So, is it difficult to learn math well? Will it be difficult for you to go back to primary school math now? Of course not. That's right. On the one hand, it is because primary school mathematics is really not difficult; On the other hand, you are now a junior high school student, standing at another height of life. You look down on (or despise) the content of primary school mathematics that you have studied. First of all, you are a winner psychologically. In fact, we also need this kind of psychology when we study mathematics. Imagine, if you were a high school student, what would you think of the content of junior high school mathematics?
Nothing in the world is difficult for one who sets his mind to it. When you enter middle school, you should adapt to the teaching of junior high school mathematics as soon as possible and work hard on understanding. Mathematics is the most reasonable subject, and mathematical language is the most rigorous language. We should try our best to change the status quo of passive learning, study actively and catch up with our academic achievements as soon as possible. According to my years of teaching experience, I think it is very important for students to master correct mathematical ideas and methods, which is the key to get twice the result with half the effort.
The so-called "math learning, one step behind, one step behind", does it mean that you have left a lot of content behind, and you can't learn new knowledge anyway? That's not the case at all. I often tell my classmates that there are only two hopes for you to study hard, one is the classroom and the other is yourself. Listen carefully in class. If you don't know anything, it's because you didn't learn the old knowledge related to this knowledge point well, so that your thinking is stuck somewhere. What you have to do at this time is to make up the previous knowledge related to this knowledge point. In fact, the best way is to develop a good habit of previewing, preview new lessons in advance, find problems, seriously think about the causes of the problems, and see if it is because a certain knowledge point in the past has not been mastered well, so as to ensure that the new lessons can be understood. Of course, without perseverance, people will accomplish nothing. If you don't have the perseverance and determination to solve the problem by yourself, no one can do anything. The so-called evil deeds in heaven are still alive, but you can't. This is a fact.
I think that learning mathematics should be based on textbooks and achieve "four conscientiousness", that is, careful preview, careful listening, serious review and serious problem solving. There are five essentials to preview: ① draw the key points with wavy lines; ② Labeling formulas and conclusions; 3 Draw a question mark with a pencil where you don't understand and have questions; (4) Write the answers to simple exercises and the key points of solving problems at the back; ⑤ If there is more than one condition in the definition and theorem, the conditions should be numbered.
It is much better to go to class after careful preview than not to preview at all. After the lecture, before you do the exercises, you should review and check which words in the book you can't understand. Before you start doing exercises, you should think carefully and understand them. By doing problems, you can deepen your memory of what you have learned.
Below, I will explain in detail how to learn math well, hoping to help everyone.
First, put an end to negative self-suggestion and run self-confidence through the process of solving problems.
First of all, don't give up math study. Some students think that it doesn't matter that you are almost poor at math, but you can make up your total score by working harder in other subjects. This idea is very wrong. There is a "Cunningham's Law" in education: the amount of water in a barrel depends on its shortest board. Whether it is the senior high school entrance examination or the college entrance examination, only the all-round development of all subjects can achieve good results. Secondly, we should end negative self-suggestion. We have many exams every year, and it is impossible to get ideal results every time. Don't have hints like "I'm hopeless" and "I can't learn well" when I fail. On the contrary, always have confidence in yourself, believing that as long as you work hard, you will succeed in the end.
In the usual learning process, many students feel that they have a good grasp, but once they do a problem, they often can't do it. The teacher pulled it and suddenly it became clear. In other words, these problems are not absolutely impossible. As long as you think carefully, analyze and synthesize, use various mathematical ideas and methods, compare drawing, writing and calculation, and through tortuous reasoning or calculus, you can gradually find the essential relationship between the conditions and conclusions of the topic. Self-confidence is the secret of success, not empty talk. Be confident in the face of slightly complicated problems. You know, these problems are generally not beyond our own knowledge, and we can solve them with what we have learned. Dare to think and be good at thinking, which is a very important thinking quality. When solving specific problems, we must carefully examine the questions, correctly distinguish conditions from conclusions, and grasp two main links: First, we must firmly grasp the * * * relationship between this problem and a class of problems, and think about the general ideas and general solutions of such problems; The second is to firmly grasp the particularity of this topic and the difference between this topic and this kind of topic. Choose one or several conditions as the breakthrough point to solve the problem, and see what transitional conclusions can be drawn from these conditions, the more the better, and then filter out useful conclusions for further reasoning or calculus. This is what teachers often tell students: "Smart students study together, and unintelligent students study together". You know, the ocean of problems is endless. Only by drawing inferences from others can we jump out of the ocean of problems and understand the mystery of mathematics learning.
