First, consolidate the basic knowledge.
The proportion of easy questions, intermediate questions and difficult questions in college entrance examination mathematics problems is 3:5:2, that is, basic questions account for 80% and difficult questions account for 20%.
Whether in the first, second or third round of review, the "three basics", that is, basic knowledge, basic skills and basic thinking methods, are the most important. It is dangerous to hold on to some difficult problems! Only when the "three basics" pass, can we have the ability to do difficult problems.
Second, the construction of knowledge network.
The essence of mathematics teaching is to put a large number of declarative knowledge such as mathematical concepts, theorems and formulas into practice in the teaching of mathematical knowledge, so that students can form an increasingly hierarchical mathematical knowledge network structure on the basis of active participation and construction, so that students can experience the mathematical ideas and methods contained in the whole learning process and form a way to solve problems. Therefore, on the basis of consolidating the basic knowledge, we should grasp the vertical and horizontal links and build a knowledge network in the review of college entrance examination. After strengthening the connection of each knowledge block, grasp the main knowledge and clarify the framework.
Third, pay attention to the general method.
In recent years, college entrance examination questions have focused on the examination of general methods, thus avoiding questions that are too dead, too complicated and too biased. The thinking of solving problems does not depend on special skills, and there are many ways to solve problems, flexible methods and divergent thinking. Don't "play skills" too much in review. Excessive use of skills will make students with good grades "possessed" and students with poor grades "lose confidence".
Fourth, improve the computing power.
Computing ability is the most basic ability. Due to the tight review time and heavy tasks in senior three, teachers and students do not attach importance to the cultivation of computing ability. Look at a problem and you will know how to solve it. This is the direct cause of our senior three students' poor computing ability. In fact, the rationality, correctness, simplicity and timeliness of the operation play a vital role in students' examination results. Therefore, we should further strengthen the computing ability and let students realize the importance of computing and the standardization of writing. At the same time, I constantly reflect on the rationality of my problem-solving process, the equivalence of transformation and so on.
Fifth, the answer is rigorous and standardized.
There are many small mistakes in the students' answers, and too many small mistakes accumulate and affect the final grade. When marking and reviewing examination papers, students should be tirelessly warned to pay attention to the integrity of reasoning, especially the reasoning process in "solid geometry"; Pay attention to the rigor of mathematical symbols, as well as neat handwriting and how to alter it. Answer questions and explain them to students within the prescribed scope every year, and form a rigorous and standardized style.
Stage review and system summary
Divided by time, such as weekly review, mid-term review, final review, graduation review, entrance review, etc. , and divided from the knowledge, such as chapter review, unit review, general review, etc. , can be called stage system review.
1. Tasks of phase system review
(1) Strengthen memory, so that the results of learning can be firmly stored in the brain for easy reference at any time.
Expert experiments show that only 44% of the materials just remembered can be retained after one hour, and only 25% is left after two days. It can be seen that everyone will soon forget and then slowly forget. Some scholars believe that after learning, certain neural connections have been formed in the brain. If this connection is not strengthened through repeated and effective stimulation, it will gradually fade away and show the phenomenon of forgetting. It is to strengthen and perfect this nervous system and review it in various ways.
What you understand is easy to remember, but what you understand can only be truly remembered through review. Students with good memory not only pay attention to understanding, but also pay attention to review. They review every day, summarize every week, summarize every chapter, and review from different angles and levels many times, thus producing a good memory effect.
(2) Check for leaks and fill gaps to ensure the integrity of knowledge.
There are many factors that affect learning. In the long learning process, it is difficult to ensure that all factors are in the best state. So it is inevitable that there will be loopholes and shortcomings. After reviewing and checking, you can make up lessons in time to ensure the integrity and systematicness of the knowledge you have learned. All students who study hard can correct any loopholes and deficiencies in their studies in time. So their knowledge is always relatively complete.
(3) Mastery and systematization of knowledge.
