How can I learn math well? This is a topic that many friends care about. Here I would like to introduce some of my experiences for your reference.
First, deeply understand the concept.
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. To understand the concept deeply, you need to do more exercises. What is "doing more exercise" and how to do it? I will discuss the next three points with you.
Second, look at some examples.
Careful friends will find that our teacher will always give us some extra-curricular examples and exercises after explaining the basic content, 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 are not proficient enough to use it. At this time, examples will be of great help to us, and we can put what we think in the process of reading examples. Let the understanding of knowledge be more profound and thorough, because the examples added by teachers are very limited, so we should also find some examples ourselves, and pay attention to the following points:
1。 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.
2。 We should combine thinking with observation.
Let's look at an example. After reading the questions, we can think about how to do it first, and then compare the answers to see what our ideas are better than the answers, so as to promote our improvement, or our ideas and answers are different. We should also find out the reasons and sum up experience.
3。 Examples of various difficulties are taken into account.
Looking at examples step by step is the same as "doing problems" in the back, but it has a significant advantage over doing them: 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, difficult and difficult examples, such as competition problems with moderate difficulty, without exceeding what you have learned.
This can enrich knowledge and broaden thinking, which is very helpful to improve the comprehensive application ability of knowledge.
Learning mathematics well and looking at examples is a very important link and must not be ignored.
Third, 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 or not. When we say "do more exercises", we don't mean "crowd tactics". The latter does nothing but think, and cannot consolidate concepts and broaden ideas. Moreover, it has "side effects": it confuses what has been learned, wastes time and gains little. When we say "do more exercises", we ask everyone to think about what knowledge it uses after doing a novel topic, whether it can be explained more, whether its conclusion can be strengthened and popularized, and so on.
1。 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; Extra-curricular exercises also have many basic questions, with many methods and strong pertinence, which should be done soon.
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.
2。 In the process of solving problems, we should consciously pay attention to the thinking method reflected in the topic in order to 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.
3。 Do more comprehensive questions.
Comprehensive questions are favored by proposers because of the many knowledge points used.
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.
Finally, I want to talk about 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.
First of all, kung fu should be used in peacetime, and don't surprise before the exam. You should master what you need to master in the exam at ordinary times, and don't get tired the night before the exam, so that you can have plenty of energy in the examination room. When you take an exam, you should let go of the burden, drive away the pressure, concentrate on the test paper, analyze it carefully and reason closely.
Secondly, exams need skills. After the papers are handed out, we should first look at the amount of questions and allocate time. If you don't find an idea when you do the problem, you can put it aside 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, but read it again, because at this time, your thoughts 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, as long as the source of this condition (of course, it is required to prove the topic) can be used. In addition, you must consider the test questions comprehensively, especially the fill-in-the-blank questions. Some should indicate the range of values, and some have more than one answer. Be careful and don't miss them.
Finally, be calm during the exam. Some students get hot heads as soon as they encounter problems that they can't do. As a result, when they are in a hurry, they can't do what they should. You can't get good grades in this state of mind. We might as well take advantage of the psychology of comforting ourselves during the exam: if I can't do the problem, others can't do it, and (commonly known as the spiritual victory method) maybe we can calm down and play our best. Of course, comfort is comfort.
Everyone has his own learning method. These are my views on learning mathematics for your reference. I hope I can give some inspiration and help to my friends. I'm satisfied.