When organizing classroom teaching, teachers are limited by time and space, so it is impossible to take care of every student. 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.
Write an outline 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.
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.
Methods of memorizing thoughts
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.
five
Remember your feelings.
Mathematics learning is the synthesis of intelligence, emotion, will and action. The process of mathematics learning is accompanied by positive emotional experience and will experience. Recording your feelings in the learning process can be used to better regulate your learning behavior. For example, after a complicated exercise is successfully solved by a strong will, you can write down self-encouraging sentences such as "Good things are more grinding" to motivate yourself.
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Remember mistakes and reflect.
It is inevitable to make mistakes of one kind or another in the learning process. "Smart people don't make the same mistakes or fewer mistakes." Write down your mistakes and mark them with a red pen to warn yourself. At the same time, they should also point out the reasons for their mistakes, correct their thinking methods, mature in reflection and improve in reflection.
Why take math notes?
(1) Taking notes can strengthen memory. It is easy to forget what you have learned in class, because the memory in class is only short-lived and will be forgotten soon. If you don't leave any traces in your notes, where can you find the gaps in your memory? So I think taking notes should be regarded as an important way to improve academic performance.
(2) Taking notes can make the class more attentive.
For students with learning difficulties, be sure to take notes. Except for a few students, many students listened well in class, and seemed to understand what the teacher said in class, but they couldn't do the questions after class, and they didn't know what the teacher said in class, thinking methods and problem-solving steps. These students must take notes, and the teacher must check them himself. Practice shows that it is beneficial for students to learn mathematics. Some students are qualified in Guo Jing. Then he must take notes and study again and again. Although he can't create by himself, at least he can master what the teacher teaches. If the teacher teaches well, then such students can also become useful, even great. At least getting an average score in the college entrance examination is not a problem. For students with poor self-control, taking notes can keep them awake in class. Nowadays, students tend to be distracted in class. If they get into the habit of taking notes, they will not be so easily distracted. Effectively.
(3) Notes can help students develop the habit of self-study.
The process of students taking notes is also the process of students participating in the occurrence, development and application of knowledge. Grasping the key points of knowledge, the growth point of ability and the development point of thinking in participation is convenient for students to know which knowledge is clear and systematic and which knowledge is not fully understood and systematic, reproduce the thinking process of knowledge formation and problem solving, and cultivate students' questioning ability. Taking notes can promote students' study.
(4) Taking notes helps students to experience how to choose the right learning method to succeed. Classroom teaching can't improve every student's learning efficiency to the maximum extent, but taking notes can make students of different levels combine teaching and learning inside and outside the classroom, understand what they don't understand in class, and sort out and systematize unclear and unsystematic things, thus stimulating students' autonomous learning motivation, constructing autonomous learning mechanism and situation, and promoting the development of all students.
Second, how to take math notes
Since it is very important to take good class notes when learning mathematics, how to take math notes?
(1) Remember the outline
Most teachers have an outline when giving lectures, and they will write the outline of preparing lessons on the blackboard when giving lectures. These outlines reflect the key points and difficulties of the lecture, and they are organized, so they are more important and should be recorded in the notebook.
(2), remember 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 to understand the problems.
(3) Remember the doubts
If you have any questions about what the teacher said in class, you should write them down in time. Such doubts may be your own misunderstanding or the teacher's negligence. After writing them down, it is convenient to discuss with the teacher after class.
(4), remember the method
Remembering the problem-solving skills, ideas and methods taught by teachers can enlighten thinking, broaden horizons, develop intelligence and cultivate ability, which is of great benefit to improving the problem-solving level.
(5) Remember to summarize.
Remember the teacher's summary after class, which is very helpful to condense the content of a class, find out the relationship between the key points and parts, master the basic concepts, formulas and theorems, find out the existing problems, find out the rules and integrate the classroom content.
Third, the types of math notes
1, math class notes
In the explanation of new lessons, we should record the key points, keywords and deeper understanding of concepts emphasized by teachers; For theorems, the conditions and usage of theorems should be recorded; For the formula, we should record the structural characteristics, deformation characteristics, memory methods and using skills summarized by the teacher.
In the exercise class, the examples given by the teacher are all targeted and representative, which can reflect the application methods of relevant knowledge points or special problem-solving skills. When we take notes, don't copy the teacher's problem-solving process, just copy the examples, leave appropriate gaps in the notebook, and don't affect our listening because of copying the answers. In class, we should concentrate on thinking about the teacher's questions or listening to the teacher's explanation, and pay attention to the usage of the knowledge points or problem-solving skills emphasized by the teacher. Take time to write down the detailed steps in your notes independently after class, and make a summary of each example. You should summarize the usage of a knowledge point in the example, the solution of this kind of problem and some special skills. Only in this way can we reflect the role of example.
