First, we should change our ideas.
Junior high school, especially junior high school, can obviously improve your grades through a lot of practice. This is because junior high school mathematics knowledge is relatively simple and easy to master. Through repeated practice, you can improve your proficiency and grades. Even so, your understanding of some problems is not deep enough, or even unknown. For example, junior high school asked |a|=2, and few people made mistakes in the senior high school entrance examination. However, after entering high school, the teacher asked, if | A | = 2 and A < 0, what is A? Even the students in some key schools answered without thinking: a=2. Just to illustrate this problem.
Another example is a classmate of Grade One in Beijing No.4 Middle School. After the mid-term exam of Grade One last semester, he protested to the teacher that "you usually don't have much homework and exams, so I won't study", which also shows the importance of ideological change.
Mathematics in senior high school is theoretical and abstract, so it needs to work hard, think more and learn more.
Second, improving the efficiency of class is the key.
During students' study, the time in class accounts for a large part. So the efficiency of class determines the basic situation of learning. To improve the efficiency of lectures, we should pay attention to the following aspects:
1, preview before class can improve the pertinence of listening.
The difficulty found in the preview is the focus of the lecture; You can make up the old knowledge that you haven't mastered well in the preview.
2. Science in the process of listening to lectures.
First of all, make material and spiritual preparations before class, and don't leave books and books in class; Don't do too much exercise or read books, play chess, play cards or have a heated debate before class. In order to avoid being out of breath after class, or unable to calm down.
The second is to concentrate on class.
Concentration is to devote yourself to classroom learning, from ear to ear, from eye to heart, from mouth to hand.
Listening: Listen attentively, listen to how the teacher lectures, analyzes and summarizes, and listen to the students' questions and answers to see if they are enlightening.
Eye-catching: read textbooks and blackboard writing while listening to the class, watch the teacher's expressions, gestures and demonstrations, and accept the ideas that the teacher wants to express vividly and profoundly.
Heart orientation: think hard, keep up with the teacher's mathematical thinking, and analyze how the teacher grasps the key points and solves problems.
Mouth-to-mouth: Under the guidance of the teacher, take the initiative to answer questions or participate in discussions.
Reach: Draw the key points of the text on the basis of listening, watching, thinking and speaking, and write down the main points of the lecture and your own feelings or opinions with innovative thinking.
If you can achieve the above five goals, your energy will be highly concentrated, and all the important contents learned in class will leave a deep impression on your mind.
Pay special attention to the beginning and end of the teacher's lecture.
At the beginning of a teacher's lecture, it is generally to summarize the main points of the last lesson and point out the content to be talked about in this lesson, which is a link to link old knowledge with new knowledge. Finally, he often summarizes the knowledge in a class, which is very general and is an outline for mastering the knowledge and methods in this section on the basis of understanding.
4. We should carefully grasp the logic of thinking, analyze the thinking and thinking methods of solving problems, and stick to it, and we will certainly be able to draw inferences from others and improve our thinking and problem-solving ability.
In addition, we should pay special attention to the hints in the teacher's lecture.
For some key and difficult points in lectures, teachers often give hints about language, tone and even some actions.
The last point is to take notes. Notes are not records, but simple and concise records of the main points and thinking methods in the above lectures for review, digestion and thinking.
Third, do a good job in reviewing and summarizing.
1, review in time.
On the second day after class, you must do a good job of reviewing that day.
The effective review method is not to read books or notes over and over again, but to review through memories: first, combine books and notes to recall what the teacher said in class, such as the ideas and methods of analyzing problems (you can also write them in a draft book while thinking), and try to think completely. Then open your notes and books, compare and make up what you don't remember clearly, so as to consolidate the content of the class that day, check the effect of the class that day, and put forward necessary improvement measures for improving listening methods and improving listening effect.
2. Do a good unit review.
After learning a unit, you should review it in stages, and the review method is the same as timely review. We should review retrospectively, and then compare it with books and notes to make its content perfect, and then do a good job of unit plate.
3. Make a unit summary.
The unit summary shall include the following parts.
(1) knowledge network (chapter) of this unit;
(2) The basic ideas and methods of this chapter (which should be expressed in the form of typical cases);
(3) Self-experience: In this chapter, you should record the typical problems you made wrong, analyze their causes and correct answers, and record the thinking methods or examples you think are the most valuable in this chapter, as well as the problems you haven't solved, so as to make up for them in the future.
Fourth, about the problem of doing the problem.
