The content of mathematics review can be divided into two parts: basic knowledge and basic problem-solving skills. In the review, we should pay attention to the analysis, comparison and flexible application of basic concepts, basic formulas, basic laws and rules, so as to understand, synthesize and innovate.
The so-called "understanding" means trying to integrate the basic mathematics knowledge and basic concepts learned in middle school from the part to the whole, from the micro to the macro, from the concrete to the abstract. , consciously cultivate their analytical understanding ability, comprehensive generalization ability and abstract thinking ability. For reviewing definitions, theorems and formulas, we should clarify the context, communicate with each other, master the derivation process, pay attention to the expression form, summarize the memory methods and clarify the main uses.
The so-called "synthesis" refers to the refining and processing of mathematical knowledge learned in different disciplines, different units, different grades and different times, and the establishment of vertical and horizontal links between knowledge, so that knowledge is systematic, organized and networked, which is convenient for memory, storage, extraction and application. For example, reviewing the concept of corner can be summarized as follows:
(1)* * * The angle formed by the straight line of the plane-the angle formed by the straight line of different planes-the angle formed by the straight line and the plane-the angle formed by the plane and the plane, so as to find out the formation and development of this point, how to expand the former into the latter, and how to transform the latter into the former to solve it.
(2) Analogy distinguishes the concepts of obliquity, radial angle and polar angle which are easily confused, thus making the concept of angle clearer and more accurate.
(3) Triangle: the expression and characteristics of the same angle, horizontal angle, vertical angle, quadrant angle, interval angle and azimuth angle. And sort out the application rules and methods.
The so-called "innovation" refers to the flexibility, originality, conciseness, criticism and profundity in the process of solving problems after mastering the basic knowledge. Innovation ability is not only manifested in the comprehensive application of the learned knowledge to analyze and solve problems, but more importantly, it is to discover new problems, broaden and deepen the learned knowledge field, and constantly enhance one's adaptability. To this end, every student should pay attention to discovering and excavating problems that are not in books and have not been talked about by teachers according to their own knowledge. For example, to understand the various connotations of a concept, we should think about a problem from different angles (that is, multiple solutions to a problem), sum up the law of solving problems with * * * (that is, multiple solutions to a problem), and find out the thinking method of solving problems.
2. General methods of mathematics review
(1) preview before class. The review course is large in capacity, rich in content and short in time. In order to improve the review efficiency, we must synchronize our thoughts with the teachers'. Preview is an important way to achieve this goal. Without preview, listening to the teacher will make you feel that everything the teacher says is very important and you can't grasp the key points of the teacher's speech; After previewing and listening to the teacher, you will choose what the teacher said in your memory and focus on what you don't have, thus improving the review efficiency.
(2) Review after class. Mr. Hua, a famous mathematician, believes that there are two processes in learning mathematics. One is the process of books from thin to thick, which is the process from ignorance to knowledge, from knowledge to knowledge, gradually accumulating knowledge and deepening understanding. This process alone is not enough. There must be a second process, that is, the process of books from thick to thin. The so-called book from thick to thin is to establish the vertical and horizontal connection between knowledge, so that knowledge can be systematized, organized and networked, and it is easy to store, remember, extract and apply. After-class review is an important way to make books from thick to thin.
(3) learn from each other. According to the theory of dissipative structure, a dissipative structure far from equilibrium must move from low state to high state, from disorder to order, must be open to the outside world, and must communicate frequently with the environment in terms of material, energy and housing. Any social organization and any individual is a dissipative structure far from equilibrium, because the evolution of social organizations and human beings is far from complete. Students stay away from the dissipative structure of equilibrium, because they are growing people. Therefore, as a high school student, if you want to get good grades, you must always keep in touch with your teachers and classmates, especially in the review stage. Because the problems accumulated at this stage will directly affect the exam results.
(4) Do more exercises. One of the purposes of mathematics learning is to form certain skills, such as thinking skills, problem-solving skills and operation skills. Skills are automatic activities based on existing knowledge and repeated practice. There are three main definitions of this skill: mastering knowledge is the premise of forming skills, repeated practice is the basis of forming skills, and activity automation is the symbol of forming skills. Therefore, practice plays a very important role in the formation of skills. It is necessary to do some exercises in the review stage. Attention should be paid to controlling difficult problems in practice, and the focus of practice should be on important and key knowledge points.