Wisdom is just an organized knowledge system. The "organized knowledge system" here refers to systematic knowledge. It can be said that the formation of systematic knowledge is the central task of systematic review. Through the study of subjects, chapters and sections at ordinary times, we can say that we have basically completed the task of understanding various basic concepts and basic knowledge. Through review, comprehensive review, missing and filling in gaps, the integrity of knowledge is guaranteed, but at this time, students' understanding of things has not been completed, and the central task of review has not been completed. Why? Because the knowledge in our mind is still a "semi-finished product" at this time, we need to adopt thinking methods such as analysis and synthesis, comparative classification, abstract generalization and induction and deduction to "assemble" all the parts of the long-term learning knowledge, achieve mastery through a comprehensive study and thoroughly understand it, thus forming systematic knowledge. At this time, it can be said that it has become the whole task of the learning process.
2. Procedures and methods of phased systematic evaluation
We must pay attention to "three preparations" in stage review, namely, theme preparation, time preparation and material preparation.
(1) theme preparation.
Be sure to make clear the central content of this review before reviewing, and focus on this central content when reviewing. If the central content is not clear, picking up the textbook from beginning to end can't be called review, it can only be regarded as repetition, which plays a familiar role at most, and the knowledge is still scattered and unsystematic, and the effect is not good.
(2) Time preparation.
Because of the large amount of reading, thinking, consulting materials and writing review notes, the content and time of review must be relatively concentrated, and two methods can be adopted: active allocation and passive arrangement. Actively allocate time, that is, arrange a few days according to the review content, review part of the content every day or every one or two days, and then review all the content in a few days.
Passive arrangement of time, that is, review time is limited and can not be arranged at will. It is necessary to calculate how much time there is from review to examination and how much content needs to be reviewed. If there is not enough time, we should adjust the review content according to the permission of time, omit the familiar content and ensure the key subjects.
In this way, although there is not much time left after completing the study task every day, due to proper time arrangement, we can avoid the situation of being in a hurry.
(3) Material preparation.
When the central content of the review is determined, all textbooks, notes, homework, test papers and reference books related to the central content should be prepared as fully as possible. When reviewing, you should concentrate on thinking, and you can get the information when you need to consult it. The procedure of stage review should be as follows:
Step 1: Recall first, then read.
Like after-class review, when reviewing in stages, don't read books first, and try to think and recall independently. Don't be busy turning pages when you encounter problems or things you don't understand. Think about yourself first. If you really can't remember, look up the textbook. Doing so forces you to think, which helps to strengthen your memory and improve your learning efficiency.
Step 2: Look at the questions first, and then do them.
It is necessary to review the exercises done in the past when reviewing in stages. However, don't do it again without a question, and don't do nothing. The reading topic is to read the exercises, daily homework and examination papers in the book from beginning to end. When reading the questions, just look at the questions and sort out the ideas for solving them. What you can do can be compared with the original practice. If you can't do it, you can see how you solved it, where is the card this time, and then do it again.
Besides reading the questions, we should also choose some exercises to do, especially some comprehensive exercises to do. Because the exercises you usually do in your study are all for practicing the content of the lecture at that time, and they are all individual. Comprehensive exercises can only be answered by using all the knowledge in this chapter or this system. Therefore, doing some comprehensive exercises is a necessary method to consolidate and skillfully use knowledge in stage review. Make knowledge systematic and complete by doing comprehensive questions.
Step 3: Review first, and then take notes.
Before the end of the stage review, the review results shall be recorded. The results of review can include systematic knowledge, new experience, new problem-solving methods, own difficulties and shortcomings, etc. Review notes are not copies of class notes, but should be concise and highly summarized. Just like your guide into the field of knowledge, it can lead you to every corner of knowledge. In other words, you can recall the relevant contents in the textbook one by one by reading the review notes.
3. Basic requirements for phased system review
(1) Before reviewing, you should pay close attention to your usual study time and get ready. We should make use of sporadic time at ordinary times to prepare relevant notes, books, homework, test papers and reference books around the contents of the review center.
