First of all, we should understand that the review during the third year of high school is generally divided into three stages:
The first round of review: take the knowledge system of textbooks as the main clue to review, help students recall and review what they have learned before, cover all aspects of knowledge, and summarize and reflect on basic methods and problems;
The second round of review: at this stage, the textbook system is broken, mainly focusing on the special review of the six major sections of high school mathematics, and the comprehensive application is further strengthened on the basis of the first round of review to improve the accuracy, speed and standardization of problem solving;
The third round of review: at this stage, students mainly conduct mock exams and training for college entrance examination questions, and cultivate answering skills, answering methods and adaptability in the examination room.
Therefore, in the whole review, the first round of review takes the longest time, and its review effect will directly affect the subsequent review effect. Put forward the following suggestions for the first round review of mathematics:
First, correct attitude, avoid impetuousness and rush for success.
In the process of the first round of review, it is very common to be impetuous. The main performance is that I think there is no problem in reviewing at ordinary times and I can do the questions, but I just can't get high marks in the exam! This is mainly because:
(1) Lack of systematic understanding of the knowledge points reviewed and lack of thinking level when solving problems. The first round of review focuses on the excavation of basic knowledge points, and the math teacher will repeatedly emphasize the importance of foundation. If we don't pay attention to the systematic analysis of knowledge points, we can't form an overall knowledge network framework, and naturally we can't have an overall idea when solving problems, and we can't deeply understand the thinking methods of typical examples of college entrance examination.
(2) When reviewing, my heart is not quiet. A restless heart will lead to unclear thinking, which will lead to inefficient review. I suggest that before you start reviewing a subject, you should calm down and seriously think about what you need to review next and how many things you need to do, and then do it seriously, and at the same time you need a high degree of attention. Only in this way can we have a good result.
(3) In the first round of review, the focus of study should be shifted to the basic review.
Therefore, it is suggested that students should not be eager for success in a round of review, but must calm down, carefully ponder every knowledge point and clarify every principle. Only in this way can a round of review be effective.
Second, pay attention to teaching materials, pay attention to the foundation, and avoid doing problems blindly.
Doing well the routine questions in books means doing them correctly in the least time. Some students don't pay enough attention to the basic questions in the first round of review, thinking that they can do them without training. As a result, they often make mistakes in the wrong places, and finally attribute the reason to carelessness, thus ignoring the mastery of basic concepts, the memory of basic conclusions and formulas, the training of basic calculations and the accumulation of conventional methods, resulting in the deviation between actual results and psychological feelings.
It can be seen that the basic concepts, definitions and formulas of mathematics, the connection of mathematical knowledge points and the basic ideas and methods to solve mathematical problems are the most important things in the first round of review. Take the heavy and difficult function part as an example, we should master the concept of function, establish the function relationship, master the properties of definition range, range and maximum, parity, monotonicity, periodicity and symmetry, and learn to use images, that is, the combination of numbers and shapes.
Third, grasp the weak links, do a targeted review to avoid unplanned.
Every student's problems in mathematics learning have similarities and differences. In the review class, teachers can only solve the similarities in a targeted way, while students' own individual problems need to be solved through their own thinking, discussion with students and questions to teachers, so as to encourage students to ask teachers more questions and dare to ask questions. Every student should know what he has mastered and what problems have not been solved. Obviously, only by filling the loopholes can we improve. The process of reviewing is essentially the process of solving problems. When the problem is solved, the effect of review will be realized. At the same time, please note that it is best to think for yourself before asking questions, and don't ask questions directly without thinking, because it won't play a greater role.
The review of senior three must be planned and targeted, and don't blindly do the questions. The first round of review is highly targeted, and all knowledge points should be carpet bombed. Therefore, simply doing the questions can't achieve the due effect of a round of review. Moreover, blindly doing the questions is not targeted and will not be comprehensive. In the case of vague concepts, we must return to textbooks, pay attention to the clearest concepts and principles in textbooks, and pay attention to the summary of the application methods of knowledge points.