Second, read books carefully and understand mathematical language; Listen carefully and master the way of thinking.
It is a common problem for middle school students not to like math classes. Mathematics textbooks are written in mathematics language, including written language, symbolic language and graphic language. Its language is concise, logical, rich in connotation and profound in meaning, so reading a math textbook must not be fleeting.
Mathematical concepts, definitions, theorems, etc. They are all expressed in written language, so be sure to pay attention when reading. Symbolic language is rich in connotation, so we should write, argue and remember clearly. When reading symbolic language, we should tell its meaning and distinguish its characteristics.
Graphic language can not only reflect the relative position of elements, but also directly reflect the quantitative relationship. Therefore, when watching geometric figures, we should understand the hidden internal relations and quantitative relations between graphic elements; While looking at the image, we should glimpse the essence of the function from its shape.
If reading math books before and after class can meet the above requirements, learning math is an introduction; If we form a good reading habit from this, we can improve our grades just around the corner.
Listen attentively and think positively with the teacher's explanation. Do you understand the seemingly understandable concept in the preview? Has the mystery been solved? The teacher's oral insights, supplementary examples and wonderful answers should be recorded quickly. Writing a good speech will not only leave valuable information, but also help you concentrate. Don't lose the "watermelon" when taking notes, which means it won't affect the effect of class. Some students are busy copying notes, ignoring the teacher's idea of solving problems. This is "picking up sesame seeds and losing watermelon", but it is not worth the loss.
In class, you should constantly doubt and question, and dare to ask and answer questions. Think about whether the teacher's explanation is complete and correct, and whether the answer is rigorous and flawless. If you understand the example of blackboard writing, you should come up with a new solution; When in doubt, ask questions boldly. Contending to answer questions is by no means "graphic expression", but to elaborate one's own views and improve one's oral expression ability. Even if your answer is wrong, it is easy to book a certificate after exposing the problem. The most taboo in class is to follow blindly, go with the flow, follow the trend, and not pretend to understand.
Whether it is the senior high school entrance examination or the college entrance examination, most of the questions in the math test paper are basic questions. As long as these basic questions are done, the score will not be low. If you want to do the basic questions well, the efficiency of class at ordinary times is particularly important. Generally speaking, the content of an experienced teacher's class (especially the review stage) can be described as the essence. Listening carefully for 45 minutes is more effective than reviewing at home for two hours.
Third, study independently and learn to summarize; Make good use of reference books and broaden your personal horizons.
To develop the good habit of autonomous learning, we must do the following: ① Finish the homework on time and consolidate the knowledge we have learned. Only by finishing homework on time can we consolidate our knowledge and minimize forgetting. In the process of completing homework, it will increase the repetition rate of knowledge, promote one's thinking ability and give play to the creativity of solving problems. Students who study well should also pay attention to the cleaning and collection of homework, because this is not only a treasure of their own labor achievements, but also a good review material. (2) Review lessons in time to form a knowledge network. Chapter review, unit review and exam review are indispensable parts in mathematics learning, which have the function of connecting the past with the future. When reviewing, we should sum up knowledge and methods according to a certain system to form a "latitude and longitude network" of mathematics. The "essence" here refers to the knowledge of each branch of mathematics; "Weft" refers to the application of the same mathematical method in different branches. If you want to learn mathematics well, you must weave the "latitude and longitude net" of mathematics well. ③ Attention should be paid to the standardization of writing. Mathematics is a highly specialized subject, which has strict requirements on the process of expression and narration and the rules of symbol use. Therefore, when doing exercises, homework and exams, writing should be standardized. (4) Apply what you have learned and keep on pioneering and innovating. Mathematics has a strong correlation, and there is no insurmountable gap between old and new knowledge. Therefore, learning from books and associating can not only improve students' interest in learning, but also cultivate their creative thinking ability.
