(1) Taking notes can strengthen memory. What you learn in class is easy to forget, because the memory in class is only short-lived and can be forgotten soon. If you don't leave some traces in your notes, where can you find the gaps in your memory? So I think we should take notes as an important way to improve our 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. They seemed to understand what the teacher said in class, but they didn't do the questions after class, and they didn't know how the teacher talked about these contents, thinking methods and problem-solving steps in class. These students must take notes, and the teacher should check them himself. Practice shows that it is beneficial for students to learn mathematics. Some students, whose qualifications belong to Guo Jing's category, must take notes and study repeatedly. Although they can't create by themselves, at least they can master what the teacher teaches. If the teacher teaches correctly, then such students can become useful, even overqualified, at least it is not a problem to get an average score in the college entrance examination. For students with poor self-control, taking notes can keep them awake in class. Nowadays, students tend to be distracted in class. If students get into the habit of taking notes, they will not be easily distracted. Taking notes effectively can not only accumulate learning materials, but also help students concentrate on class and prevent desertion.
(3) Notes can help students develop the habit of self-study.
The process of students' note-taking is also the process of students' participation in the occurrence, development and application of knowledge, in which they grasp the main points of knowledge, the growth point of ability and the development point of thinking. It is convenient for students to know which knowledge is clear and systematic and which knowledge is not fully understood and systematic, reproduce the process of knowledge formation and problem-solving thinking, and cultivate students' questioning ability. Notes can promote students to learn to learn.
(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 help students at different levels to combine teaching and learning in and out of class, to understand what they don't understand in class, and to clarify and systematize what is unclear and unsystematic. So as to stimulate students' autonomous learning motivation, construct autonomous learning mechanism and situation, and promote 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 and make the questions clear.
(3) Remember the doubts
If you have any questions about what the teacher said in class, you should write them down in time. This doubt 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.
Pay attention to remember the teacher's after-class summary, which is very useful for concentrating the content of a class, finding out the relationship between key points and parts, mastering basic concepts, formulas and theorems, discovering existing problems, discovering laws and integrating 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, use skills and so on 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 down 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 explanations, and pay attention to the usage of knowledge points or problem-solving skills emphasized by the teacher. After class, I will take the time to write down the detailed steps in my notes independently and make a summary of each example. It is necessary to summarize the usage of a knowledge point in the example, the solution of such problems, and some special skills. Only in this way can we reflect the role of example.
In the examination questions (or exercises), some topics have unique skills, and some topics reflect the special usage of a knowledge point, so we should record them. In addition, there are some topics, whether it is a formula or a regular conclusion. Let's call it the second kind of formula or the second kind of theorem. We should not only record it, but also memorize it, which can provide us with a broader vision, at least when we do multiple-choice questions or fill-in-the-blank questions.
2, wrong questions to sort out notes
Problems in homework, a good homework ring, 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, recurrent errors and accidental errors. In fact, it is a process of re-learning, re-understanding and re-understanding, and it is also a process of further understanding the key and difficult points of the textbook. By recording the problems in the homework, you can know which knowledge you are easy to confuse and make mistakes, take corresponding 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
Learning knowledge by "using one method for multiple purposes" and "changing one question" should form a good habit of exploring laws. It can achieve the effect of "drawing inferences from others" by stringing mathematical propositions with internal relations to form a problem chain and recording them in notes. Learn a problem, know 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 whether you have done it before, but about how it changed from a simple form and how to turn it into a standard proposition. In the long run, you can eliminate the influence of negative thinking mode, make the basic knowledge you have learned clear, and solve problems vividly without confusion. "One method is multi-purpose" is the divergence of proposition angle and the convergence of solution angle, and "one problem is changeable" is the divergence of proposition angle and solution 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 said 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 by himself, reviews the back and imitates the exam". After a class, they often take a few pages of notes. These students rely too much on notes, ignoring 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 will often ignore some wonderful analysis of teachers, make their understanding of knowledge superficial, increase the learning burden, reduce learning efficiency, and easily form a vicious circle.
Myth 2: Notebooks have become problem sets.
Doing problems is the basic method of learning mathematics, so we should 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 a notebook, but we should not focus on the topic, but should focus on the excavation of the value of the exercises, that is, pay attention to writing problem-solving comments. It's like road signs installed on both sides of the expressway. They 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. For mistakes or important problem-solving ideas, we should use short and concise words as annotations and write down the flashing wisdom, which is of great benefit to accumulating experience and improving mathematics literacy. After a period of time, if you take it out and look closely, you will often learn something new. In short, notes should be 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 have not played 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 also necessary to regularly arrange supplementary notes in stages and establish a personalized learning material system. If we can establish a "set of wrong questions" through classification, we can sort out and analyze the mistakes in each exercise and exam; You can also organize your notes into categories such as "clever questions and clever solutions", "method comments" and "error-prone questions". 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, it will be easy and orderly, and you can spare more energy and time to systematize and informatization the knowledge you have learned.