Moderator: Good afternoon, netizens. Welcome to Netease College Entrance Examination Chatroom and participate in a series of face-to-face activities organized by Netease Education Channel. Today, we are very honored to invite Xiong Yuenong, a teacher from Guangzhou Development Zone Middle School, to have an interview on the sprint of math review for the college entrance examination.
Moderator: Mr. Xiong, please introduce yourself first!
Xiong Yuenong: Good afternoon, netizens. We are very grateful to Netease Education Channel for providing us with opportunities to communicate and learn from each other. I am a senior math teacher in Guangzhou Development Zone Middle School. So far, I have been teaching middle school mathematics for 26 years, half of which is in senior three.
Moderator: There are still 17 days before the college entrance examination. How should candidates review at this stage?
Xiong Yuenong: Now it is getting closer and closer to the college entrance examination, with only half a month left, the majority of candidates have entered a state of war. Candidates review a lot of materials and have a lot of simulation questions. Where did you get the time? Candidates are under great pressure. The mountains and rivers are vast and there are endless questions. Some candidates are "buried" in the mountains of books, and some candidates are "soaked" in the sea of questions, which is unscientific. How to review the last test before the exam? I want to talk about some views for students' reference. One is to return to textbooks and emphasize textbooks. Don't neglect the teaching materials. For many years, the college entrance examination has emphasized the examination foundation, which is the carrier of the examination content, the basis of the college entrance examination proposition, the main source of the college entrance examination questions and the growing point of students' intelligence. The second is to weave the network and have more contact. The basic knowledge and basic thinking methods of middle school mathematics are connected into a network vertically and horizontally, because the college entrance examination often designs test questions at the intersection of knowledge networks. The third is to grasp the trunk and main points. The main knowledge points and main problem-solving methods should be mastered. The fourth is to practice properly and find the feeling. I'm talking about proper training, don't get caught up in a lot of training. The main manifestations of questioning strategies are random topics, enlarged questions, simplified teaching methods and mechanized operation. We are opposed to sea tactics, but we can't just look at the problems every day without solving them. Keep a certain amount of problem-solving training every day. The fifth is to exercise regularly and adjust your mentality. From now on, we should adjust our biological clock according to the examination time of the college entrance examination, and adjust our daily state to the best effect during the period of the college entrance examination, that is, 9: 00 a.m.-1:00 a.m. and 3: 00-5: 00 p.m., so as to create the best mood and play the highest level in the examination.
Only in this way can we be proud of the college entrance examination, grasp the essence of middle school mathematics knowledge, and show our mathematics ability.
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Second, what kind of math problems can I do now?
Moderator: You just said that the college entrance examination is still half a month away. When reviewing, you can't take the tactics of asking questions and solving problems. You need proper training. Now, what kind of questions should you do?
Xiong Yuenong: Training should be targeted. In recent years, the college entrance examination, it should be said that the structure of the test questions is basically stable, closely related to the outline, keeping the tradition, close to the teaching materials, and the orientation is relatively clear. When we are training, we should focus on our own "blind spots" and train for the important knowledge points and main methods of the college entrance examination. For example, function, analytic geometry and solid geometry occupy a large proportion in the mathematics test paper, which constitutes the main body of the mathematics test paper and is the main test center of the college entrance examination questions. These are the three "giants" and also the key test sites for previous candidates. When we are training, we should pay attention to the meticulous examination of questions, the accurate operation and the standardization of solving problems. Only in this way can training be targeted and have good results.
Generally speaking, there are six questions behind the answer, mainly including function, solid geometry, analytic geometry, triangle, sequence, inequality, derivative, probability and statistics.
Moderator: Now, we should look for suitable training questions according to these key points. Does the teacher collect better training questions for the candidates, or do the candidates find some review materials to do these exercises themselves?
Xiong Yuenong: Many senior three math teachers have accumulated rich experience in guiding candidates to review effectively after many teaching practices in senior three. As the leader of preparing for the exam, teachers usually choose some highly targeted questions for candidates to train, and candidates should carry out intensive training according to the teacher's review plan. Stay close to the teacher, consolidate your knowledge, follow the teacher, never make another set, go your own way and follow your feelings. We should combine the teacher's guidance with our own reality, find a good combination point and give full play to the best review effect.