Fourth, we should develop good problem-solving habits and avoid thinking.
1. Build confidence and develop good calculation habits. Some students usually lack self-confidence in the learning process, so it is inevitable to check each other's answers when doing homework, and they have not carefully found out the reasons for the mistakes and corrected them. "Meeting without being right" is a big taboo in mathematics learning in senior three. There are common mistakes in exams and calculations, which are usually considered to be carelessness. In fact, this is a very bad habit, which must be gradually overcome in the first round of review. Otherwise, there will be endless trouble. We can combine the specific problems existing in solving problems at ordinary times, find out the reasons one by one, see if it is the cause of behavior habits or the defect of knowledge, and then solve them in a targeted manner. Make some notes when necessary, that is, the wrong question book, which is necessary for every student to inquire in the future.
2. Do a good job of expansion and extension after solving problems, and cultivate the ability to solve multiple problems and draw inferences from others. The cultivation of problem-solving ability can be improved by solving a problem in many ways and drawing inferences from others, so it needs to be recalled and extended after solving the problem, which includes the development and extension of problem-solving methods, that is, a math problem can be analyzed from different angles, with different ideas and different solutions.
The broader and deeper the consideration, the broader the ideas and the more diverse the solutions; Expanding topics, extending new problems and new solutions are conducive to cultivating students' divergent thinking, stimulating creative spirit and improving problem-solving ability:
(1) Conditions for expanding the topic.
① Summarize special circumstances; (2) Specialization of general conditions; ③ Special conditions and general conditions alternate.
(2) Expand the conclusion of the topic.
(3) Expanding the types of questions and giving different formulations to the same topic can become different types of questions. It is often called "a problem is changeable", but its solution is still similar. According to their solutions, these problems can also be called "multiple solutions to one problem" or "multiple uses in one method".
3. Improve the problem-solving speed and master the problem-solving skills. There are two main factors to improve the speed of solving problems: one is clever and simple method of solving problems; The second is whether the mastery of conventional solutions has reached a high level of proficiency.
Five, learn to summarize, induction, training in place, to avoid problems.
Many students begin to do the questions as soon as they see them, which is also the place to avoid in a round of review. If you don't pay attention to the analysis of ideas and the application of knowledge points, the effect can be imagined. Therefore, it is suggested that students review the knowledge reviewed by the teacher in class before doing the questions, sort out the knowledge system, review all the knowledge points, have a complete and clear understanding of the knowledge structure they have learned, carefully analyze the knowledge, ideas and methods examined in the questions, and learn to summarize them without leaving any knowledge blind spots. In a round of review, we should pay attention to the refinement of all knowledge points. This process does not take a long time, and it will become more and more skilled in the subsequent stage. Therefore, developing a good habit of doing problems is helpful to train thinking and improve the ability to solve problems.
Practice makes true knowledge, and sufficient questions are the guarantee to turn theory into ability. With enough practice, we can not only master the knowledge points more firmly, but also understand the knowledge points more deeply, and avoid the phenomenon of "meeting but not right, right but not complete". Because the college entrance examination is still based on doing problems, the ability to solve problems is a direct reflection of the results of the college entrance examination, especially math problems. The ability to solve problems can not be improved by three or two questions, but requires a lot of repeated training and careful deliberation. There is a saying that "quantitative change leads to qualitative change". Therefore, when reviewing each chapter, students must do enough questions, fully understand the content of this chapter, and skillfully use the knowledge points of this chapter.
However, a lot of training is definitely not a crowd tactic. Because each chapter has goals, and training needs to be constantly summarized, both horizontally and vertically. As long as the questions in each chapter are done to a certain extent, we can feel what the knowledge points, typical questions, methods and skills in this chapter are. In other words, you can do it if you randomly select some college entrance examination questions about this chapter in recent years.