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 schools from the part to the whole, from the micro to the macro, from the concrete to the abstract, and consciously cultivate their own 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 and pay attention to the expression form.
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, the concept of review angle 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 analyzing and solving problems by comprehensive application of learned knowledge, but more importantly, it is to discover new problems, broaden and deepen the field of learned knowledge, and constantly enhance its adaptability. To this end, every student should pay attention to discovering and excavating problems that are not mentioned in books and teachers according to their own knowledge, such as understanding the various connotations of a concept, thinking about a problem from different angles (that is, multiple solutions to one problem), summing up the law of solving problems with * * * *, and discovering 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. To improve the efficiency of review, we should synchronize our thinking with that of teachers, and preview is an important way to achieve this goal. Without preview, listening to the teacher will feel that everything the teacher says is very important, and we can't grasp the key points. After previewing the teacher's lecture, you will choose what the teacher has said in your memory and focus on what you have not mastered, 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, from unknown to many, from little to many, knowledge gradually accumulates and knowledge gradually deepens. 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 vertical and horizontal links between knowledge.
(3) learn from each other. According to the theory of dissipative structure, a dissipative structure far from the equilibrium state must go 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 are further away from the dissipative structure of equilibrium state. Because they are growing. 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 your 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 the use of existing knowledge and repeated practice. There are three 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. In the review stage, it is necessary to do some exercises. We should pay attention to control difficult problems and pay attention to important and key knowledge points when practicing.