Use your hands and brains to take notes.
To learn high school mathematics well, we must change and improve our learning methods. Doing math notes well is undoubtedly a very effective link, and being good at taking math notes is a reflection of a student's good at learning. So, what should I write in my math notes?
First, an overview of the content. Most teachers have an outline when giving lectures. When giving lectures, the teacher will present the clues, key points and difficulties of a lesson on the blackboard concisely and clearly. At the same time, the teacher will make it organized and intuitive. Write down these outlines so that you can review after class, grasp the knowledge framework as a whole, and be clear and complete about what you have learned.
Second, the problem. Write down the questions you don't understand in class in time, so that you can ask your classmates or teachers after class and make the questions clear. When organizing classroom teaching, teachers are limited by time and space, so it is impossible to take care of every student. Therefore, some questions are difficult for some students. Because there is no time to think mature in class, write down the difficult questions, continue to think and explore after class to understand and master, and avoid the fault of knowledge and the defects of methods.
Third, the way of thinking. The problem-solving methods and analytical ideas introduced by the teacher in class should also be recorded in time and digested after class. If you are in doubt, analyze it independently first, because it may be your own misunderstanding or the negligence of the teacher. After writing it down, it is convenient to discuss it with the teacher in time after class. Remembering the problem-solving skills, ideas and methods taught by teachers is helpful to inspire thinking, broaden horizons, develop intelligence, cultivate ability and improve the level of problem solving. On this basis, it will be more valuable if we can actively study and find another way.
Fourth, summary. Paying attention to the teacher's after-class summary is very useful for concentrating the content of a class, finding out the relationship between the key points and each part, mastering the basic concepts, formulas and theorems, finding the rules and integrating the classroom content. At the same time, many experienced teachers, when summing up after class, on the one hand inherit what they have learned, on the other hand assign preview tasks or point out what to learn later. Taking notes can master the initiative of learning, make preparations in advance, and make clear the objectives and tasks.
Fifth, wrong reflection. It is inevitable to make mistakes of one kind or another in the learning process. Write down your mistakes and mark them with a red pen to warn yourself. At the same time, you should also point out the causes of mistakes, correct ideas and methods, mature in reflection and improve in reflection.
Do the questions well and form good habits.
If you want to learn math well, it is inevitable to do more problems, and you should be familiar with the problem-solving ideas of various questions. At the beginning, we should start with the basic problems, take the exercises in the textbook as the standard, lay a good foundation repeatedly, and then find some extracurricular exercises to help broaden our thinking, improve our ability to analyze and solve problems, and master the general rules of solving problems.
Selected themes. Only by solving high-quality and representative problems can we get twice the result with half the effort. However, the vast majority of students are still unable to distinguish and analyze the quality of the questions, so they need to review the exercises under the guidance of the teacher to understand the form and difficulty of the questions in the college entrance examination (Q bar).
Analyze the topic. Before you solve any math problem, you must analyze it first. Analysis is more important than more difficult topics. We know that solving mathematical problems is actually to build a bridge between known conditions and conclusions to be solved, that is, to reduce and eliminate these differences on the basis of analyzing the differences between known conditions and conclusions to be solved. Of course, in this process, it also reflects the proficiency and understanding of the basic knowledge of mathematics and the flexible application ability of mathematical methods. For example, many trigonometric problems can be solved by unifying angles, function names and structural forms, and the choice of trigonometric formulas is also the key to success.
Reflect in time. Solving problems is not the goal. We test our learning effect by solving problems, and find out the shortcomings in learning so as to improve and improve. Therefore, in the learning process of high school mathematics, it is very important to summarize after solving problems, which is a great opportunity for us to learn. For a complete topic, there are the following aspects to be summarized: ① Knowledge, which basic knowledge such as concepts, theorems and formulas are involved in the topic, and how to apply these knowledge in the process of solving problems. ② Method: How to start, what problem-solving methods and skills are used, and whether they can be mastered and used skillfully. (3) Whether the problem-solving process can be summarized into several steps (for example, there are three obvious steps to prove the problem by mathematical induction). (4) Can you sum up the types of questions, and then master the general problem-solving methods of such types of questions?