You can take the teacher's advice and choose reference books. Generally speaking, teachers will give some suggestions according to their own teaching methods and progress, and the number is basically around 1-2, not too much. After selecting reference books, we should do them carefully and completely. Every good reference book has a knowledge system. Some students do a little in this book and a little in that book. In the end, they made a lot of books, but they didn't finish reading them, so they couldn't form a complete knowledge system and the effect was not good. Doing more basic questions and setting a good time can improve the speed of solving problems.
In the sprint stage before the exam, it takes 1-2 days to make a set of test papers to maintain the state. The most important thing is to find and solve your own problems by doing problems, sum up the solutions to various problems and master them skillfully.
Here's a little suggestion: when you fill in the blanks, you can write some problem-solving processes in the blank space next to it for later review.
Four, remember the necessary basic knowledge is the key to skilled problem solving.
Some students think that only Chinese, English, politics, history, geography, biology and other subjects need to be memorized, while mathematics depends on operation, reasoning and analysis, and no memory is needed. This kind of understanding is all wet. "Learning from others" is the only way to learn. If you don't remember the necessary basic knowledge of mathematics, your mathematical thinking space will become narrower and narrower, which will inevitably lead to a dead end in your mathematics study. For example, I can't remember the "99 multiplication table" in primary school. Can I multiply smoothly? Although you understand that multiplication is the operation of the sum of the same addend, when you do 9×9, it is not cost-effective to add 9 9s to get 8 1. It is much more convenient to use "998 1" to find the results. For another example, when you solve the equation 2x2+3x- 1=0, if you don't remember the root formula of the quadratic equation with one variable, you can only use the complicated collocation method to reason step by step. In addition, this formula is the basis of learning the relationship between roots and coefficients of quadratic equations, quadratic functions, quadratic inequalities and other knowledge. Without this formula as the basis, the learning of these knowledge can only be in a dilemma. In fact, math learning is more like a game, such as playing China chess. If you don't remember the rules of the game, such as walking on the court and shooting every other player, how can you play China chess well? These rules of the game are like the basic knowledge in mathematics learning.
The New Curriculum Standard for Junior High School Mathematics in Nine-year Compulsory Education describes the basic knowledge in junior high school mathematics as follows: "The basic knowledge in junior high school mathematics includes concepts, laws, properties, formulas, axioms and theorems. Algebra and geometry in junior high school, as well as the mathematical ideas and methods reflected in their contents. "
Mathematical definitions, rules, properties, formulas, axioms, theorems, etc. Be sure to memorize it. It's catchy. We often say that we should remember on the basis of understanding. But some basic knowledge, such as definition, is unreasonable. For example, the definition of a linear equation with one unknown quantity, whose highest degree is 1 and whose coefficient cannot be 0, is called a linear equation with one unknown quantity. In this definition, why there is only one unknown instead of two or three, why the highest number of unknowns is 1 instead of 2 or 3, why the coefficient of unknowns cannot be 0, and so on. These questions are of little value, or the definition is just a prescribed or inherent meaning for a certain thing or phenomenon. And some basic knowledge, such as laws, formulas, theorems, etc. Know not only why, but also why. For example, the nature of parallel lines: two parallel lines are parallel, the same angle is equal, the inner angle is equal, and the inner angles on the same side are complementary. We should not only remember, but also be able to use what we have learned to explain why two parallel lines have such properties. This is what we call memory based on understanding. In the process of learning, it is inevitable that you will not understand some basic knowledge for a while. In this case, remember even by rote. After remembering it, you will gradually understand it in the learning process of the post-thread. In addition, some important mathematical methods and ideas also need to be remembered. Only in this way can you solve mathematical problems with ease, so as to experience the aesthetic value of mathematics and cultivate confidence in learning mathematics well.
