The so-called "math learning, one step behind, one step behind", does it mean that you have left a lot of content behind, and you can't learn new knowledge anyway? That's not the case at all. I often tell my classmates that there are only two hopes for you to study hard, one is the classroom and the other is yourself. Listen carefully in class. If you don't know anything, it's because you didn't learn the old knowledge related to this knowledge point well, so that your thinking is stuck somewhere. What you have to do at this time is to make up the previous knowledge related to this knowledge point. In fact, the best way is to develop a good habit of previewing, preview new lessons in advance, find problems, seriously think about the causes of the problems, and see if it is because a certain knowledge point in the past has not been mastered well, so as to ensure that the new lessons can be understood. Of course, without perseverance, people will accomplish nothing. If you don't have the perseverance and determination to solve the problem by yourself, no one can do anything. The so-called evil deeds in heaven are still alive, but you can't. This is a fact.
To learn high school mathematics well, we must start from the following aspects:
First, run self-confidence through the process of solving problems.
In the usual learning process, many students feel that they have a good grasp, but once they do a problem, they often can't do it. The teacher pulled it and suddenly it became clear. In other words, these problems are not absolutely impossible. As long as you think carefully, analyze and synthesize, use various mathematical ideas and methods, compare drawing, writing and calculation, and through tortuous reasoning or calculus, you can gradually find the essential relationship between the conditions and conclusions of the topic. Self-confidence is the secret of success, not empty talk. Be confident in the face of slightly complicated problems. You know, these problems are generally not beyond our own knowledge, and we can solve them with what we have learned. Dare to think and be good at thinking, which is a very important thinking quality. When solving specific problems, we must carefully examine the questions, correctly distinguish conditions from conclusions, and grasp two main links: First, we must firmly grasp the * * * relationship between this problem and a class of problems, and think about the general ideas and general solutions of such problems; The second is to firmly grasp the particularity of this topic and the difference between this topic and this kind of topic. Choose one or several conditions as the breakthrough point to solve the problem, and see what transitional conclusions can be drawn from these conditions, the more the better, and then filter out useful conclusions for further reasoning or calculus. This is what teachers often tell students: "Smart students study together, and unintelligent students study together". You know, the ocean of problems is endless. Only by drawing inferences from others can we jump out of the ocean of problems and understand the mystery of mathematics learning.
Second, remember third, talk about "method" and "thought", and use "thought" to guide "method". The two complement each other. Necessary basic knowledge is the key to skilled problem solving.
Fourthly, forming good thinking quality is the basic mathematics to understand mathematical problems. As a discipline to cultivate people's thinking ability, it is fascinating with its rational thinking. Unlike sightseeing in the mountains, it is pleasing to the eye because of its charming scenery and lingering. Mathematics learning is to study the spatial form and quantitative relationship of things through thinking and reflection, so that the spatial form and quantitative relationship of things can be presented. Only by forming a good thinking quality and pulling away the appearance of things with the sharp blade of good thinking quality can we "see" the essence of things.
In the process of learning, we often have such a phenomenon. In class, the teacher made it very clear, and the students just nodded, which made me feel very clear. And let the students do the questions themselves, and they don't know where to start. The main reason is that students do not think deeply about what they have learned and do not understand the essence of what they have learned. Just like passing by, every time we go to other people's homes, we should remember the geographical environment around them, especially the special signs. To understand the characteristics of what you have learned and what you need to remember, especially what mathematical ideas and methods are involved in this part of knowledge, you need to master it in time. The content of this kind of memory should be carefully remembered, and only by remembering the necessary knowledge can thinking be based. In addition, pay attention to taking notes. Bacon said in On Knowledge: "Taking notes can make knowledge accurate. If a person is unwilling to take notes, his memory must be strong and reliable. " Pay attention to the key points the teacher said, especially some empirical and regular knowledge summarized by the teacher, so as to review in time after class. After-class review, we should think about which problems have been passed and which problems have not been passed, and do a good job of checking and filling gaps in time.
The above talks about how to learn high school mathematics well from four aspects. Besides what I said above, the key to learning mathematics well in senior high school is diligent study spirit, earnest and careful study attitude and good study habits. In the classroom, we should not only learn new knowledge, but also subtly learn the teacher's way of thinking to solve problems. In the face of a problem, we should think ahead, find out our own way of thinking, and then compare our own way of thinking with the way of thinking of teachers, learn from each other's strengths and form our own way of thinking. Change "I want to learn" into "I want to learn", cultivate the initiative of learning and overcome the situation of passive learning. Really master the essentials of mathematics learning. The test of whether you can learn math well is whether you can solve problems. Understanding and memorizing the basic knowledge of mathematics, mastering the ideas and methods of learning mathematics is only the premise of learning mathematics well, and the ability to solve problems independently and correctly is the symbol of learning mathematics well.