Fifth: 1, develop associations around teachers' remarks; 2. Clarify the narrative ideas of teaching materials; 3. Listen to the teacher's key points and difficulties; 4. Overcome the learning obstacles without interference in class; 5. Take brief notes on the basis of understanding.
Five first: 1, preview before class; 2. Try to remember before reading; 3. Read a book before doing your homework; 4. Understand first and then remember; 5. Organize your knowledge before going to bed.
The fifth meeting: 1, will make a study plan; 2. Will make full use of time to study; 3. Will make a study summary; 4. Ask questions, discuss and study; 5, will read the reference materials to expand learning.
Second, what kind of ability should we pay attention to in learning mathematics?
1 computing power. 2. Spatial imagination. 3 logical thinking ability. 4 the ability to abstract practical problems into mathematical problems. 5. The ability to combine shapes and numbers and convert them to each other. 6 Ability to observe, experiment, compare, guess and summarize problems. 7. Ability to study and discuss problems and innovation.
Third, master preview learning methods and cultivate mathematics self-study ability.
Preview is a learning method to learn new knowledge in textbooks before class. To learn junior high school mathematics well, we must first learn to preview new knowledge of mathematics, because preview is the premise of listening to a good lesson and mastering classroom knowledge, and it is an essential link in mathematics learning.
The preview of mathematics is mainly reading math books, which requires us to think and practice more. Mathematics preview can have "one stroke, two batches, three trials and four points"
Take the section "Equation and its Solution" as an example to illustrate this preview method. "One stroke" is the key point to delimit knowledge, and several basic concepts such as "known number", "unknown number", "solution of equation" and "attention" tips in the following examples 1 and Example 2 should be delineated. "The second batch" is to annotate the temporarily incomprehensible experiences, viewpoints and contents in the book, and judge whether Y2+2 = 4Y- 1 and 2x2+5x+8 are examples of the equations in 1, and why? If there is no reason, you can put the question next to these two questions. "Three tests" means trying to do some simple exercises to test the effect of your preview. "Four points" is to list the main points of this section of knowledge that you have previewed, and to distinguish which knowledge you have mastered through preview and which knowledge you can't understand through preview, and you need to learn further in class. For example, in the preview section, we can list the following knowledge requirements: (1) What is a known number, what is an unknown number, what is an equation, what is its solution and what is its solution. (2) it will judge whether a formula is an equation, (3) it will list a linear equation, and (4) it will test whether a number is the solution of an equation.
Fourth, master classroom learning methods to improve classroom learning effect.
Classroom learning is the most basic and important link in the learning process. Mathematics learning should adhere to the "five points", that is, listening, watching, speaking, thinking and hands.
Ear listening: that is, in the process of listening to the class, we should not only listen to the key points and difficulties of the knowledge told by the teacher, but also listen to the contents of the questions answered by the students, especially pay attention to the questions that we didn't understand beforehand.
Eye-catching: Look at the meaning expressed by the teacher's expressions and gestures, see the teacher's demonstration experiments and the contents on the blackboard, look at the contents of the textbook that the teacher asks to see, and connect the knowledge in the book with the knowledge that the teacher said in class.
Mouth to mouth: I didn't master it when I previewed it. I always ask freshman questions in class, asking teachers or classmates.
Heart orientation: that is, we should think carefully in class, pay attention to understanding new knowledge in class, and think positively in class. Mathematics classroom learning is sometimes to master the solution of examples and sometimes to learn to use formulas.
The key is to understand and be able to integrate and apply flexibly. For example, prove that the center line of any triangle is equal to half of the bottom line. The teacher gave an example to inspire students to think. Many students think of the nature of parallelogram and the practice of parallel auxiliary lines, and will soon think of the following four proofs:
It is necessary to grasp the key words and understand the new concept spoken by the teacher from another angle. For example, the proposition that only the arithmetic square root of 0 and 1 is itself can be rewritten as "If the arithmetic square root of a number is itself, then this number is 0 or 1".
Reach out: while listening, watching and thinking, take some notes appropriately.
Fifth, master the practice methods and improve the ability of solving mathematical problems.
The ability to solve mathematical problems is mainly improved through practical exercises.
What problems should we pay attention to in math practice?
