Concept is the cornerstone of mathematics. Learning concepts (including theorems and properties) requires not only knowing why, but also knowing why. Many students only pay attention to memorizing concepts and ignore their own background, so they can't learn math well. For every definition and theorem, we should know how it comes from and where it is used on the basis of remembering its content. Only in this way can we make better use of it to solve problems. Read more examples.

Careful friends will find that after explaining the basic content, the teacher will always give us some extra-curricular examples and exercises, which is of great benefit. The concepts and theorems we learn are generally abstract. In order to make them concrete, we need to apply them to the theme. Because we have just come into contact with this knowledge, we don't have enough skills to use it. At this time, examples will be of great help to us, and we can put the existing concepts in our minds in the process of reading examples.

You can't just look at the fur, not the connotation.

When we look at the examples, we really want to master their methods and establish a wider way to solve problems. If we look at something, we will lose its original meaning. Every time we look at a topic, we should clarify its thinking and master its thinking method. If we encounter similar topics or the same type of topics again, we will have a general impression and it will be easy to do, but we must emphasize one point unless we are very sure.

We should combine thinking with observation.

When we look at the examples, after reading the questions, we can first think about how to do it, and then compare the answers to see what is better than the answers, so as to promote our own improvement, or find out the reasons and sum up our experience.

Examples of various difficulties are taken into account.

Looking at the examples step by step is the same as "doing the questions" in the back, but it has a significant advantage over doing them: the examples have ready-made answers and clear ideas, and you can draw conclusions as long as you follow their ideas, so you can look at some skillful and difficult examples that are difficult to solve by yourself, but not beyond the scope of your study, such as competition questions with moderate difficulty. Do more exercise.

If you want to learn math well, you must do more exercises, but some students can learn it well by doing more exercises, and some students still can't learn it well after doing a lot of exercises. The reason is whether "doing more exercise" is correct. When we say "do more exercises", we don't mean "crowd tactics". The latter just can't think, but it can't consolidate concepts and broaden ideas, and it has a "side effect": applying what you have learned. When we say "do more exercises", we want everyone to think more about what knowledge it uses, whether it can explain more, whether its conclusion can be strengthened and popularized, and so on. We must really master the methods and do the following three things to make "doing more exercises" really work.

You must be familiar with all kinds of basic problems and master their solutions.

Every exercise in the textbook is aimed at a knowledge point, which is the most basic topic and must be mastered skillfully; Extracurricular exercises also have many basic questions, which are used in many ways and have strong pertinence. Do them quickly.

Many comprehensive problems are just the organic combination of several basic problems. If you master the basic problems, you can't worry about solving them.