Of course, it is not enough to be interested. Still have to study hard. At the very least, you have to memorize the conceptual formulas you have learned in books, and you'd better preview the new lessons when you have time, so that you can master the new lessons faster, more and better the next day. Simply take notes in class, write down the main points, review and summarize at home at night, and learn new things by reviewing the old ones. If you have any questions you don't understand, ask the teacher until you understand them. When there is a simpler way to solve the problem than the teacher, you can bring it up and discuss it with the teachers and classmates. Don't be afraid to ask questions, because you may be wrong. Asking questions is a good opportunity to exercise. Teachers are people who inspire us, not "crutches". The key is to work hard and use more brains. You can usually do more flexible questions after class. Sometimes a difficult problem can't be solved, and after thinking for a few days, there will be a joy of success.
Careful and earnest are also indispensable. Answer every question carefully and concentrate. A math test paper needs to calculate most of the questions. You should calculate carefully. Some questions have traps, you must be careful. You must check the paper carefully after you finish it.
When you do a problem, you have to find out the key conditions according to the previous one and understand them carefully. Generally speaking, every sentence and condition is useful, so we should make good use of it to solve problems.
Part I: What kind of people are easy to learn math well?
A person with a broad knowledge background
Educator Suhomlinski said, "The more complicated the materials that must be memorized, the more generalizations, conclusions and rules that must be memorized, and the wider the' knowledge background' of the learning process." In other words, if a student can firmly remember, understand and flexibly use formulas, rules, conclusions, etc. He must read and think about many materials that don't need to be memorized.
In the survey, we found that college students with excellent math scores often have a wide range of knowledge, like reading some famous literary works and biographies, and also like reading some math books, such as The Secret of Quick Calculation, Mathematical Physics for Middle School Students, and interesting knowledge books in libraries and bookstores. In addition, books related to mathematics are recommended: interesting mathematics series, mathematics books for training thinking ability, and mathematics in stories.
In addition to establishing a broad knowledge background, reading is also of great help to improve the ability to examine questions and interest in learning.
Second, people who like "lazy"
Can you believe it? People who like "laziness" often learn mathematics well, and their personality characteristics are often advocating simplicity. Why? Because this kind of person will think, "Is there an easier way?" Think like this often, and you will gradually have the ability to grasp the key points and key links at a glance and see the most convenient solution at a glance.
Third, people with rich life experience.
The first step to learn mathematics well is situational understanding. Mathematics is a subject to solve practical problems. Without life experience, it is often difficult to turn mathematical knowledge into problem-solving methods. During the investigation, we found that people who learn mathematics well have the following life experiences:
1. I often experience with my elders and even help them do some housework, such as selling things, buying things, accounting for holidays and so on.
2. Have practical interest. In their spare time, many people will play ball games and go shopping, but these college students we surveyed are more willing to do something meaningful. A college student mentioned that when he was in junior high school, he used to measure the area of the new campus with a bicycle and a tape measure with a good friend.
Part two: How to learn mathematics.
First, proper study methods and habits.
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. Proper methods can 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. According to the essence of excellent college students' mathematics learning experience, we believe that more scientific learning methods and habits are mainly embodied in the following five basic links.
1, prepare well before class and take the initiative in class. Everything is established in advance, and it is abolished if it is not foreseen.
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.
3. Review in time and turn knowledge into skills. Review is an important part in the learning process. 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, an educational authority, answered the question of how middle school students learn mathematics well in just three sentences: First, practice more on the basis of understanding; Second, accumulate more on the basis of understanding; Third, step by step. The exercise here is to do the problem and finish the homework.
5. Summarize in time and systematize what you have learned. After learning a topic or a chapter, you should make a summary in time. 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 points are indispensable, otherwise there will be no guarantee of high-quality lectures the next day.
[Tip: Use the wrong book skillfully.
In the usual study, the teacher will ask the students to prepare a wrong book for students to review after class, but usually the teacher only emphasizes that students review and browse their own wrong books after class, and rarely asks to read others' wrong books. In fact, it is necessary to often borrow students' wrong questions. Note when borrowing:
First, borrow the wrong books of students who are taller than themselves to enrich and broaden their knowledge. Second, look at the wrong problem books of students who are lower than themselves, so as to often sound the alarm for themselves. At the same time, you should make your own reading notes for your reference. Read it at least twice a week at the beginning, and then read it for a week after two weeks, so that it is gradual. This method can be applied to other disciplines. ]
Second, good learning motivation and interest.
Learning motivation is the direct driving force to promote students' learning, which enables students to learn actively. There are many factors that affect students' learning motivation and interest. In this survey, there are: words of encouragement from teachers and parents, through some small skills, such as math jingles, interesting math problems, math storytelling, etc., to cultivate students' interest in math learning from an early age. The sense of accomplishment and honor gained after solving practical problems with mathematical knowledge or obtaining results, such as calculating the area of the book, the circumference of the tire, winning the competition prize, etc.
Hua said, "If you are interested, you will never get tired, and you will never get tired, so you will find time to study."
Third, strong will.
