Teachers should leave a proper amount of homework after a class. Homework has three functions: one is to consolidate the relevant knowledge points learned that day, the other is to examine students' understanding and mastery of various knowledge points, and the third is to cultivate students' rigorous and orderly style. Because of the pertinence of homework, you should review the knowledge points, questions, problem-solving methods and skills you learned that day before writing homework.
The key to doing the problem is to analyze the problem and have a correct analysis method. Introduce it to the students here? Double-sided clamping analysis? That is, from two aspects: known topics and conclusions.
On the one hand, from the conclusion analysis, what is this problem for us. What kind of questions do you belong to? Think about how many methods there are for this kind of topic, and what conditions and background each method needs; On the other hand, from the analysis of known conditions, it depends on how many known conditions there are, what information each known condition can provide us, analyze the relationship between conditions, and judge what kind of problem-solving background each condition can create for us. Next, we should think about whether the information provided by the known conditions is the information needed for solving. If so, the train of thought of this problem will be opened. If not, it depends on how different the known and the conclusion are, and there are other secrets. Can implicit conditions be deduced from the known conditions, so that the known information can communicate with the required information?
Double-sided clamping analysis? It boils down to one sentence? From conclusion to method, from known to essential thinking? . Clever use? Double-sided clamping analysis? We are required to master every knowledge point skillfully in our usual study, and at the same time accumulate various problem-solving methods for a certain topic. In this way, when we analyze the problem, we are as comfortable as taking something from the bag.
When a question is done, we should not stop thinking, but also let our thinking by going up one flight of stairs. You can try the following methods:
(1) This problem can be solved with the knowledge in this lesson, and whether it can be solved with the knowledge (or tools) in other chapters. For example, an inequality problem can be solved by function method, vector method, trigonometry method, plane geometry method, analytic geometry method and so on. This can not only solve many problems, but also connect the knowledge of different chapters.
Think about whether the known conditions of this problem can be reduced or changed, then what will happen to the conclusion and the method of solving the problem?
(3) whether the conclusion of thinking about this question can change the method of asking questions and what will happen to the method of solving problems?
④ Think about whether the known and the conclusion are interchangeable, and construct a new topic through reverse thinking. Can this problem be solved? How?
If we can do the above thinking, it will be of great benefit to train our thinking ability.
Finally, I want to tell you that the steps to do the problem should be complete, the reasoning should be strict and the drawing should be accurate. Only by forming such good habits can we get more in the exam? Step by step? .