(2) Review around a central content.
When reviewing, we must first determine the central content of the review, which should be determined according to the knowledge system. When reviewing, as far as content is concerned, try to choose the content that is most closely related to the new lesson to review. In this way, not only the review task is completed, but also the learning of new courses is promoted. In addition, the content of each review should not be too much, be appropriate, and pay attention to the alternation of arts and sciences.
(3) Adhere to the method of cyclic review.
The so-called "cycle review method" means: after learning part of the content, review it in time. Then learn the next part. After learning the second review. The last review shall include the contents of the last review. That's it, ring by ring. At the same time, at a certain stage, the whole review content should be divided into several units, and there should be a big cycle after each unit is reviewed. More content can also be interspersed with loops.
(4) Do some comprehensive topics.
The purpose is to test the effect of review, deepen the understanding of knowledge and cultivate the ability to use knowledge to solve problems. What questions to choose should be determined around the center of review, and the key point is to do some comprehensive exercises. The types of comprehensive exercises should be consistent with the scope of knowledge involved in review. As comprehensive exercises, we should further improve and systematize our knowledge and cultivate our ability to use knowledge comprehensively.
(5) Concentrated time and quiet environment.
When reviewing, we should deal with more knowledge, such as reading, thinking, writing, looking up information, designing system tables and comparison tables. This is a time-consuming mental work, so it needs relatively concentrated time and a quiet environment without interference. Otherwise, the normal review thinking will be interrupted due to time and environmental problems, which will affect the review effect.
(6) Take review notes.
When reviewing, after hard thinking, a complete and systematic knowledge is formed. We should cherish this learning achievement and record it in the form of notes in time for future use. Pay attention to review your notes, grasp the essence of knowledge, and you will certainly get excellent results in the exam.
4. Common methods of phased systematic review
(1) time operation method.
Time management refers to the method of making objective plans objectively and is the art of arranging time. Time management includes long-term behavior, medium-term behavior and short-term behavior. The methods used for review are mostly medium-term operation and short-term operation. Mid-term operation method refers to the unit of month and year, and is limited to the time progress of completing a review goal. The specific review plan of each part should adopt the method of short-term operation. Short-term operation method mainly refers to the review method of learning time in weeks, days and hours.
This method has the following aspects:
① Key operation review method: it refers to putting the difficulties that must be overcome in review into the most flexible and energetic period of the day. Or put the difficult review on a relatively concentrated day.
2 insulation operation method: refers to the review method of being isolated from the outside world for a period of time and studying behind closed doors. In order to review some contents or knowledge suddenly in a period of time, it is necessary to prevent unnecessary interference from the outside world so as to concentrate on reviewing.
(3) The double-track operation method refers to putting another knowledge that can be reviewed at the same time together during the review of one knowledge. This can save time and improve efficiency. For example, for Chinese majors, when reviewing the development of free verse in modern literature, many works of contemporary writer Ai Qing are reviewed, and the artistic characteristics of Ai Qing's works in the three stages before and after and the ideological changes caused by them are compared. It is conducive to deepening the understanding of contemporary literature and modern literature.
④ Staggered operation method, in the review process, exchanging review contents can reduce the brain's fatigue for a certain content, thus maintaining the best and efficient working condition. There are two kinds of staggered operation: one is the mutual conversion of different review contents, but attention should be paid to maintaining the relative integrity of time and not dividing large chunks of time into inefficient fragments. You can spend two hours reviewing Chinese knowledge and two hours reviewing math knowledge. This is a reasonable staggered operation method. Second, review progress and rest are staggered. In order to fully adjust the mechanism of the brain, you can review for a while when the review efficiency is high, take a break when the efficiency is low, or change other contents. Relax after a tense review. In short, time management plays a macro-control role, which is interrelated with other review methods and sometimes inseparable, and should be correctly grasped from a macro perspective.