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Third, the key knowledge and questions of this year's college entrance examination mathematics investigation
Moderator: Just now, Mr. Xiong also mentioned the key points of the college entrance examination in previous years, such as function, analytic geometry and solid geometry. Please make a bold prediction. How will this year's college entrance examination examine these knowledge points and solve problems?
Xiong Yuenong: The sound of the waves remains the same. The structure of the test questions will not change. There are also 10 multiple-choice questions, 4 fill-in-the-blank questions and 6 answers. The scores of the three types of questions will not change, and they are still 50, 20 and 80 points. Multiple choice questions and fill-in-the-blank questions are mainly used to test the basic concepts and basic operations of middle school mathematics. In multiple-choice questions and fill-in-the-blank questions, there will also be some "obstacles", which will make candidates find a multiple-choice question and fill-in-the-blank question difficult, but this situation is very rare.
The main purpose of solving problems is to examine students' comprehensive ability to analyze and solve problems by using mathematical knowledge, and to comprehensively test candidates' mathematical literacy. Generally speaking, the first few questions are relatively easy. For example, 15, 16 and 17 are relatively easy.
Moderator: Please predict what will be tested in the first three questions and the last three questions.
Xiong Yuenong: The first three questions may be trigonometry, sequence, probability statistics and solid geometry, which may not be accurate. This is my analysis. Judging from the subtle changes in the examination syllabus, people feel that they are testing the image and essence of trigonometric functions, but we should also be wary of a diversion. Solid geometry is mainly based on prisms and pyramids, which can be solved by traditional methods, or by establishing space coordinate system and space vector method.
Among the last three questions, there may be application problems. It is reported that after a lot of efforts, the proposition group has constructed an application problem that comes from life, is close to students, is full of the flavor of the times and is skillfully designed, and may appear in this year's college entrance examination paper. This problem can replace the probability and statistics problem. In this case, there will be probability statistics in the small question. Function can be tested together with other knowledge, such as function and derivative, function and sequence, function and inequality. In this case, the test questions can be designed from the overall height of the subject and the height of thinking value, and the test ability reaches the necessary depth, so the test questions are more difficult.
There may also be problems with abstract functions. In this case, the requirements for students' algebraic reasoning ability are higher. It is precisely this aspect that is the weakest point for candidates, and candidates will feel uncomfortable. It may lead candidates to "see flowers in the fog" and "half awake and half drunk", giving candidates a sense of arrogance.
Analytic geometry often has two or three questions, and the first question is equivalent to the difficulty of a multiple-choice question and a fill-in-the-blank question. The requirements of the second and third questions on thinking ability are gradually improved, and candidates can take by going up one flight of stairs. Examination questions should distinguish candidates of different levels through examinations. Judging from the examination questions in recent years, analytic geometry is often related to trajectory equation and classification discussion. Conic curves can also be designed as research-oriented problems, exploratory problems and open-ended problems. Proposers have many ingenious ways to examine rational thinking. If they take this test, the amount of thinking and calculation will be larger. Attention should be paid to the intersection of knowledge points and the examination of mathematical thinking methods in the examination. Especially the combination of numbers and shapes, classified discussion, function equation and equivalent transformation. For example, when solving small problems, the conventional methods are time-consuming, but the idea of combining numbers and shapes can change the angle of thinking and solve problems quickly.
Moderator: With the integration of multiple knowledge points, the test questions will be more complicated. How to sort out these complicated knowledge points? Is there any effective method? Don't be intimidated by these tests.
Xiong Yuenong: The examination questions pay attention to the level of examination, emphasizing ability and conception, but also reasonably stipulate the comprehensive degree and control the difficulty of the examination questions. Usually review, we should contact knowledge points in many directions, not single review, but build a network. In recent years, college entrance examination questions have combined some knowledge points. A set of college entrance examination questions generally needs to examine 80-90 high school mathematics knowledge points in 138. Test questions often come from textbooks, which are higher than textbooks. Everyone has higher requirements and needs a certain comprehensive ability to answer. Be sure to contact the knowledge points when solving problems. The second knowledge point should be used accurately, and the choice of mathematical problem-solving methods should be appropriate. If you can't get full marks, you can get some points and take as much as you can. Don't leave any blank space.