In the teaching and evaluation of test questions (or exercises), some topics have unique skills, and some topics reflect the special usage of a knowledge point, which we need to record. In addition, there are some topics that are a formula or a regular conclusion, which we can call second-class formulas or second-class theorems. We should not only record it, but also memorize it, which can provide us with a broader vision, at least in doing multiple-choice questions or filling in the blanks.
2, wrong questions to sort out notes
Problems in homework A good homework can truly reflect the effect of learning and expose the defects in learning. Errors in homework can be divided into general errors and individual errors, frequent errors and occasional errors. Recording the problems in homework, analyzing the causes of errors and re-establishing correct answers is actually a process of re-learning, re-understanding and further understanding the key points and difficulties of the textbook. By recording the problems in the homework, you can know which knowledge you are easy to confuse and make mistakes, take appropriate remedial measures in time, thoroughly understand and master the knowledge, and leave no tail and future troubles. Insisting on taking such notes is conducive to finding the weak links in your study in time. Conducive to the in-depth understanding of the knowledge learned; It is conducive to cultivating the ability to think and solve problems independently.
3, good topic highlights notes
To learn knowledge by "using one method for multiple purposes" and "changing one question", we should form a good habit of exploring laws. The mathematical propositions with internal relations are strung together to form a problem chain, which can be classified and recorded in notes to achieve the effect of "drawing inferences from others". When learning a problem, you will learn a kind of problem, do a problem and solve a series of problems. When you encounter a new proposition in the future, you will not think about the previous one, but consider it. What means can be used to turn it into a standard proposition? In the long run, it can eliminate the influence of negative thinking mode, make the basic knowledge learned clear, and solve problems vividly without confusion. "One method is multi-purpose" is the divergence of proposition angle and the convergence of problem-solving angle, and "one problem is changeable" is the divergence of proposition angle and problem-solving angle at the same time. Therefore, it is an effective way to cultivate creativity.
Fourth, several misunderstandings in taking notes
As the saying goes, "a good memory is not as good as a bad writing." Indeed, writing down the concepts, formulas and problem-solving skills that the teacher talked about in class and clearly saving the important information you have heard or seen will help to reduce the burden of review and improve learning efficiency. However, in actual learning, many students are too busy taking notes to deal with the relationship between listening, watching, remembering and thinking, thus affecting the learning effect.
One of the misunderstandings: notes have become teaching records.
Students are accustomed to the study of "the teacher speaks, remembers, recites and imitates the exam". After a class, they often take down a few pages of notes. These students rely too much on notes and ignore the teacher's explanation and thinking, thinking that it doesn't matter if the teacher doesn't understand, as long as they read the notes carefully after class. Doing so often ignores some wonderful analysis of teachers, making their understanding of knowledge superficial, increasing the learning burden and reducing the learning efficiency.
Myth 2: Notebooks have become problem sets.
Doing problems is the basic method of learning mathematics, and it is also necessary to accumulate more exercises. However, if you blindly copy the questions without seriously understanding the important mathematical ideas and methods contained in them, it will rarely involve the connection between knowledge points, the refinement of thinking methods and the arrangement of problem-solving strategies. Without your own research experience, notebooks become problem sets. You can't learn math well.
It is true that several typical exercises and their solutions should be recorded in the notebook, but we should not focus on the topic, but on the excavation of the value of the exercises, that is, pay attention to writing the comments on solving the problems. It's like road signs installed on both sides of the expressway, which will remind you when to slow down, when to turn sharply, when to meet a fork in the road and so on.
The same is true for solving problems. You should use short and pithy words as annotations and write down the flashing wisdom in the words, which is of great benefit to accumulate experience and improve mathematics literacy. After a period of time, you will often review the old and learn new things. In short, your notes should become your own experience in learning mathematics and guide your learning direction.
Myth 3: Notebook has become an expired "periodical"
Unfortunately, some students' notebooks, like overdue periodicals, have been abandoned for a long time and failed to play their due role. In fact, one of the experiences of many college entrance examination champions is to make their notes into personal "study files", the most important review materials.
Rational use of notes can save time, highlight key points and improve efficiency. Of course, it is necessary to regularly arrange supplementary notes in stages and establish a personalized learning material system. For example, a set of "wrong questions" can be established by classification, and the mistakes in each exercise and exam can be sorted out and analyzed. You can also organize your notes into categories such as "ingenious solution to wonderful problems", "method notes" and "error-prone problems". As long as we persist in doing this and constantly expand our achievements, we can overcome the "blind spot" and get out of the "misunderstanding". In the tense comprehensive review stage, you will be relaxed and orderly, and you can also spare more energy and time to systematize and informatize the knowledge you have learned.