In fact, mathematics is a simple subject, because the answer is unique, the question is clear, it is easier to master than other subjects, and the score is easier to improve. Those students who think that mathematics is difficult, have no clue when they meet new problems, and have done a lot of exercises, but the results are not great, in fact, they still have not grasped the learning tips of mathematics. On the whole, students don't know what learning is. From a small point of view, it is that students lack appetite for mathematics learning and have no mathematical thoughts. Learning is to let us discover an inner way of existence, and ideas are the process of connecting knowledge with problems. If you know this clearly, you will be relaxed and have a sense of direction. Then, like Archimedes, you will find the world.
First of all, you should cultivate three abilities:
These three abilities play a key role in the level of mathematics achievement. The three abilities of solving math problems in college entrance examination are:
1, know knowledge, know where knowledge comes from and where it is used;
2, good at analysis, a topic, can quickly find the conditions that can be used, corresponding to the appropriate knowledge in front;
3, good at thinking management, flexible thinking, good at active thinking, can solve problems quickly and accurately.
When describing this problem-solving ability, Mr. Cao gave a very appropriate example: a problem gave us some conditions and a goal. But there are still some gaps between the goals and conditions we need to fill. How to fill them? Fill in the blanks with the knowledge we understand and our problem-solving ideas. Well, you did this problem beautifully. In fact, study and work are the same, just like we deal with any problems in life. We can recall that when we encounter a problem, will we all take the lead in grasping the crux of the problem (people who are good at grasping the key points will deal with the problem efficiently and accurately. Instead, everything is in a mess? Grasping the key point is to grasp the target. In order to achieve this goal, let's first count what are the favorable conditions at present, and then create some conditions to accomplish the goal. In math problems, the topic is the goal; The favorable conditions are known conditions; Creating conditions is to find knowledge points with problem-solving thinking. Do you still think mathematics is abstract when you look at the problem like this? I often tell students not to study hard, and the words persistence, hard work, dedication and painstaking are all painful, which is not the best way to learn. The bright realm of learning is to learn an internal form of existence and find out what it is. When we understand the forms of knowledge, we can easily correspond to them. We know all the knowledge, and they know us. Only in this way can we get along happily.
In the thinking of solving problems, by constantly looking for "goal premise", that is, necessary thinking, it is possible to change with constancy, and the road is invisible. Teacher Zhuang gave a speech about mathematics to students all over the country: "Mathematics has infinite charm! She has the harmony of music, picturesque beauty and poetic realm; She gives life to truth and adds luster to our thoughts; She clarified wisdom and washed away all ignorance in history; There is novelty in plainness and art in novelty, which is mathematics. I will swim in the ocean of mathematics with my classmates, appreciate the beauty of mathematics, solve the mystery of mathematics, enjoy the wonder of mathematics, and keep exploring on the road of enjoying mathematics ... "
Secondly, in addition to the three abilities of solving math problems in NMET, you should also have a set of well-trained math review standard steps. Let's follow the road of full marks in mathematics and see how to control our thoughts and take a shortcut to high marks in mathematics.
First, the understanding and source of problem-solving ideas
Usually, people judge a child as "smart" or "not smart" based on his reaction to something or many things and whether he has his own opinions. For example, a "smart" child is often quick-witted, clear-headed and has his own opinions. Then we think that "quick response, clear thinking and independent mind" is the premise of cleverness. Students with good academic performance are required to be quick-thinking, clear-headed and independent.
Then the same is true for solving problems. You must be quick-thinking, clear-headed and independent. It is inevitable that different students will understand the same problem from different angles, and different viewpoints will eventually converge into the correct problem-solving process. Whether it is derivation, rigid application or doing problems by experience, it is a kind of thinking. Some students have gradually changed from unclear thinking at the beginning to clear thinking, and some students have no thinking at all, forming a gap in doing the problem.
If students can be taught the shortest thinking path when dealing with mathematical problems, and it is extremely clear, so that every student is a "smart child", they can be invincible in solving problems.
The source of problem-solving ideas is the view on the problem, that is, where is the first starting point.
Second, how to train problem-solving ability in a short time
In fact, we only need to master one kind of mathematical problem-solving thought, and that is necessary thinking. This is a general method to solve math test questions, and it is also the most direct and fastest way to answer questions. What is necessary thinking? Inevitable thinking is the idea of seeking premise through conclusion or a certain limited condition. Almost all mathematical propositions can be solved by this way of thinking. Here I use video to give two simple examples to illustrate how mathematical inevitability thinking is applied.
Looking at the mathematics test questions of the college entrance examination in recent years, we can see that the test questions have strengthened the investigation of the flexible use of knowledge points. This greatly strengthens the thinking ability of candidates. How can I improve my thinking ability? Many candidates rely on naval battles, hoping to do more questions to cope with the changeable examination questions. However, it is still difficult to obtain a scientific way of thinking with the skills of sea tactics, and even the results are minimal. The main reason is the random thinking of solving problems, not the so-called "not working hard enough" and other reasons. Because of the thinking ability, candidates form certain obstacles in solving college entrance examination questions. Mainly in two aspects, one is that we can't find the breakthrough point to solve the problem, and the other is that although we have found the breakthrough point to solve the problem, we can't continue to do so. How to solve these two obstacles? This chapter will introduce effective methods, so that candidates can get useful inspiration.
Third, find the basic method to solve the problem-starting with solving (proving)
When we encounter some difficult problems, we will find that the questioner has set up various obstacles. Starting from the known, there are many forks in the road, and it is more and more complicated to push forward, so it is difficult to get the answer. If we start with the problem, we will find out what we have to do to get what we want. After finding the "need to know", we will take the "need to know" as a new problem until we can communicate with the "knowable" we can get from the "known" and solve the problem. In fact, the "analysis method" used in inequality proof is the full embodiment of this kind of thinking, which we call "reverse thinking"-goal premise thinking.