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Fourth, how to solve the unfamiliar problems in the college entrance examination mathematics?
Moderator: Some topics often appear in innovative forms, which makes candidates daunting. What do you think of this problem?
Xiong Yuenong: The college entrance examination is held every year, and the questions are new every year. Innovation is the life of college entrance examination. Every year, there are one or two innovative questions in the college entrance examination questions, which have become the highlights of the college entrance examination questions of that year. Where is the new one? For example, multi-dimensional unconventional knowledge synthesis, large-span knowledge transfer and long-distance knowledge convergence, and some problems in the background and method transfer. Innovative questions are generally distributed in fill-in-the-blank questions and multiple-choice questions, and small questions (referring to fill-in-the-blank questions and multiple-choice questions) are the "experimental fields" for the reform of college entrance examination propositions. Innovative test questions can examine students' innovative thinking and ability to accept new things and solve new problems. For candidates, novel questions are a real difficulty, because candidates have never seen them before, and it takes a process from understanding to understanding to analysis to answering, so it is difficult. Examination questions will better control the difficulty of novel questions, so that new questions are not difficult and the questions are not surprising. Of course, there will not be many such problems. Novel topic+novel topic+novel topic ≠ Good paper. Most of the questions should be routines, and the background is familiar to candidates. The focus is on general methods, and the special skills are downplayed. Candidates need not be afraid.
Moderator: What is the score of the innovation question?
Xiong Yuenong: Generally, these questions are 5~ 15.
Moderator: If you encounter such a problem, the topic is relatively novel, and the candidates can't find the knowledge points at once. How to start and what are the good solutions?
Xiong Yuenong: Carefully examine the questions, master the framework, distinguish the levels, develop associations, find connections and decompose them one by one. If you still have no idea after thinking for two minutes, then jump over and solve the following problems and see if you can get some inspiration by solving the following problems. Once you have an idea, you should "kill the carbine" and then answer. If you are still not inspired by solving the following problems, it is time to be decisive-guess! Being able to guess boldly is also an ability.
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5. What are the common points of losing points in college entrance examination mathematics?
Moderator: Some netizens responded that they thought they had done it and used all the knowledge points, but when scoring, they lost points in places they didn't pay attention to. What do you think are the common situations of losing points in the college entrance examination?
Xiong Yuenong: As can be seen from the answers of the college entrance examination in previous years, there are a lot of phenomena of "meeting but not right" and "being right but not complete" on the candidates' papers. Candidates lose points mainly in five aspects:
1. Slow problem solving. The result is that there is no time to do the following solutions, and there is no time to even look at the questions. The reason for the slow speed of solving problems is that the basic knowledge and methods are not skilled, which is caused by insufficient training at ordinary times. Therefore, we often say that the purpose of returning to textbooks is to let candidates master the basic knowledge and methods in textbooks comprehensively and systematically, and thoroughly understand the examples and exercises in textbooks.
2. There are many operational errors. When answering questions, he often makes some low-level mistakes, and he also makes mistakes that others can't make. This is a matter of computing power, not simply carelessness. In this respect, we should strengthen the training of computing ability.
3. The answer is not standardized. After finishing a question, I think it's right, and I think it's a perfect score. In fact, the discount is greatly reduced, mainly because the answer is not standardized, and it is taken for granted to skip, such as not answering the application question, not writing the definition domain of the resolution function, not first proving that a certain angle is a plane angle of a dihedral angle, using mathematical symbols indiscriminately, and typing mathematical symbols indiscriminately. I lost points, and I don't know yet.
4. Review the topic in a hurry. If you don't see the meaning of the question accurately, you will answer the question rashly without understanding it clearly, which will lead to mistakes in solving the problem.
5. Poor psychological quality. Some candidates are so nervous during the exam that they can't think of anything as a result.
