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.