How did Gao Xin adapt to high school mathematics study all his life?

With the deepening of learning, the differentiation of math scores is inevitable, so what are the reasons for falling behind? How should freshmen who have difficulties in math study get through the adaptation period smoothly?

The first reason is that high school mathematics is more difficult than junior high school mathematics. So there will be a small number of new highs that you can't adapt to for a lifetime. The performance is that everyone understands in class and can't do homework; Or even if I did, the teacher didn't know there were many mistakes until I changed it. This phenomenon is dubbed as "you can understand it as soon as you hear it, you can understand it as soon as you look at it, and you are wrong when you do it." Therefore, some parents think that their children's junior high school math exam is close to full marks. How did they fail in high school? !

Coping methods should thoroughly understand the contents supplemented by books and teachers in class, sometimes think and study repeatedly, draw inferences from others on the basis of understanding, and ask questions on the basis of diligent study.

The second reason is that junior high school and senior high school have different requirements for mathematics at different learning stages. The average score of high school exams is generally required to be around 70 points. If there are 50 students in a class, generally less than 10 will fail, and even less than 90%. Some students and parents don't understand these situations, and they feel incredible about the gap between the grade of nearly full marks in senior three and the failure in the first year of senior one. Students in key middle schools and their parents are under great pressure.

Coping methods: students' grades can't just look at scores. The key depends on the relative position of the class or grade, but also on the location of the school where the students are located in the city. Comprehensive consideration will lead to psychological balance, and unnecessary burdens will follow.

The third reason is the inadaptability of learning methods. Compared with junior high school, high school mathematics has more contents, faster progress and more difficult topics, but the homework in class is often difficult to understand. Due to the large amount of information in each subject, if you can't review effectively, the phenomenon of forgetting before school will be more serious.

We should not only understand the coping methods in class, but also write down the contents added by the teacher properly. After class, it is best to digest what you have learned before doing your homework. Don't look at notes or formulas when you do the problem. Try to choose some related questions to practice after class and avoid analogy.

The fourth reason is mental relaxation. Because of the hard work of senior three, some senior three students will have the idea of relaxing, because there are still three years before the college entrance examination, especially some senior three students who are desperately trying to make up classes, and they still expect to "relive their old dreams." This is a very dangerous idea. If the foundation of senior one is too poor, expect a surprise attack from senior three. Practice shows that most students will fail. Some boys with better intelligence are "arrogant", they only pursue the correct answers when solving problems, their writing is not standardized, and they lose points seriously in exams.

Senior one should not slack off on the content of the course. Function knowledge runs through high school mathematics, and function thought is a sharp weapon to solve many problems. Learning functions well is very important for the whole senior high school mathematics. It is very important to develop a diligent and diligent study attitude, rigorous and serious study habits and methods. There are more than ten chapters in high school mathematics. Mathematics in senior one mainly focuses on functions. Some students can't learn functions well, but they can learn solid geometry and analytic geometry well in Grade Two. Therefore, we must treat students with a changing point of view. Encouragement and self-confidence are educational magic weapons that never fail.

Basic theory+appropriate exercises:

Learn the most basic knowledge in class and explain the ins and outs of the principle clearly. Because all college entrance examination questions are variations of basic principles, especially functions, which are basic knowledge and compulsory contents, the most direct way to master the basic principles is to do all the textbook examples three times by yourself, complete them independently, and find your own blind spots by comparing the solutions of the examples.

The topic must be done, but to get the so-called "problem", you first need to find out where you are wrong, whether the basic formula skills or the theory are not thorough enough, understand where your bottleneck is and then consciously solve it, that is, you should always reflect on your knowledge system.

Have confidence and believe that you can overcome the difficulties, instead of blindly avoiding them, or you will pull more and more.

There are many students who do well in math in junior high school. After entering high school, they found mathematics difficult to learn. When they do exercises or extracurricular exercises, they often feel at a loss and don't know where to start. So after a period, their math scores declined seriously. What is the main reason for this phenomenon? According to my years of teaching practice, there are mainly the following reasons:

Textbook reason: Most knowledge points in junior high school mathematics textbooks are close to students' daily life, and junior high school textbooks follow the law of rising from perceptual knowledge to rational knowledge. The narrative method is simple, the language is easy to understand, intuitive and interesting, the conclusion is easy to remember, and the test-taking effect is ideal. Therefore, students are generally easy to accept, understand and master. Relatively speaking, high school mathematics concepts are abstract and logical, teaching materials are more rigorous and standardized, knowledge is more difficult, abstract thinking and spatial imagination are obviously improved, there are many types of exercises, problem-solving skills are flexible, and calculation is relatively complicated, which embodies the characteristics of "high starting point, great difficulty and large capacity". This change inevitably causes some students not to adapt to high school mathematics learning, which in turn affects the improvement of their grades.

Reasons for teaching methods: junior high school mathematics content is less, knowledge is not difficult, teaching requirements are low, and teaching progress is slow. For some key and difficult points, teachers can have enough time to explain and rehearse repeatedly to make up for the shortcomings. However, after entering senior high school, the content of mathematics textbooks is rich, the teaching requirements are constantly improved, and the teaching progress is also accelerated accordingly. The key points and difficulties of knowledge can not be solved by repeated emphasis as in junior high school, but high school teaching is often inspired and guided by guidance, questions, traps and changes, and then students think and answer by themselves, paying more attention to the process of knowledge, the infiltration of students' thinking methods and the cultivation of their thinking quality. This makes some students who have just entered high school not adapt to the teaching methods, and they have thinking obstacles in class and can't keep up with the teachers' ideas, thus creating learning obstacles and affecting mathematics learning.