Fifth, emphasize the connection between "method" and "thought", and guide "method" with "thought". The two complement each other.
The so-called mathematical thought is an essential understanding of mathematical knowledge and methods, a rational understanding of mathematical laws, and an abstract thing belonging to mathematical concepts. The so-called mathematical method is the fundamental procedure to solve mathematical problems, the concrete embodiment of mathematical thought and the means to implement mathematical thought. Mathematical thought is the soul of mathematics, and mathematical method is the behavior of mathematics. The process of solving problems by mathematical methods is the process of accumulating perceptual knowledge. When the accumulation of this quantity reaches a certain procedure, it produces a qualitative leap and thus rises to mathematical thought. If mathematical knowledge is regarded as a magnificent building built by a clever blueprint, then mathematical methods are equivalent to architectural means, and this blueprint is equivalent to mathematical thoughts.
In the study of junior high school mathematics, we need to understand the mathematical ideas: equation function, combination of numbers and shapes, reduction, classified discussion, implicit condition, whole substitution, analogy and so on. The methods of "understanding" are: classification, analogy and reduction to absurdity; The methods that require "understanding" or "being able to use" include: undetermined coefficient method, elimination method, reduction method, collocation method, method of substitution method, image method and special value method. In fact, thoughts and methods cannot be completely separated. All kinds of methods used in junior high school mathematics reflect certain thoughts, and mathematical thoughts are rational understanding of methods. Therefore, it is an effective way to understand mathematical thoughts through the understanding and application of mathematical methods.
In the process of mathematics learning, we must fully infiltrate mathematical thinking methods, learn a knowledge point or do a problem, and seriously think about what mathematical thinking methods are used. Although the mathematical thinking method is different, it is limited after all. Correct use of mathematical ideas and methods to learn mathematics or solve problems is conducive to the comparison and classification of knowledge. Only in this way can we learn what we have learned systematically and flexibly, and truly integrate what we have learned into your knowledge structure and become your own wealth.
In addition, due to the abstraction of mathematical thought, although the mathematical method is more specific, the method itself is a science, a more important knowledge, and it is still more difficult. Therefore, when you first come into contact, it is inevitable that you can't sort out the clue. This is normal, you don't have to be afraid. In particular, mathematical thought is a gradual infiltration process, which should be understood in combination with specific mathematical knowledge or topics in the gradual learning process.
For example, when learning rational numbers, triangles, quadrilaterals, the proof of the theorem of circle angle and tangent angle, and the derivation of the root formula of quadratic equation in one variable, the idea of classified discussion will be involved. The principle of classified discussion is: unify the standard, and don't weigh or leak. Its advantage is that it has obvious logical characteristics and can train a person's thinking order and generality.
The idea of equation has realized the transformation from the arithmetic method in primary school to the algebra method in junior high school, which is a substantial leap in mathematical thought. The idea of equation refers to the relationship between unknown quantity and known quantity in mathematical problems, which can be solved by constructing equations. We will find that many problems can be solved easily if they are solved by the method of column equations.
The idea of combining numbers and shapes is conducive to visualizing abstract knowledge. In junior high school mathematics learning, "number" and "shape" are inseparable. For example, the concept and operation of rational numbers can be well understood with the help of the number axis. Many problems in solving application problems of series equations can easily find out the equal relationship between quantities by drawing the meaning of the questions, and function problems can not be separated from graphs. Often with the help of images, the problem can be clearly explained, and it is easy to find the key to the problem, thus solving the problem.
The idea of transformation is embodied in the transformation from unknown to known, from general to special and so on.
