The best way to learn any knowledge is to discover it by yourself, because this kind of discovery is the most profound to understand and the easiest to grasp the internal laws, nature and connections. Believe in every student, let them learn by themselves, and believe that they will learn well through their own efforts. Admit that there are differences among students, but firmly believe that this difference is a exploitable resource. As long as we provide necessary study guidance and basic study conditions, almost all people can learn well.
First of all: preview is essential. Preview is to read the upcoming mathematics content before class, understand its outline, and be aware of it, so as to grasp the initiative in class. Preview is an attempt of autonomous learning. Whether you understand the learning content correctly, whether you can grasp the key points and hidden thinking methods, etc. It can be tested, strengthened or corrected in time in class, which is conducive to improving learning ability and forming the habit of self-study, so it is an important part of mathematics learning. Mathematics has a strong logic and coherence, and new knowledge is often based on old knowledge. Therefore, when previewing, you should find out what you need to learn new knowledge, and then recall or review it again. Once we find that the old knowledge is not well mastered or even understood, we should take timely measures to make up for it, overcome the learning obstacles caused by not mastering or forgetting, and create conditions for learning new content smoothly.
Secondly, let students master the method of preview. Preview, in addition to recalling or reviewing the old knowledge (or preparatory knowledge) needed to learn new content, should also understand the basic content, that is, know what to say, what problems to solve, what methods to adopt, where the focus is, and so on. In preview, reading, thinking and writing are generally used to draw out or mark the main points, levels and connections of the content, write down your own views or places and problems that you can't understand, and finally determine the main problems or solutions to be solved in class to improve the efficiency of class. In the arrangement of time, the preview is generally carried out after review and homework, that is, after finishing homework, read the content to be learned in the next class, which requires flexibility according to the specific situation at that time. If time permits, you can think more about some problems, study deeply, and even do exercises or exercises; Time does not allow, we can have fewer questions and leave more questions for lectures to solve. There is no need to force unity.
Second, how can teachers guide and urge students to learn first?
First of all, teachers should cultivate students' habit of previewing before class and take effective measures to supervise. Because junior high school students' self-awareness is not strong and their self-learning ability is limited, in order to make students preview before class to achieve the best effect, teachers must formulate a set of effective methods, such as classroom questioning, classroom quizzes, and randomly selecting students to do problems before class. In order to promote students to complete the task of self-study consciously, actively and effectively, teachers should also put forward specific self-study requirements according to the needs of teaching objectives, focusing on establishing students' learning motivation, such as specific reading scope, thinking content or experimental content, how long it will take, what goals to achieve, and how teachers will test after self-study. At the same time, we should guide students to learn by themselves, such as how to read books, how to practice, what matters should be paid attention to during the experiment, and thinking must be carried out independently. And according to the needs of specific teaching objectives and contents, let students try first under the premise of independent thinking, say whatever they want and start as soon as they want.
Second, in the teaching process, teachers should study the characteristics of the subject and help students find the best learning method. Mathematics is responsible for cultivating students' computing ability, logical thinking ability, spatial imagination ability, and the ability to analyze and solve problems by using what they have learned. Its characteristics are high abstraction, strong logic, wide applicability and high requirements for ability. Learning mathematics must pay attention to "living", not just reading books without doing problems, not burying one's head in doing problems without summarizing and accumulating, and must be able to access textbook knowledge and combine one's own characteristics. Find the best learning method. This is the truth of the learning process of "from thin to thick" and "from thick to thin" advocated by Mr. Hua. The methods vary from person to person, but the four links of learning (preview, class, assignment and homework) and one step (review and summary) are indispensable. In addition, teaching objectives have a strong guiding role. To implement quality education in classroom teaching, teachers should first do. Of course, in the teaching process of learning before teaching and teaching with learning, every step is inseparable from teachers. Cai Linsen, president of Yang Si Middle School, said that the specific process of the teaching mode of "learning first and teaching later" is like a car entering the expressway, and it can't get on without an approach bridge; If there is no road sign, you can take a fork in the road. Teachers should be "approach bridges" and "signposts" and play a leading role, which is the premise for students to learn well.
Third, teachers should teach students in accordance with their aptitude and guide them according to the situation.