Having the right learning motivation does not mean that students can successfully complete the whole learning process. In the process of learning mathematics, they will encounter many difficulties, large and small. It requires a strong will to enable students to establish firm confidence, face difficulties bravely, and then overcome difficulties and acquire knowledge and skills. Many students have poor academic performance, not because of intelligence or other problems, but because they lack the strong will to overcome difficulties. When you encounter difficulties, you "retreat", so your academic performance is always failing. To cultivate students' tenacious will and perseverance, we should start with improving students' learning consciousness and tenacity. Self-consciousness means that students deeply understand the purpose and significance of learning mathematics, so as to study hard consciously. When students realize the relationship between current learning and the future of their motherland and their own future, and clarify their responsibilities, they can eliminate external interference and temptation and make learning a conscious action. The clearer the purpose of learning, the clearer the understanding of the meaning of learning, and the stronger the consciousness of learning. Perseverance refers to the quality of persistently overcoming difficulties when completing learning tasks. In the process of learning, students will always encounter some difficulties. It is a sign of perseverance to meet them with confidence and work hard to overcome them. This is a very valuable quality. With this quality, you will not be discouraged when you encounter difficulties or setbacks in your study; When you get good grades, you won't be complacent, but you should be good at summing up experiences and lessons, exploring the laws and methods of learning and going forward bravely. This will quality is very necessary for cultivating creative talents.
Fourth, self-confidence and diligence
Self-confidence and diligence are also two non-intelligence factors that have an important influence on mathematics learning. It is more important for underachievers to establish self-confidence and believe that they can learn math well through hard work. Because if students lose their confidence in learning, then they lose their spiritual strength to overcome difficulties. The acquisition of mathematical knowledge and skills and the improvement of mathematical ability are inseparable from the diligence and efforts of students. Therefore, it is very important to cultivate students' studious and assiduous spirit. Mathematician Zhang Guanghou said: "There is no shortcut on the road of learning mathematics, let alone opportunism. Only by diligent study and perseverance can we achieve excellent results. " It can be seen that diligence can make up for some intellectual deficiencies of students and promote the development of students' mathematical ability.
Fifth, a positive attitude.
Emotion is an attitude and psychological experience of human beings towards objective things. In our research, we found that all college students who have always maintained good math scores often communicate with their primary and secondary school teachers, establish a good teacher-student relationship, and constantly communicate with their classmates about the problems they encounter in their studies, constantly learn from each other, share experiences and make progress together.
Let me give you an example: Li Ming's math score is better. When his classmates ask him questions about mathematics, he always helps them patiently. Through this process, he not only helped his classmates, but also had a deeper understanding of mathematics knowledge. "You have an apple and I have an apple. Exchange is still an apple; I have an idea, and so do you. If you exchange, it will become two ideas. " Li Ming's deskmate thinks that he studies well and is afraid that others will learn some of his knowledge and abilities. He had to block his notes with his hand for fear of being seen by others, so his knowledge could only be passed on to him by himself and his teacher, and he soon fell far behind Li.
Through the above analysis, we find that it is not difficult to learn mathematics well. This is closely related to the family, society and school where children grow up. Parents are advised to show their children more useful books and videos, and let them participate in some useful activities to provide a good growth environment for their children.
I like math, and I'm afraid of math at the same time. I'm afraid I can't understand and learn. As it turns out, I did encounter difficulties in my study. But when there is plenty of time, you can preview the course, and the teacher can barely understand. The problem is that I found my own shortcomings-I can't apply what the teacher said. I really don't want to do the problem that I can't do, but it's useless. I have to think carefully about the examples, analyze them slowly, and sum up the solutions. If I do more, I will use them gradually. At the beginning of school, I can spend a lot of time doing such programs, but in the end, the busier I am, the less time I can squeeze in to preview, and even have no time to do exercises and ask questions after class. There are so few teachers in class that I have no time to consolidate, and the math content is getting more and more difficult. I've reached another low point. At that time, I could only simply put down math and take time to review when I was busy. This review period is very difficult. Sometimes I can only do more than 20 questions in a few hours, but I persisted and basically found the lost content. I got satisfactory results in the exam.
Junior high school mathematics is mainly divided into algebra and geometry, and the proportion of algebra and geometry in senior high school entrance examination is slightly larger than geometry (I don't know where you are from, but our senior high school entrance examination in Jinan, Shandong Province is like this).
Algebra mainly has the following points: 1, the operation of rational numbers, mainly about the three-level operation of rational numbers (addition, subtraction, multiplication and division). Here we should pay attention to the symbolic consciousness of numbers and letters, that is, don't be influenced by primary school numbers, and don't do problems as soon as you see letters. 2. Three-level operation of algebraic expressions, pay attention to the cultivation of symbol consciousness, factorization interchangeable with multiplication of algebraic expressions, and pay attention to the positive, negative and deformation of square difference formula and complete square formula. 3, the equation, will be one yuan once, two yuan once, three yuan once, one yuan twice four equation solutions and applications, remember, the equation is a method, is a means of solving problems. 4. Functions will recognize the images of linear functions, quadratic functions and inverse proportional functions, remember their characteristics and apply them according to conditions. Pay special attention to quadratic function, which is the key and difficult point of the senior high school entrance examination. It will be used to create a difficult problem in an application problem.
Geometry mainly has the following points: 1, and you should be familiar with recognizing various plane and three-dimensional figures. 2. Translation, rotation and axial symmetry of graphics. This examines your spatial imagination and does more questions. 3. Prove the congruence and similarity of triangles, pay attention to the complete process and strict steps, recite five methods to prove the congruence of triangles and four methods to prove similarity; There are also properties such as isosceles triangle, right triangle and golden triangle, which will be of great help to prove the problem if they can be applied. 4, quadrilateral, grasp the concepts of parallelogram, rectangle, square, diamond and trapezoid, make a big fuss about the subtle differences between them in the selection, pay attention to their judgment and nature, and will also be tested in the proof. 5. Circle, I haven't studied it in detail here, because this is not the focus of our senior high school entrance examination, but the circle will be very difficult, and its knowledge is very broken. The problem of circle is composed of many tiny points.