There are many reasons for losing points in the exam, mainly these points, which should be overcome in the usual mock exam and accumulated experience in the exam. It stands to reason that a high school student should have rich experience in taking exams after one hundred "exams".
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Sixth, how to improve the speed of solving problems in college entrance examination mathematics?
Moderator: The speed of solving problems can't keep up. As a netizen also asked, the speed of answering math problems is too slow. How to improve the speed of solving problems?
Xiong Yuenong: To improve the speed of solving problems, we should have solid basic knowledge, skilled basic methods, careful thinking, solid calculation skills and fast writing and expression. Some candidates write too slowly and pursue the perfection and neatness of the test paper, which leads to hidden loss of points and is not desirable. We should not seek perfection, but perfection; Not neat, but accurate. An answer sheet completed within the specified time can be read clearly as long as the words, formulas and symbols are written.
In addition, the use of the draft is also particular. You can fold the draft paper in half and then fold it in half, so there are 16 rectangular areas. Numbering each area can correspond to 16 questions. The advantage of this is that when checking whether some operations are wrong, don't look around for the operation process and waste time and energy. First of all, we should examine the questions, clarify our thinking, strengthen mental arithmetic, strive for a stroke of the pen, put pen to paper successfully, and try not to use draft paper.
Compere: Can you give yourself limited time to do the corresponding questions through limited training now? For example, maybe you are slow in doing the problem. Does this help?
Xiong Yuenong: This is a very good way. Some candidates made a "wrong question book" by themselves, recorded all the wrong questions in previous exams, and conducted limited training for these wrong questions. This is very effective training. The wrong textbook basically condenses the key points, difficulties and basic points of senior high school mathematics and the "blind spots" in their own learning process. It is necessary to arrange enough time to sort out knowledge and methods, reflect on test papers, and check for leaks.
Moderator: The "wrong title book" records the individual scores of candidates. It's a good idea to train with the wrong textbook.
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7. What should I do if I want to improve the 10 score of students who go to work in basic schools?
Netizen: I am a liberal arts candidate. I have a good foundation in mathematics. Usually I can get 1 10 points. Now I still have half a month to review. Can you score above 120?
Xiong Yuenong: Hurry up, make scientific arrangements and review effectively for half a month. It is entirely possible to jump from 1 10 to 120, and you will break through 120 with a good attitude.
Moderator: He has a good foundation. He can get a lot of points in multiple-choice questions and fill-in-the-blank questions. Losing points may be the next big topic. How can he improve the scores of the next six questions?
Xiong Yuenong: The allocation of time should be reasonable. The time for solving the previous 14 small question should be controlled at about 50 minutes. Accelerate the improvement of multiple-choice questions and fill-in-the-blank questions. We should also pay attention to several aspects. The first is to examine the questions more accurately. Don't worry when reviewing the questions. Second, the answer should be more standardized, especially where it is easy to lose points, and special attention should be paid to the standardization of the answer. Third, the calculation is more accurate. We should use the strategy of "four first and four later" to answer questions, that is, easy questions first, then difficult questions; Mature first, do familiar questions first, and then do unfamiliar questions; First more, then less, first do the questions with more scores, and then do the questions with less scores; Similarities before differences, first do the same branch problems, such as function and trigonometry, it is easy to communicate between knowledge and methods, and then do different branch problems. Only in this way can we ensure time and confidence to break through the problem.
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Eight, how do students with a solid foundation impact full marks?
Moderator: This is asked by candidates with above-average grades, and some candidates ask themselves that their usual grades are OK. Usually you can test 65,438+020,65,438+030, how to get full marks and high scores.
Xiong Yuenong: This kind of candidate is quite powerful, and can be stable at 120 and 130, which shows that the candidate has a good mathematical foundation and mathematical literacy and strong mathematical problem-solving ability. The influence of high score and perfect score, the overall quality should be very good, largely depends on the examinee's mentality and state at that time. There is a certain chance to get high score or perfect score, but it is not necessarily the case to change a set of questions.
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Nine, how to overcome the tension, normal or even extraordinary?