(2) Decentralized review method.
Dispersion refers to time dispersion, content dispersion and location dispersion. Everything is inseparable from time and space. Spreading review time is like saving. Broken content can be preserved in scattered time. "Accumulate over time" will become "rich people". The decentralized review method is especially suitable for the content with less close knowledge connection. Decentralized review method should pay attention to overcoming the influence of forgetting. Due to the dispersion of time and the interference of various environments, the impression is not deep and easy to forget. It is necessary to review constantly to consolidate the memory. Decentralized review is not a blind struggle for study time, but a planned, purposeful and targeted study. This is how it works. Therefore, it is best to combine decentralized review with overall layout and time operation.
(3) Centralized review method.
The centralized review method refers to the long-term centralized review. Like final review, exam review, self-study review and so on. This kind of centralized review is characterized by more content, concentrated time and less external interference. If arranged properly, it is easy to calm down and review well. So how to master the method of centralized review? It is to make full use of time to conduct a comprehensive review, synthesize the main points of various knowledge, compare them, find out similarities and differences, contact knowledge, and understand the outline of knowledge development in order to make a leap. Due to the concentration of time, review nervously, sort out what you have learned at ordinary times, re-recognize their relationship, find out the key points, and deepen your impression, which is of great help to get good grades in the exam and form a permanent memory. Centralized review should combine time management.
(4) General layout method.
When we write an article, after the topic comes out, we must first make an overall idea, which is the so-called "planning article". Outline, temper the theme, arrange the materials, plan the paragraphs, then form the structure and expression of the article, and then officially start the "opening". The same is true for the review of the overall layout method. In terms of content, what to review first, what to review later, the weight of each Kobe, the review order and the overall layout. In this way, a comprehensive consideration of the proportion of review time and content can not only highlight the key points but also give full consideration to them, which is conducive to ensuring the smooth completion of the review task.
(5) Easy first, then difficult.
As the name implies, it is easy to review, open a breakthrough, and gradually contact the difficult or difficult to remember, step by step review method.
Psychologically speaking, people's endurance is limited. As far as spiritual strength is concerned, positive factors must be mobilized to complete the review task. As the saying goes, the joy of victory motivates people, and the pain of failure depresses people. A person's career success, especially his first success, is particularly exciting in spirit. According to this truth, arranging simple content for review first can gradually eliminate the fear of difficulties, avoid self-interference in review, reduce mental stress and easily achieve complete success. Arrange the review content according to the difficulty of memory, which is very suitable for the exam. It will be very effective to review those that are not easy to forget first, then those that are difficult to remember later, and arrange those that are easy to forget before the exam.
The reason why it is easy before it is difficult is that breaking the easy is a step and weapon to attack the difficult. Just like climbing a mountain, climbing a gentle slope first and then a steep slope is very inspiring and easy to succeed.
Difficult and easy are relative, and the composition of every knowledge follows the law of easy first and then difficult. If it is easy to break first, it should be regarded as a ladder and breakthrough to attack difficulties. But we should pay attention to: first, don't cut off the continuity of knowledge; Second, we should firmly grasp the transition from "easy" to "difficult".
(6) Diagram of outline.
Summarize and refine knowledge in the form of outline, simplify the complex, turn the many into the few, and make it easy to master and remember, that is, outline diagram method. Summarizing and reviewing knowledge with outline graphic method can prevent local forgetting. The graphic method is intuitive, simple and easy to remember. But it should be noted that:
(1) You must sort out, process and understand what you have learned before you can extract contours or figures.
(2) Be clear and accurate. The graphic method cannot cover everything, and it is impossible to take care of all factors and conditions when considering it. It can only be the skeleton of knowledge, and the filling of flesh and blood should be coordinated with the review of other methods.
(7) Cross-infiltration method.