1. Correct attitude and fully understand the importance of mathematical practice. Whether it is preview exercise, classroom exercise, homework or review exercise, we can't just be satisfied with finding a solution to the problem without practicing in detail. Practice can not only improve the answering speed and master the answering skills, but also often lead to many new problems in practice.
2. Have confidence and willpower. Mathematical exercises often involve complicated calculations and profound proofs. You should have enough confidence, tenacious will and patient and meticulous habits.
3. We should form the good habit of thinking first, then answering, and then checking. When encountering problems, we can't practice blindly, and the calculation is invalid. You should first deeply understand the meaning of the question, think carefully, grasp the key, and then answer. After you answer, you should also check it.
4. Observe carefully, use flexibly, find the rules and become a skill.
For example, the following set of exercises of linear equations with one variable, through careful observation, you will get a clever solution.
The skills and precautions of removing brackets and denominator in the above three questions should be carefully observed.
The above two questions should be carefully observed by using holistic thinking, flexibly deformed and solved correctly and quickly.
If we don't observe this problem, it will be very complicated to solve it according to the conventional method. We can get a subtle answer by connecting it with the concept of equation root.
As another question, if we boldly associate, flexibly use formulas, make concrete abstract, and use letters instead of numbers, we can get ingenious answers.
Known: a =1993019819810/993, b =199301.
Solution: Let x =199301981and y =1981992.
Then: A=x(y+ 1)=xy+x, b = y (x+1) = xy+y.
∵x>y,∴A>B.
Sixth, master review methods and improve comprehensive mathematics ability.
Review and consolidate should pay attention to master the following methods.
1. Arrange the review time reasonably, "strike while the iron is hot", and the lessons learned on the same day must be reviewed on the same day. No matter how difficult the homework is, we must consolidate the review, and we must overcome the bad habit of doing homework without reviewing books, turning over books if we can't afford them, and reading books as reference books.
2. The comprehensive review method is widely used, that is, by finding out the left-right relationship of knowledge and the internal relationship between vertical and horizontal, the overall improvement is achieved. This method is not only suitable for the usual review, but also suitable for unit review, mid-term review, final review and graduation review.
Comprehensive review can be divided into three steps: first, look at the overall situation, browse all the contents, and initially form a complete impression of the knowledge system by evoking memories; Second, deepen understanding and make a comprehensive analysis of what you have learned; Finally, organize and consolidate, as Hua said, "find another way, repeat the old things" and form a complete knowledge system.
3. Pay attention to practical review methods. Mathematics review can't be like reviewing the main backrest of liberal arts. It should be achieved by "completing practical work". Educators clearly pointed out in the mathematics curriculum that "we should attach importance to the practical application of knowledge as an important review method". For example, to review a quadratic equation, you can do the following four questions.
(1) Equation 3x2-5x+a=0, one of which is greater than -2 and less than 0, and the other is greater than 1 less than 3. The range of real number a.
(2) Equation 2mx2-4mx+3(m- 1)=0 has two real roots, and the range of real number m is determined.
(3) If both equations x2+(m-2) x+5-m=0 are greater than 2, then the range of real number m is determined. ..
(4) It is known that the two side lengths A and B of a triangle are two in the equation 2x2-mx+2=0, and the side length C is 8, which is the range of real number M. ..
Through practice, we can understand the knowledge of quadratic equation in one variable from three different angles: positive, negative and negative, which is convenient to grasp the essence and strengthen memory. Actively review the concept of quadratic equation with one variable; Discuss the properties of roots with discriminant; The relationship between root and coefficient, understand the quadratic equation of one variable with the knowledge of function, and solve the problems related to equation and inequality from the perspective of quadratic function. After trial and error, the causes and solutions of the errors were found, which left a deep impression on the opposite side.
4. Broaden the collection and break through the review methods of weak links.
In order to improve the comprehensive ability of mathematics, we should also break through the weak links of our own knowledge. First, we should work hard on weak links and strengthen the consolidation of textbook knowledge. Second, reading these extra-curricular books properly, collecting and sorting them out, and reading them widely will help to break through this weak link and improve the overall comprehensive ability of mathematics.
Seven, master the review method, improve the comprehensive ability of mathematics.
