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 exercises.
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, so that "doing more exercises" can really play a role.
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.
Consciously pay attention to the thinking method embodied in the topic in the process of solving problems, and form a correct thinking mode.
Mathematics is a world of thinking, and there are many thinking skills, so every problem will reflect certain thinking methods in the process of proposition and problem solving. If we consciously pay attention to these thinking methods, after a long time, we will form a "universal" solution to each kind of problem in our minds, that is, the correct mindset, and it will be easy to solve such problems at this time; At the same time, I have mastered more thinking methods and laid a certain foundation for doing comprehensive problems.
2. Do more comprehensive questions.
Comprehensive questions are favored by proposers because they use more knowledge points.
Doing comprehensive questions is also a powerful tool to test your learning effect. By doing comprehensive questions, you can know your own shortcomings, make up for them, and constantly improve your math level.
Do more exercise for a long time and do it several times a day. After a long time, there will be obvious effects and greater gains. How to treat exams?
Learning mathematics is not only for exams, but also for exam results, which can basically reflect a person's mathematics level and quality. In order to get good grades in the exam, the following qualities are essential.
Kung fu should be used in peacetime, and there will be no accidents before the exam. What you need to master in the exam should be mastered at ordinary times, and don't be tired the night before the exam. In this way, you can have abundant energy in the examination room. You should also let go of the burden, drive away the pressure, concentrate on the test paper, analyze it carefully and reason closely.
Examination requires skill. After the papers are handed out, we should first look at the questions and allocate time. If you spend too much time on a problem and haven't found a way of thinking, you can put it in the past for a while and finish what you have to do. Think about it later. After one question is finished, don't rush to do the next one, read it again, because the ideas in your mind are still clear and easier to check. For the answers to several questions, you can use the conclusion of the previous question when answering the following questions. Even if the previous question is not answered, just make it clear that the source of this condition can be used (of course, it is required to prove it with a title). In addition, you must consider the test questions comprehensively, especially the fill-in-the-blank questions. Some must specify the range of values, and some have more than one answer. Be careful and don't miss them.
Be calm during the exam. Some students get hot heads when they encounter questions that they can't understand. As a result, when they are anxious, they can't do what they can. This state of mind is an exam.