Moderator: Do you have any suggestions on how to overcome nervousness and play a normal or even extraordinary level in the exam?
Xiong Yuenong: Overcoming nervousness, taking the exam with a peaceful mind and controlling the exam time reasonably are the requirements of the exam syllabus for the personality quality of candidates. Candidates have taken the exam so many times that they should have accumulated some experience. Usually, we should pay attention to some training and statistics in this area when simulating the exam. For example, count the time to solve problems, how long it takes to choose multiple-choice questions, fill-in-the-blank questions and answer questions. Through such data, we can analyze our own strength. Through such training and statistics, we will have a psychological bottom. The time of the college entrance examination is the same as that of the usual examination, so we can treat the usual examination as the college entrance examination, constantly adjust it from the aspects of psychological adjustment, time allocation and rhythm control, and gradually adapt to it, so that the college entrance examination will be regarded as the usual examination and we will not be nervous. Usually the knowledge and methods are kept in mind, and the happy smile is written on the face during the exam.
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Ten, the college entrance examination mathematics problem-solving skills.
Moderator: Are there any problem-solving skills for multiple-choice questions? At school, the teacher said that there was a method of exclusion, and different questions used different methods.
Xiong Yuenong: Generally speaking, the number of minor problems is 14. Unrealistic, there is no time to solve major problems. To solve small problems, we should try to avoid "making a mountain out of a molehill", making a mountain out of a molehill and doing it skillfully. There are four answers to multiple-choice questions, excluding three, and the other is a positive answer. When training at ordinary times, there are many problems that have not been directly solved. Pay attention to the accumulation of some methods, such as the exclusion method, the combination of numbers and shapes, the image method, the verification method and so on. These are all good methods.
Moderator: When you get some functions and trigonometric functions, what kind of methods are there?
Xiong Yuenong: If there are multiple-choice questions with function images, we can find the answer by substituting a point. The solution set of inequality has four answers: A, B, C and D. You can find the answer by substituting one or several values. This will save a lot of time, which requires students with a certain mathematical foundation to think of these methods immediately. Many candidates are used to the direct method, and they will start to calculate after reading the questions, which will be very confusing. This inspires us to think about special methods when we get questions. There is really no way to answer them directly, so you will find that there are often shortcuts.
Having an image awareness of function problems, drawing more images, skillfully drawing trigonometric problems, solving problems such as monotonous interval, period, symmetry axis and symmetry center, simplifying formulas of trigonometric functions and estimating the range of formulas of trigonometric functions, accurately memorizing trigonometric formulas and solving problems flexibly are important aspects of computing ability.
Moderator: Some candidates say that solid geometry is compulsory every year, but it is difficult to review. I don't know how to practice. Do you have any good suggestions for such candidates?
Xiong Yuenong: Solid geometry mainly examines and proves the positional relationship, angle, distance and volume, and examines the spatial imagination of candidates. The most difficult thing here is to find the dihedral angle, which has always been a difficult problem. Once the dihedral angle is tested, many candidates have fear in their hearts. Judging from the answers of college entrance examination in previous years, many candidates are not clear about the concept of dihedral angle. Starting with the concept of dihedral angle, relevant training is carried out to properly train the solution of dihedral angle.
Moderator: When solving solid geometry problems, you can use traditional methods or vector methods. If you encounter the problem of dihedral angle, which method is better?
Xiong Yuenong: If it is convenient to establish a spatial coordinate system, the solid geometry problem can be solved by the coordinate system method, and the calculation of dihedral angle can be converted into the calculation of vector, which reduces the difficulty of thinking and reasoning.
Moderator: If the candidate's computing ability is better, it is also good to do so.
Moderator: How to review the function?
Xiong Yuenong: Functions mainly test the properties of functions, such as definition range, range, parity, monotonicity, periodicity and symmetry. These properties must be mastered skillfully. If the problem of a function is not an abstract function, you can draw a picture to help you understand it. In this way, we can get some perceptual information to help us analyze problems and draw more pictures.
Moderator: Draw more pictures to solve the problem of function.
Xiong Yuenong: Yes.