Cross-infiltration method is a special case of systematic review method. It has its own special purpose. Psychologists have done an experiment: Stimulating nerve cells in the brain with electrical pulses of the same frequency will make them quick at first. The longer the time, the weaker the response. After a period of stimulation, the response will return to its original state. This experiment shows that reviewing a knowledge for a long time will produce a kind of self-control shielding inhibition and reduce efficiency. When brain power and energy permit, it is beneficial to adjust the excitement center of the brain and insert some other content review that has nothing to do with it. For example, the intersection of thinking modes has changed from abstract concept thinking to image thinking; From calculation review to problem-solving reasoning and so on. The cross-infiltration of review content will often change the way of thinking, change the excitement center of the brain, and make the brain rest.
Using the cross-infiltration review method, we can adjust the boring monotony brought by reviewing a certain knowledge for a long time. At the same time, it is also conducive to the mutual penetration and mutual help of interconnected knowledge, deepening the understanding and application of knowledge and enhancing the ability to solve problems. Even in the cross-infiltration review, I will be inspired and achieve unexpected results.
(8) Strong stimulation method.
Strong stimulation is one of the review methods to help memory from psychological interest. That is, the memory formed after psychological stimulation will produce an unforgettable impression. In the process of study and review or other experiences, I was particularly impressed by things that caused drastic changes in my spirit and emotions and shocked my feelings. For example, the questions that were not answered correctly in the exam were deeply impressed afterwards, and they were remembered more firmly than other questions after understanding. Strong stimulation is sometimes imposed by the outside world, but it is often unconscious. Such as epiphany, epiphany, epiphany, etc. , are on the basis of their own efforts, inspired by the outside world and immediate changes. Literary creation is called inspiration and psychological communication is called nerve communication. The ancients called it epiphany. The intense stimulation generated in this review is benign, and it is a reflection of the full start of brain mechanism. Strong stimulation often appears in the state of high concentration and high tension during review. Seeking this efficient review method is called strong stimulation. The high efficiency of this review, accompanied by spiritual excitement, makes all aspects of knowledge come in droves, which is very beneficial to solving difficult problems, clarifying the essence and analyzing thoroughly. Once there is a strong stimulus, it is a good time to review.
(9) the method of "doing mutual test".
We should put what we have learned.
It is not easy to review and consolidate several classes. It is even more difficult for all students to do it, and everyone has something to gain. Different from individual free review and teacher-led review, students should look for "problem-making" materials in review, not only to reflect the key points and difficulties of the textbook, but also to think about the way of proposition and the reasonable distribution of difficult and general questions in the test questions according to their own experience in many exams, which will inevitably arouse students' great interest. If the question is well written, it is a great pride for students. In addition, the questioner is also responsible for making answers, marking papers and marking papers, which makes the questioner have to be very serious to avoid making mistakes. This is the psychological basis of "mutual test method".
This method can be used for unit review and comprehensive review. The practice is to explain the practices and requirements to the students first, and prompt the methods and steps, so that students can pay attention to the scientific and objective effect of "doing the problem". It can be divided into four steps:
The first step is to ask questions. It can also be divided into four small steps: finding knowledge points, classifying knowledge points, selecting topics and copying. Three requirements should be put forward: first, fill in the blanks with reference to standardized multiple-choice questions and non-standardized questions and answers; Second, plagiarism should be serious, and the author should be clearly stated; The third is to answer and prepare for marking.
The second step is the answer sheet. The test questions are prepared, collected in order, then exchanged and distributed, and the answers are given according to the specified time. No consultation or inquiry is allowed in the process of answering questions.
The third step is to return the answer sheet to the questioner for marking. We should emphasize seriousness and a high sense of responsibility.
The fourth step is to comment and discuss. Ask each student to explain the requirements of the topic, the standard of grading and the reasons for the wrong answer, so as to deepen the understanding of knowledge. When using this method, in order to save time and make the topic reasonable, you can also use the method of issuing blank test papers with the title and model of the test paper for the questioner to choose the topic and fill in the blanks in the review.