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 each definition and theorem, we should know how it came from and where it is applied on the basis of remembering its content. Only in this way can we.
It is best to use it to solve the problem.
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 don't have enough skills to use it. At this time, examples will give us great help.
Busy, we can concretize the existing concepts in our minds in the process of reading examples, so as to have a deeper and more thorough understanding of knowledge. Because the examples added by the teacher are very limited, we should also find some by 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 example, we should really master its method and establish a broader problem-solving idea. If we look at a problem together and only remember the topic but not the method, we will lose our original meaning. Every time we look at a topic, we should sort out 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 in our hearts and it will be easy to do it.
But it should be emphasized that unless you are very sure, don't rely on subjective assumptions, which will make mistakes in experience and lead to a dead end.
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 the examples step by step is the same as the following "doing the questions", but it has a significant advantage over doing them: the examples have ready-made answers and clear ideas, and we can draw conclusions as long as we follow their ideas, so we can look at some skillful and difficult examples that are difficult to solve by ourselves without exceeding what we have learned, such as the competition questions with moderate difficulty.
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, the palm
I have mastered more thinking methods and laid a certain foundation for doing comprehensive questions.
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 test paper is handed out, let's take a look at the amount of questions and allocate the time. If you don't find an idea when you do the problem, you can put it in the past for the time being and finish what you want to do. We'll think about it later. When one topic is finished, don't rush to do the next one. You should read it again, because at this time, your mind is still clear, which is better than looking it up.
It's easier When answering questions with several questions, you can use the conclusions of the previous questions. Even if the previous question is not answered, as long as the source of this condition is clear (of course, it is a question of proof), it can be used. In addition, we must consider the questions thoroughly, especially the fill-in-the-blank questions. Some should indicate the range of values, and some have more than one answer.
Well, be careful and don't miss it.
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 anxious, they can't do what they could have done. This state of mind is that they can't do well in the exam. We might as well use the psychology of comforting ourselves during the exam: others can't do the questions I can't do, and (commonly known as the spiritual victory method) may calm our mood.
, so as to play their best level, of course, comfort is comfort, for those problems that can't be done at once, we still have to think hard and try our best to do it. There are certain steps.