Review and consolidate should pay attention to master the following methods.
1. Arrange the review time reasonably, "strike while the iron is hot", and you must review the lessons you have finished on the same day. To consolidate review, we must overcome the bad habit of doing homework without reviewing books and consulting books as reference books.
2. The comprehensive review method is widely used, that is, by finding out the left-right relationship of knowledge and the internal relationship between vertical and horizontal.
Comprehensive review can be divided into three steps: first, look at the overall situation, browse all the contents, and initially form a complete impression of the knowledge system by evoking memories; Second, deepen understanding, comprehensively analyze what you have learned, and finally consolidate it.
3. Pay attention to practical review methods. By "completing practical homework" to review mathematics, educators clearly point out that "we should attach importance to the practical application of knowledge as an important review method" in mathematics courses. For example, if you review the quadratic equation of one variable, you can do the following four questions.
(1) Equation 3x2-5x+a=0, one of which is greater than -2 and less than 0, and the other is greater than 1 less than 3. The range of real number a.
(2) Equation 2mx2-4mx+3(m- 1)=0 has two real roots, and the range of real number m is determined.
(3) If both equations x2+(m-2) x+5-m=0 are greater than 2, then the range of real number m is determined. ..
(4) It is known that the two side lengths A and B of a triangle are two in the equation 2x2-mx+2=0, and the side length C is 8, which is the range of real number M. ..
4. Broaden the collection and break through the review methods of weak links.
Mathematics is one of the compulsory subjects, so we should study it seriously from the first day of junior high school. So, how can we learn math well? Introduce several methods for your reference:
Eight, pay attention to the lecture in class and review in time after class.
The acceptance of new knowledge and the cultivation of mathematical ability are mainly carried out in the classroom, so we should pay attention to the learning efficiency in the classroom and seek correct learning methods. In class, you should keep up with the teacher's ideas, actively explore thinking, predict the next steps, and compare your own problem-solving ideas with what the teacher said. In particular, we should do a good job in learning basic knowledge and skills, and review them in time after class, leaving no doubt. First of all, we should recall the knowledge points the teacher said before doing various exercises, and correctly master the reasoning process of various formulas. If we are not clear, we should try our best to recall them instead of turning to the book immediately. In a sense, you should not create a learning way of asking questions if you don't understand. For some problems, because of their unclear thinking, it is difficult to solve them at the moment. Let yourself calm down and analyze the problems carefully and try to solve them by yourself. At every learning stage, we should sort out and summarize, and combine the points, lines and surfaces of knowledge into a knowledge network and bring it into our own knowledge system.
Nine, do more questions appropriately and develop good problem-solving habits.
If you want to learn math well, it is inevitable to do more problems, and you should be familiar with the problem-solving ideas of various questions. At the beginning, we should start with the basic problems, take the exercises in the textbook as the standard, lay a good foundation repeatedly, and then find some extracurricular exercises to help broaden our thinking, improve our ability to analyze and solve problems, and master the general rules of solving problems. For some error-prone topics, you can prepare a set of wrong questions, write your own problem-solving ideas and correct problem-solving processes, and compare them to find out your own mistakes so as to correct them in time. We should develop good problem-solving habits at ordinary times. Let your energy be highly concentrated, make your brain excited, think quickly, enter the best state, and use it freely in the exam. Practice has proved that at the critical moment, your problem-solving habit is no different from your usual practice. If you are careless and careless when solving problems, it is often exposed in the big exam, so it is very important to develop good problem-solving habits at ordinary times.
Ten, adjust the mentality, correctly treat the exam.
First of all, we should focus on basic knowledge, basic skills and basic methods, because most of the exams are basic topics. For those difficult and comprehensive topics, we should seriously think about them, try our best to sort them out, and then summarize them after finishing the questions. Adjust your mentality, let yourself calm down at any time, think in an orderly way, and overcome impetuous emotions. In particular, we should have confidence in ourselves and always encourage ourselves. No one can beat me except yourself. If you don't beat yourself, no one can beat my pride.
Be prepared before the exam, practice routine questions, spread your own ideas, and avoid improving the speed of solving problems on the premise of ensuring the correct rate before the exam. For some easy basic questions, you should have a 12 grasp and get full marks; For some difficult questions, you should also try to score, learn to score hard in the exam, and make your level normal or even extraordinary.