Everyone knows things in his own unique way, and every student has his own specific learning method. Even if defined by the meaning of learning, some students' learning methods are naive and immature, but in teaching, we can take these immature learning methods as the starting point of learning, and temper scientific and effective learning methods by constantly strengthening guidance. It is an arduous task to strengthen the guidance of learning methods in classroom teaching. Teachers must fully understand the learning situation, understand and master the dynamics of classroom learning, and teach students in accordance with their aptitude. At present, it has become the consensus of teachers to strengthen the guidance of learning methods, but how to master the strength of the guidance of learning methods and enhance the artistry of the guidance of learning methods is worth further discussion. It should be said that heuristic teaching, from shallow to deep teaching and so on are all effective teaching methods, which are very flexible and do not stick to fixed procedures; It can inspire students in a timely and appropriate way, which varies from person to person and from material to material.
4. What are the basic qualities that teachers must have before learning?
In the book Classification of Educational Goals, Bloom divides teaching objectives into three areas, namely, cognitive area, emotional area and motor skill area. Therefore, when preparing lessons, teachers should choose teaching strategies, methods and media around these goals and reorganize the necessary content. In mathematics teaching, through the joint efforts of teachers and students, students can achieve the predetermined goals in knowledge, ability, skills, psychology, ideology and morality, so as to improve their comprehensive quality. Specifically, the following aspects should be realized:
The first is to prepare a starting point. The so-called starting point is the growth point of new knowledge on the basis of original knowledge. A suitable starting point is conducive to promoting knowledge transfer and enabling students to learn and be willing to learn. The starting point is too low, students are not interested and unwilling to learn; The starting point is too high for students to understand and learn.
The second is to prepare the key points. Emphasis is often the starting point and main part of new knowledge. Give prominence to the key points when preparing lessons. In a class, first of all, we should ensure that the key contents are focused in time, closely focus on the key points, and take this as the center, supplemented by knowledge and practice, to guide and inspire students to strengthen their understanding of the key contents, so that the whole class has a soul.
The third is to prepare for difficulties. The so-called difficulty is the knowledge point that most students in mathematics can't understand and master. Difficulties and priorities sometimes coincide. When preparing lessons, it should be determined according to the breadth and depth of the teaching materials and the students' foundation. We must pay attention to analysis, study carefully, grasp the key points and break through the difficulties. For example, in geometry teaching, we should combine specific teaching methods (such as origami, paper-cutting, physical demonstration, etc. ) and adopt intuitive teaching to concretize abstract and difficult knowledge, thus slowing down the slope of knowledge and slowly cultivating students' spatial imagination.
Fourth, prepare the intersection. That is, the connection point between old and new knowledge. Mathematics knowledge itself is very systematic, and chapters, examples and exercises are closely related. Only by truly understanding the intersection of old and new knowledge can we integrate knowledge, communicate the vertical and horizontal links between knowledge and form a knowledge network. Teachers can use variants to explain examples, so that students can draw inferences when doing problems, which is more conducive to the flexible use of knowledge.
Fifth, be prepared to doubt. It is that students are easy to mix and make mistakes. When preparing lessons, we should combine the students' basic and practical ability, find out the doubts and make full preparations. For example, when reviewing the difficult content of the proportional line segment related to the circle in the general review of the senior high school entrance examination in the third grade, a poetic and easy-to-remember formula is introduced: replace it with equal product and equal ratio, search horizontally and search vertically, if you can't find it, don't worry, equal line and equal ratio; Satisfy the equal proportion, change the equal product, projection and circle power instead. This not only increases the literariness of mathematics, but also deepens students' memory, enabling students to master this important content comprehensively and systematically. Because I have been teaching for a short time, students sometimes have not mastered the foundation and their own thinking ability, and there are still many deviations in choosing students. The biggest experience is to make full preparations in advance, consciously set suspense in teaching, use more inspiration, let students think positively, but the quality is difficult to question, guide students to analyze and judge, stop under the guidance of teachers, and let students give full play to their abilities and make clear their doubts.
In a word, the practice of learning before teaching and teaching with learning has many successes, but there are still many problems in the specific operation process. For example, at first, students were very interested and conscious, but after a period of time, some students began to fail to finish their tasks on time, which brought great difficulties to teaching; Classroom practice is a little more difficult, some students are a little at a loss, and their self-confidence in learning mathematics declines; Classroom teaching has no time to analyze difficulties and so on. In view of these problems, we are combining the characteristics of many local students, optimizing students' learning environment through home visits, holding parent-teacher conferences and other ways, and strengthening their own learning, often summing up their own exploration, and finding a teaching plan suitable for the local special environment, so that it is feasible to learn first and then teach.