Reasons for learning rules: In junior high school, some students are used to surrounding teachers, and their ability to think and summarize rules independently is poor, so they are satisfied with the acceptance of knowledge and lack the initiative to learn. High school mathematics learning requires students to be diligent in thinking, be good at summing up laws, master mathematical thinking methods, and draw inferences from others. However, freshmen in senior high school often follow the learning methods of junior high school, and they have difficulties in learning, even the homework of the day is difficult to complete, not to mention self-digestion and self-adjustment such as review and summary.

Other reasons: students' emotion, interest, personality, will quality, learning purpose and learning attitude can also affect senior one students' mathematics learning in a certain sense.

In view of the above reasons that affect mathematics learning, how should students make up for these deficiencies? Let's talk about several routine steps of high school students' mathematics learning:

Thoroughly understand what you have learned: High school mathematics is theoretical and abstract, which requires students to make great efforts in knowledge understanding, not only to understand the essence of mathematical concepts, but also to understand the background of concepts and their connections with other concepts. For example, students in grade three can solve quadratic equations in one variable. I made this survey among freshmen in senior high school: Why does the quadratic equation of one variable have roots when △≥0? The correct answer rate is less than 15%. What does this mean? Students don't understand the concept of quadratic equation in one variable thoroughly, and the related knowledge is lack of connection.

Treat preview scientifically: for some students whose math foundation is not ideal, I advocate preview before class. The correct way is not to open the book first, imagine the content and structure of this lesson, and then open the book; When you see that you want to define a concept, immediately cover the book and try to define it yourself; See the first statement of a theorem, then cover the book and guess his conclusion; The same is true when you see the formula. When you see an example, don't understand it first. Do it on paper first, then compare it with the solution in the book and think about it ... This preview is conducive to mastering knowledge and training thinking.

I don't advocate previewing before class for students with good math foundation and sharp thinking response. Because we already know the content, conclusion, derivation process and example solution in class through preview, what else can we talk about in class? "Think ahead, be a good class leader, and train your thinking in the thinking movement?" This wastes the opportunity to develop personal intelligence in the classroom.

Improve the efficiency of class: during the study in senior high school, students spend a large part of their time in class. So the efficiency of class determines the learning effect. In my opinion, to improve the efficiency of attending classes, we should pay attention to the following aspects:

First of all, we should make material and ideological preparations before class to avoid losing books and other things in class; Don't do too intense physical exercise before class, so as not to be breathless and restless after class.

The second is class. What matters is not "listening" but "thinking". Listening is the premise, followed by positive thinking. We should devote ourselves to classroom learning, so as to listen, see, feel, speak and touch.

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, follow the teacher's teaching ideas, 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 textbook 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. Make a brief record of the main points and thinking methods in class for review, digestion and thinking.

In short, the "do-it-yourself" classroom listening is the most scientific.

Pay attention to review and summary;

1, review in time

The second day after listening to the class, you must do a good job of reviewing that day.

The effective review method is not to read or take notes over and over again, but to review by remembering: first, put the books and notes together, recall what the teacher said in class, analyze the ideas and methods of the problem (or write them in the draft book while thinking), and try to think completely. Then, I opened my notes and books, compared what I didn't remember clearly, and made up, which not only consolidated the content of the class that day, but also checked the effect of the class that day, and also put forward necessary improvement measures to improve the listening methods and improve the listening effect.

2. Do a good unit review.

After learning a unit, you should review it in stages. Review method is the same as timely review. We should review by recalling, and then compare it with books and notes to make its content more perfect. Then we should 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.

Do proper exercises: Many students pin their hopes of improving their math scores on doing a lot of exercises, which is inappropriate. In fact, to improve math scores, it is important not to do more problems, 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 will deepen 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, the formation of skills can not be separated from certain exercises (homework assigned by teachers).

In addition, whether it's homework or exams, we should put accuracy and regularity in the first place, instead of blindly pursuing speed or skills, which is also an important aspect of learning mathematics well.

After-school self-study and research: The purpose of after-school self-study and research is to broaden knowledge, broaden horizons and further improve the ability to apply what they have learned to solve problems. The scope of extracurricular self-study should not be too large. We should read some extracurricular reference books and math magazines and do some fresh or difficult exercises around the progress of the textbooks we have learned. After-class self-study should be carried out in a planned and controlled way. Don't lose big because of small things, and don't affect the study of other subjects. In the process of extracurricular self-study, some novel and valuable exercises, some good thinking methods and problem-solving methods are found, which should be recorded for further study and mastery. Students with good foundation and strong analytical ability can choose one or two topics, conduct in-depth discussion and research, write research results into papers, and cultivate and exercise their thinking ability. Students with poor foundation and average analytical ability should often study and discuss some mathematical problems with students with good foundation and strong analytical ability, and learn their good mathematical thinking methods from them.

Method is a necessary condition for learning mathematics well. In addition, remember two sentences; "For everything, only love is the best teacher", "Learning to be excellent is an official, learning to be excellent is an official, and learning to be excellent is an official." With interest, methods, and diligence, I believe that every aspiring student will be able to learn high school mathematics well.