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XI。 How to treat the reference value of mathematical simulation examination?
Moderator: Guangzhou's first and second modes are over. How do you view your achievements in the first and second modes? Is there any reference value?
Xiong Yuenong: From the perspective of proposition, I think the quality of proposition is very good and the level of proposition teachers is very high. The test questions basically cover the main test sites and important mathematical methods of the college entrance examination. The data of the first model is more reliable, because it is a unified reform and unified marking. The second model is that each school marks its own papers according to the scoring standard of the Municipal Teaching and Research Office, which is not objective. In this case, volunteers had better fill in their volunteers according to the results of the first model.
When I was a model, because of the exam in April, my classmates struggled for another month and took the second model, and their grades improved. You can add a certain score according to the car model and my own strength.
Moderator: Just now I have said six big questions, and I will try to get as many as possible, because some questions are divided into several small questions. Please give candidates specific instructions on how to get all the points as much as possible, or how to get the step points for candidates.
Xiong Yuenong: At present, many candidates give up some available scores because they don't have enough time to review the following questions. The time ahead should be compressed and cannot be delayed. It is necessary to master some problem-solving methods skillfully, such as some good solutions, to save time for later problem-solving.
There are also some students who can't do a problem and don't do it. It's terrible not to write a word. We can turn the written language in the topic conditions into mathematical symbol language, and then take a step forward, and there will be points. For example, if the eccentricity of an ellipse tells you that it is half, it will generally be written as c/a= 1/2, and then a=2c, and then the relationship between a, b and c can be further substituted, so that you can get a score, and all understandable conditions should be transformed into mathematical symbol language.
Moderator: You can boldly write out the known formula of a question and set it up.
Xiong Yuenong: Write down every answer and formula you know, take a step forward, and walk like this, and the problem will be almost solved. Don't do it if you can't do it as a whole. This is a loss. Read every sentence, change every condition, take a step forward and the score will find you.
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Twelve, do 8- 10 questions every day before the exam to keep fit.
Moderator: Today's interview is coming to an end. Mr. Xiong, please say a few words to the candidates.
Xiong Yuenong: We still require candidates to do a certain number of questions at regular intervals every day, such as 8- 10, so as to keep warm. If you don't solve the problem for the time being, you will become a stranger.
Moderator: What types of questions are included in the 8- 10 questions every day?
Xiong Yuenong: Yes, you can choose, fill in the blanks and answer questions according to 4, 2, 2 or 4, 3, 2. You need planned training. You should spread out the main knowledge points for training and make a good training plan. Today is these knowledge points, tomorrow is another knowledge point. So you can practice every day and keep feeling good. You will feel better when you take the college entrance examination.
Moderator: One week before the exam, the school asked students to relax. Do you have to do the problem like this?
Xiong Yuenong: Yes, you can't relax completely. We should pay attention to this problem in strategy. If you give up completely, you will feel very tired and strange during the college entrance examination. Insist on doing a certain amount of questions and training in a limited time every day, so as to go into battle lightly and maintain a good feeling.
Just now, I said that I should always read the wrong book. This is the best material for me. I once taught a candidate. When reviewing for the college entrance examination, she set up a set of wrong questions. One or two months before the exam, many candidates find that there are many books to read and many questions to do. The examinee just misread the problem set because everything she didn't understand was in it. She read the book Thin.
Moderator: Just now, Mr. Xiong added two points. The first one is to keep the feeling of doing problems, 8- 10 problems every day. The second is to look at more problems, which are targeted and often considered wrong, and the effect is much more obvious than looking for information.
Moderator: What does the teacher place on the majority of candidates?
Xiong Yuenong: I hope that the majority of candidates will have no distractions, be calm as water, travel lightly and be proud of the college entrance examination.
Moderator: Thank you very much, Mr. Xiong, and thank you very much for coming to Netease Education Channel to meet the famous college entrance examination teachers face to face. 16: 00- 17: 00 Lin Jiaming, a teacher from provincial experimental middle school, will continue to be a guest. Please stay tuned for our interview. Thank you very much, Mr. Xiong, and thank you very much for your enthusiastic participation.
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