Many students pin their hopes of improving their math scores on doing a lot of exercises. I don't think this is appropriate. I think, "Don't judge heroes by how many questions they do." The important thing is not to do more questions, but to do them efficiently. The purpose of doing the problem is to check whether you have mastered the knowledge and methods well. If you don't master it correctly, or even have deviations, the result of doing so many questions is to consolidate your shortcomings. Therefore, we should do a certain amount of exercises on the basis of accurately mastering the basic knowledge and methods. For intermediate questions, we should pay attention to the benefits of doing the questions, that is, how much we have gained after doing the questions. This requires some "reflection" after doing the problem, thinking about the basic knowledge used in this problem, what is the mathematical thinking method, why do you think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem have been used in solving other problems. If you connect them, you will get more. Of course, it is impossible to form skills without a certain amount of practice (homework assigned by the teacher), and it is also impossible.
In addition, whether it is homework or exams, we should put accuracy first and general methods first, instead of blindly pursuing speed or skills, which is also an important issue to learn mathematics well.
Finally, I want to say that "interest" and confidence are the best teachers to learn math well. The "interest" here does not mean studying mathematics and becoming a mathematician in the future, but mainly means not being bored and not becoming a burden. Great motivation comes from great ideals. As long as you understand the importance of learning mathematics, you will have unlimited motivation and gradually become interested in mathematics. With a certain interest, your confidence will be enhanced, and you won't be discouraged because of an unsatisfactory exam result. In the process of constantly summing up experience and lessons, your confidence will continue to increase, and you will increasingly realize that "interest" and confidence are the best teachers in your study.
Do more questions, and understand each question thoroughly. If it cannot be realized at the same time, the latter is preferred.
In fact, getting full marks in the exam doesn't mean how good he is at math. The key is mentality. Doing more questions and thinking can make you get into the state quickly during the exam without being nervous or anything.
I am a sophomore. Math used to be my weakness. After training last summer, I can get full marks in the basic exam now. :)
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In fact, as long as you work hard, there is no reason not to learn well.
I prefer to classify questions rather than read blindly. This helps to form your own problem-solving ideas.
I feel that when you do the problem, treat it as your favorite girl, just like talking to her. There are no difficult questions or simple questions, and the questions on the test paper are all equal. I used to learn difficult questions, but simple questions often lose a lot of points. This will overcome this problem.
Knowledge is the most important thing, or mentality. :)
Mathematics is a multi-functional subject, which is very logical and systematic. There should be more scientific learning methods to learn and master mathematics knowledge. If the method is right, you can "hard work pays off" and get twice the result with half the effort; If the method is wrong, it will be "thankless" and get twice the result with half the effort. If learning is effective, the more you learn, the greater your interest; If your academic performance is always low, you will gradually lose your confidence in learning. Whether to master more scientific learning methods is the key to learning success or failure. Especially in the new learning stage, with the increase of learning subjects and the acceleration of learning rhythm, it is necessary to adjust learning methods in time to meet the learning requirements of the new stage. Otherwise, you will fall behind and fall behind. We should learn to manage our own learning and master more scientific learning methods. Combined with many years of teaching experience, we believe that a more scientific learning method is mainly embodied in the following five basic links.
First, preview before class and take the initiative to attend classes.
"Everything is established in advance, and if it is not planned, it will be abolished." Classroom is a battlefield, learning is a war, and you can't fight an unprepared battle. If you have a math class the next day, you should be fully prepared on the first day. On the one hand, we should read through the relevant contents in the textbook to see what we know and what we have learned; What you don't understand is new knowledge that can only be understood through the teacher's explanation. Mark the parts you don't understand, do preliminary thinking and put forward the problems that need to be solved. On the other hand, you should do the exercises at the back of the textbook for the first time, and the questions you can't do should be marked and brought to class to solve. Doing so will enhance the purpose of attending classes, master the initiative of attending classes and improve the effect of attending classes. Long-term adherence to preview can also cultivate the habit of reading and form the ability of self-study.
2. Listen carefully in class and take notes.
You should enter the state in advance in class. The quality of preparation before class directly affects the effect of listening to lectures. Before the formal class bell rings and the teacher walks into the classroom, you should put the relevant textbooks (including notebooks and exercise books) and stationery on the desktop in advance and wait for the teacher to arrive. Don't expect the teacher to stand on the podium and wait for everyone to slowly rummage through the closet, looking for this and that. When teachers enter the classroom, they should take the problems that need to be solved in the preview process and concentrate on listening. We should also master the rules of teachers' lectures, pay attention to the particles of teachers' lectures, think positively and answer teachers' questions enthusiastically. Especially in class exercises and homework, we should strive to answer quickly and accurately. We should also grasp the main points of the teacher's lecture, take class notes and write down the main points, key points, difficulties, keys and typical examples of the teacher's lecture. There are still some questions that you don't understand, so that you can continue your study after class or ask a teacher for guidance.