It can be seen that if you want to learn mathematics well, you must find a suitable learning method, understand the characteristics of mathematics and let yourself enter the vast world of mathematics.
XI。 Some suggestions on learning mathematics.
1, take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extra-curricular knowledge added by the teacher to prepare for the college entrance examination.
2. Establish a mathematical error correction book. Write down error-prone knowledge or reasoning in case it happens again. Strive to find wrong mistakes, analyze them, correct them and prevent them. Understanding: being able to deeply understand the right things from the opposite side; Guo Shuo can get to the root of the error, so as to prescribe the right medicine; Answer questions completely and reason closely.
3. Memorize mathematical laws and conclusions.
4. Establish a good relationship with classmates, strive to be a "little teacher" and form a "mutual aid group" for math learning.
5. Try to do extra-curricular math problems and increase self-study.
6. Repeatedly consolidate and eliminate forgetting before school.
7. Learn to summarize and classify. Ke: ① Classification from mathematical thoughts, ② Classification from problem-solving methods and ③ Classification from knowledge application.
8. Listening carefully in class is the most critical part.
Although the teacher will read the textbook when reviewing, the content has been greatly simplified, which is not as good as the first lecture. There are many things that the teacher said for the first time and then stopped talking. Moreover, in the first lecture, teachers often explain the basic principles of knowledge clearly. Let you know not only why, but also why. Only by understanding the context of knowledge can we grasp the essence of the problem. For example, many students only know that "integers and fractions are collectively called rational numbers", but he doesn't know why they are called rational numbers and why they are not called irrational numbers. If the origin of rational numbers is clarified, the understanding of rational numbers will certainly be much clearer. Therefore, it is very important to listen carefully, especially to the teacher's new lecture.
9. Recite related concepts in time.
No wonder many students are not interested in the concept of rote learning. Because many students like science so much, because there is no boring recitation. But if you don't grasp the basic concepts firmly, a lot of related knowledge will often be confused. In fact, doing problems is only a means to improve basic skills. The real purpose of our study is to master basic concepts and principles. After a few years, you may forget all the problems you have done, but the basic principles of mathematics you have learned will accompany you for life.
10, develop good study habits.
① Mark wrong questions, difficult questions and good questions in time. Especially for the mistakes in calculation, most students think it's just their own mistakes, not that they won't. But during the exam, the teacher will not care what you did wrong. Especially in filling in the blanks and choosing, mistakes are all wrong, and missing a symbol is also 0 points (don't blame the teacher for being too black! Therefore, everyone is still strict with themselves according to the principle of "miscalculation".
Prepare and use your own "error correction book" and "essence book". Marking wrong questions, difficult questions and good questions in time can't be all right, because for most students, those wrong questions, difficult questions and good questions need to be repeated three or four times before they can really master them (the possibility that they can really master them once is not ruled out, but such students are only a few, but some of them are students who "understand at a glance and make mistakes once they do it"). Therefore, most students should put these questions into their own correction books and essence books and review them every once in a while (don't be self-righteous).
3 Review in time. Our brain is not the hard disk of a computer, and forgetting is inevitable for everyone. According to the law of forgetting, the shorter the review interval, the better the memory effect. So I hope everyone can develop the good habit of reviewing in time, which may save you a lot of time.
4 preview in advance. If you preview in advance, the goal is clear and the focus of the class is prominent. Not only can you improve your self-study ability, but you can also check whether your thinking is correct according to the teacher's thinking. Especially for two holidays, it is undoubtedly a waste if you play for more than two months. So I suggest that you can study the next issue in advance during the holidays. Because, for learning mathematics, the second time is much clearer and deeper than the first time, so the effect is far better than the first time.
Mathematics is a basic subject, which plays an irreplaceable role in cultivating a person's thinking ability. Therefore, it will always be said that people who learn mathematics, or those who learn mathematics well, are always smarter, which is inseparable from the unique advantages of mathematics in cultivating people's thinking ability.
For individual students, the ability to learn mathematics is innate, which is what we call talent. But for most students, the cultivation of mathematical ability needs "sweat+methods" to succeed. References:
oneself