to make radioactive contact and get rid of the bondage of "stereotype".
Sixth, change teaching concepts, teaching methods and learning methods.
Whether satisfactory teaching results can be achieved depends on the change of teachers' concepts and teaching methods. Judging from the author's personal experience, this is a rather painful thing, and it will not happen overnight. Teachers need to have a great sense of responsibility, patience and courage, constantly strengthen theoretical study and training with their accustomed teaching methods and teaching behaviors, and more importantly, strengthen reflective teaching, that is, the process in which teachers take their own teaching activities as the object of thinking and examine and analyze their own behaviors and the resulting results.
Nowadays, mathematics teaching should no longer be a single model of example, practice, explanation and test, but should focus on students' brain learning, supplemented by teachers' guidance and correction. In class, teachers should actively mobilize every student's brain cells and let them think and explore. Make the traditional boring math class lively.
In a word, the cultivation of senior high school students is not accomplished overnight, but a long-term, complex and arduous task. Making mathematics teaching serve the improvement of students' comprehensive quality is the theme of current mathematics teaching reform, and it is also an urgent and arduous task for our mathematics teachers. We educators should actively explore and practice hard to make our own contribution to cultivating high-quality talents to revitalize China.
refer to
Lin Chongde. Intellectual development and mathematics learning [M]. Beijing: Science Press, 1982.
[2] Wang Yunmin. The holistic view of mathematics of dialectical materialism is the cornerstone of understanding mathematics [J]. Science and Technology and Dialectics, 2002, (1).
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