3. Review in time and turn knowledge into skills.
Review is an important part in the learning process. When reviewing, you should read the textbook again, recall what you learned that day, recall the process of the teacher's lecture, reproduce what you learned in class, read the examples that the teacher said (these examples usually have a strong inspiration and demonstration effect on completing the homework), and understand and remember the basic definitions, theorems, formulas and rules (these are all knowledge points that must be mastered). Reviewing in time on the same day can reduce knowledge forgetting and make it easy to consolidate and remember. Regular review can systematize knowledge, deepen the understanding of knowledge and master the relationship between knowledge. At the same time, only systematic knowledge is beneficial to application, the transition from knowledge to skills and the mastery of updated knowledge. Review should be planned, not only to review the lessons of the day in time, but also to review all stages in time.
4. Seriously finish homework, form skills and skills, and improve the ability to analyze and solve problems.
Academician Yang Le answered the question of how middle school students learn mathematics well in three sentences: First, practice more on the basis of understanding, second, accumulate more on the basis of understanding, and third, step by step. The exercise here is to do the problem and finish the homework. Homework is the main means to practice using knowledge. Be sure to review your homework first. In addition to requiring independent completion of homework and opposing plagiarism, homework must also be written neatly and in a standardized format. Read and copy the questions carefully. If you copy the questions carefully, you can hone your will and examine the meaning of the questions. In the learning stage of the new lesson, copying questions is not an unnecessary burden, and you can't be lazy to copy questions on the pretext of taking up time. You should examine the questions before you answer them, and the answers should be correct. Check homework, reduce unnecessary mistakes and lose points, ensure the quality of homework, and form a good habit of being serious and responsible. Through homework practice, we can deepen our understanding of knowledge, consolidate what we have learned, form skills and skills, and cultivate our ability to analyze and solve problems. Homework should be handed in on time, and on the basis of independent completion on time, it should be correct, neat and rapid. All the mistakes pointed out by the teacher when correcting must be understood in time and corrected seriously. At the same time, multiple solutions to one problem are allowed, independent thinking is advocated, and creativity is encouraged.
5. Summarize in time and organize and systematize what you have learned.
After learning a topic or a chapter, you should make a summary in time. Summing up is to sort out the relevant knowledge of each topic and chapter, compare similarities and differences, find mutual connections, and extract substantive things, such as definitions, theorems, formulas, laws and so on. Summarize with concise words or make it organized and systematic with charts. The second sentence of Academician Yang Le's Introduction to Learning Methods requires "accumulating more on the basis of understanding". This materialized and systematic process is actually a process of accumulation, which can not only deepen the understanding of knowledge, but also promote the accumulation and memory of knowledge. There should be a summary at the end of each topic and a systematic summary at the end of each stage. When summing up, in addition to summing up what you have learned, you can also write down the associations, conjectures and discoveries inspired by relevant knowledge for further thinking and research. You can also sum up your own experience, experience, experience and lessons in learning methods. Especially after the half-term and semester exams, it is more necessary to summarize the learning methods in combination with the results of various subjects, and make the next stage of learning plan on this basis. At this time, experienced teachers will also organize students to communicate with each other, learn from each other's strengths, constantly adjust and improve, constantly improve their learning methods, and gradually learn to manage their own learning scientifically, so as to learn easily and effectively and constantly improve their academic performance.
The above five links are interrelated and influence each other. The degree of implementation of each link is directly related to the progress and effect of the next link. Be sure to preview before listening, review before homework, and often make a stage summary. When you come home from school every day, you should review your homework for the day, finish your homework for the next day, and then preview your homework for the next day. These three things are indispensable. Otherwise, there will be no guarantee of high-quality lectures the next day.
Methods of learning mathematics well
Mathematics is highly abstract, but it is widely used. It is naturally not so easy to learn mathematics well and make it work for us. As we all know, primary school students learn arithmetic mainly by finding specific examples and methods from practical topics. It meets the requirements of correct and rapid calculation and intuitive understanding of some simple plane graphics and three-dimensional graphics. After entering middle school, we should further study the knowledge of quantitative relations on the basis of elementary school arithmetic, systematically study the knowledge of spatial form, and learn the knowledge of the combination of form and number. Therefore, the task of learning mathematics in middle schools, especially high schools, is relatively heavy. It's also important. How well you learn mathematics is not only related to whether you can learn physics, chemistry and other subjects well today, but more importantly, whether you can solve practical problems in production practice after graduation, and whether you can approach and catch up with the advanced world level on the road of climbing the scientific peak in the future. Therefore, laying a good foundation for middle school mathematics is of great significance for building China into a powerful socialist country with agricultural modernization, industrial modernization, national defense modernization and scientific and technological modernization.