These mathematical ideas and methods will also run through the teaching process of teachers. Pay attention to the lectures, learn from the teachers and learn from the classroom. Bruner pointed out that mastering mathematical thinking methods can make mathematics easier to understand and remember. It fully illustrates the importance of mathematical thinking methods.
6. Forming good thinking quality is the basis of understanding mathematical problems.
Mathematics, as a discipline to cultivate people's thinking ability, is fascinating with its rational thinking. Unlike sightseeing in the mountains, it is pleasing to the eye because of its charming scenery and lingering. Mathematics learning is to study the spatial form and quantitative relationship of things through thinking and reflection, so that the spatial form and quantitative relationship of things can be presented. Only by forming a good thinking quality and pulling away the appearance of things with the sharp blade of good thinking quality can we "see" the essence of things.
So what is a good thinking quality? Let's take the phenomenon of "visiting" in our life as an example to illustrate. Many people have this kind of life experience, let others take it to others' homes once, twice, maybe many times. One day you have to go to someone else's house by yourself. When you walk near someone's house, facing the same building, you are at a loss and don't know where someone is.
In the process of learning, we often have such a phenomenon. In class, the teacher made it very clear, and the students just nodded, which made me feel very clear. And let the students do the questions themselves, and they don't know where to start. The main reason is that students do not think deeply about what they have learned and do not understand the essence of what they have learned. Just like on the way, every time we go to other people's homes, we should remember the geographical environment around them, especially the special signs. To understand the characteristics of what you have learned and what you need to remember, especially what mathematical ideas and methods are involved in this part of knowledge, you need to master it in time. The content of this kind of memory should be carefully remembered, and only by remembering the necessary knowledge can thinking be based. In addition, pay attention to taking notes. Bacon said in On Knowledge: "Taking notes can make knowledge accurate. If a person is unwilling to take notes, his memory must be strong and reliable. " Pay attention to the key points the teacher said, especially some empirical and regular knowledge summarized by the teacher, so as to review in time after class. After-class review, we should think about which problems have been passed and which problems have not been passed, and do a good job of checking and filling gaps in time.
7. Be willing to give up during the exam.
For most students whose math foundation is not very solid, it should be a wise choice to give up the last two questions. Generally speaking, the last two questions of a high-quality math test paper require higher ability. Students with weak math foundation should not spend too much time here, but should focus on the previous basic problems, so that their grades will be improved. The big questions in the college entrance examination are graded according to the process, so don't leave them blank in case you encounter any questions that you can't. You should write as many steps as possible according to the meaning of the question.
In dealing with the common problem of carelessness, I have a suggestion, that is, to develop the habit of drafting, and to standardize the draft and do it as a standardized assignment (just don't copy the topic), so that your draft will be clear at a glance, and there will be fewer mistakes or mistakes.
Calculators can sometimes be used in exams to improve the speed of solving problems and solve difficult problems. But after the exam, we must clearly understand the formal problem-solving ideas of the topic. The examination papers of each exam are precious review materials, so they must be kept properly.
The above talks about how to learn junior high school mathematics well from seven aspects. In order to learn junior high school mathematics well, in addition to the above, the key to learning mathematics well is hard study spirit, serious and careful study attitude and good study habits. In the classroom, we should not only learn new knowledge, but also subtly learn the teacher's way of thinking to solve problems. In the face of a problem, we should think ahead, find out our own way of thinking, and then compare our own way of thinking with the way of thinking of teachers, learn from each other's strengths and form our own way of thinking. Change "I want to learn" into "I want to learn", cultivate the initiative of learning and overcome the situation of passive learning. Really master the essentials of mathematics learning. The test of whether you can learn math well is whether you can solve problems. Understanding and memorizing the basic knowledge of mathematics, mastering the ideas and methods of learning mathematics is only the premise of learning mathematics well, and the ability to solve problems independently and correctly is the symbol of learning mathematics well.