In middle school mathematics textbooks, some basic concepts are gradually introduced. It can be said that understanding the basic concepts clearly is the first step to learn mathematics well. If you don't understand the concept clearly, you must prove the theorem and do exercises in a hurry. Some students will pick up a pen and do exercises after listening to the teacher's lecture in class. At this time, it is probably difficult to calculate the following two types of exercises: one is exercises that have correctly understood the basic concepts used. Because of the correct understanding of the concept, it is easier to solve the assigned exercises. Conversely, through the calculation of the exercises, the concept and the conclusions derived from the concept can be further clarified. The other is an exercise similar to the example that the teacher showed you in class. For such exercises, as long as it is "painting a gourd from the script", even if the basic concepts are not clearly understood, it can be worked out, but if you change the exercises a little, you will feel at a loss. Nowadays, middle school students seem to be able to calculate, but it is not uncommon to "draw red". Many students feel difficult about the problems in the math contest because they have never seen such problems before.
It is very important to understand the basic concepts of mathematics correctly, because this is the premise of mastering the basic knowledge of mathematics. Just like building a house, the foundation is firmly laid, and the house built on it will not collapse in the future. Therefore, the advantage of correctly understanding basic concepts is not only that you can solve several exercises. The only way to lay the foundation is to study repeatedly. Don't think the basic concepts are abstract and difficult to understand, so just put them away, and don't think they are easy to understand, but don't delve into them. Some mathematics contents learned in high school are often easy to ignore because they have been learned before junior high school. I don't see that these contents seem to be repeated with some contents of junior high school, but they are actually spiraling up. From addition of rational numbers to algebraic expressions and fractions. It developed to the addition of functions, and later to the addition of force and velocity (vector) in physics. This is a concrete example. Don't be afraid to do the calculations in these courses, and don't be impatient. All basic things are always monotonous and lack of change, which easily makes people feel bored and leads to the incorrect idea that "it doesn't matter if you don't pay attention now". On the contrary, the foundation is not well laid today. At that time, I thought like this: to really learn, I am afraid it is too little to learn once, and I have to repeat it. Some people learn to read it once, but I am often not so fast myself. What should I do? Then read more, read more and think more until you understand. I once read a book or a paper and never let it go. Either I don't look at it, I see it thoroughly, once or twice, as many as five or six times. Every time I watch it, I always feel that I have a new experience than before. It can be seen here that the so-called "understanding" usually has a depth between the two. There must be a high standard. The harder you work, the more you will gain. If you want to learn the basic knowledge in a down-to-earth manner, you must work hard. I always read a foreign language before translating it. All the books I have read have notes, which I have kept all the time, and some of them are still often used now. Because I often read and work hard with my hands and brains, I am impressed. Sometimes, I can often say the answer to this question on that book, that volume and that page, and I can take it out from somewhere on the bookshelf at once. I don't believe that the human brain is so powerful. Learn it once, do a few exercises, and with little or no actual visualization, they will fully understand it, consolidate it, and never go out of shape for the rest of their lives. Learn to ask questions, never know, never. It is not easy to "print" clearly. To achieve such a state, we must go through hard work, repeated study and practice. It's better to spend more time studying mathematics, so that you can learn more accurately, deeply and thoroughly, and the knowledge you have learned is more solid and reliable, so that you can "be prepared" and "just in case". You should have enough estimates of the difficulties in your study.
Scientific research, first of all, is "seeking truth from facts, step by step", and then on this basis, we can "go hand in hand and catch up". How can it blossom and bear fruit without foundation and further leap in soil?
In this way, students have no objection to reading extracurricular books on the premise of completing their homework; Not only do you not oppose it, but you should also encourage it. Just be careful, even in this case, don't be greedy and cheap, and swallow the jujube without digesting it. If you want to read this extra-curricular book and find another one, it is easy to have problems such as poor reading effect, vague concept and confused thinking. Originally, you wanted to read some extra-curricular books to help improve your professional level, but the result may be counterproductive. Therefore, we are teachers in our university. I hope that students with excellent grades can choose a math book with appropriate degree under possible conditions, read it carefully, calculate it carefully, do the exercises well and complete them in a down-to-earth manner, and then consider the second one. When reading extracurricular books, you should practice your hands-do more exercises, practice your brain-think more. Because, to understand the basic concepts and theorems in mathematics, we must go through practical calculus, otherwise it is impossible to read well. However, if you don't think about it after reading a book and doing exercises, you will only be satisfied with doing arithmetic. It is also impossible to accumulate experience, improve understanding and master the essence of mathematics. To learn mathematics well and make good use of one's own thinking organs, one must advocate thinking, learn how to analyze things, and form the habit of analysis. Mathematics, especially advanced mathematics, contains more and more abstract concepts, although you feel that you understand them all when you read them. If we don't think and analyze the development of concepts and the relationship between concepts, we will often finish reading a book or learning a branch. Looking back, you will feel that the part is "clear", but the whole does not understand, or even puzzling. In this way, if you apply this branch of knowledge to another architectural theory or practical problem, there will be problems. In short, the way to learn math well is to lay a good foundation and do more.