1. the change of students' concept: the characteristics of high school mathematics learning focus on thinking and research.

2. Improve the efficiency of attending classes: prepare four books (typical problem set, correction book, exercise book and exercise book).

1) preview in advance is an important part of classroom efficiency, which can not only find difficulties, but also cultivate self-learning ability.

2) In class, concentrate on your study, so that you can hear, see, touch, speak and touch.

3) Take effective notes: 1 key questions; 2. Important mathematical ideas and methods; 3 Correct the wrong version

Remember the misunderstanding of taking notes: you can remember everything by grasping your beard and eyebrows, and you can't tell what to remember, which means that you didn't preview in advance or the preview was not in place.

3。 Review, consolidate and reflect; (Make good use of evening self-study and Saturday and Sunday)

Review every day: organize notes, do problems, etc.

Review each unit: organize the unit notes and do the questions. (knowledge system and type)

Examination or homework reflection-accuracy and general methods are the first, not speed and cleverness.

Interest is the best teacher in learning: it is the driving force of learning, so only when you feel that you have fun, enrichment and gain in learning can you gradually cultivate interest; Interest is based on a certain degree of perception. With thorough study, you won't be discouraged by an unsatisfactory exam. You should learn from it, analyze the shortcomings and constantly improve yourself.

Second, eliminate the thinking obstacles in learning mathematics.

There is a big gap between junior high school students and senior high school students in thinking, so don't have mathematical thinking obstacles.

It is very important to cultivate good mathematical thinking in senior high school-it refers to the basic methods of comparison, analysis, synthesis, induction and deduction based on perceptual knowledge of senior high school mathematics.

The formation of senior high school students' mathematical thinking is based on their understanding of the basic concepts, theorems and formulas of senior high school mathematics. The most effective way to develop mathematical thinking in senior high school is to solve problems.

(A) the reasons for high school students' mathematical thinking disorder

1。 In the classroom, teachers are allowed to instill teaching according to their own thinking or knowledge logic, and students are at a loss when reviewing or learning by themselves.

2。 The connection between old and new knowledge, the deviation of students' understanding and the obstacles to solving problems affect the improvement of problem-solving ability.

(B) the specific manifestations of mathematical thinking disorders

1. The shallowness of mathematical thinking cannot change the flexibility of thinking.

2。 Lack of sufficient abstract ability, good at dealing with some intuitive and familiar mathematical problems; We can't grasp the essence of its abstract problem. For example, in order to solve analytical problems, f [g(x)] is known to solve f (x). (Solving the domain of compound function).

Comprehensive literature review

1. handle the relationship between single subject and comprehensive.

Principle: Do a good job in single subject and learn to change it.

Myth: Work hard on interdisciplinary synthesis.

Doing a good job in a single subject means putting 95% of your energy into the study of a single subject. Why? Analysis of the comprehensive college entrance examination questions of liberal arts in recent years is basically a single subject platter. Among them, almost all small problems and the first few big problems only involve one theme; The last two big questions, called "interdisciplinary synthesis", are actually several questions of each subject, and then they are stiffly spliced together. Therefore, we should focus on single-subject study, avoid exultation and sorrow, and engage in interdisciplinary topics.

Learning to switch means that thinking can switch quickly between disciplines. This is the technical requirement for dealing with "assorted dishes". Technical problems are not difficult to solve, as long as you do more practice. Of course, because politics, history and geography are naturally related, we should focus on a single discipline when analyzing some problems, and other disciplines can play a supplementary role (for example, political issues often involve history). But this point cannot be overemphasized.

2. Handle the relationship between knowledge and ability.

Principle: lay a solid foundation and pay attention to ability.

Myth: Put aside knowledge and engage in "ability"

To lay a good foundation is to attach great importance to the study of knowledge. First, this is determined by the characteristics of liberal arts. Liberal arts have a strong memory. Without endorsement, the ability to engage is a castle in the air. Second, this is proved by the practice of comprehensive college entrance examination for liberal arts. The most prominent feature of the 2004 examination syllabus is to emphasize the examination of the backbone knowledge of the subject. Judging from this year's test paper, many people's "hot ability questions" did not appear; On the contrary, a typical knowledge problem, such as "how to adhere to the principle of being responsible to the people", has been highlighted.

Paying attention to ability means consciously exercising ability in knowledge learning. After all, the comprehensive liberal arts examination is different from the single subject examination. The most obvious point is to ignore the rote learning content of low-level students and pay attention to analytical and open content. This is the meaning of "ability". How to improve the ability? First, we should focus on mastering the analytical and expository contents in textbooks (rather than simply memorizing them); Second, pay attention to the application of causal analysis, analysis and synthesis, especially the method of multi-factor comprehensive analysis, which is a hot spot in the college entrance examination.

About the back, add a few points. First, absolute endorsement. This is the foundation of the foundation, and it is impossible without hard work. Second, we should focus on reciting. First, pay attention to subject knowledge and oppose tedious philosophy; The second is to focus on analytical knowledge. Third, we should recite on the basis of understanding and oppose rote learning. In short, learn liberal arts and try to recite; Learn comprehensive literature and memorize it by rote.

3. Handle the relationship between hot spots and knowledge.

Principle: Refine the materials and implement them in an integrated way.

Misunderstanding: no focus, ignoring implementation

The important feature of the comprehensive examination of liberal arts is that it is problem-centered, and these central problems are mostly social hot issues. In recent years, the hot topic of study is a headache for liberal arts students, which is reflected in the following aspects: (1) reciting a lot and not taking exams; I am familiar with the exam, but I am not sure. Why? There is no refinement and implementation.

(1) refined materials

Refining is the principle of handling hot materials. During the review period, each school will issue teaching AIDS (mainly politics) for many hot issues. The processing steps of these materials are as follows:

The first step is to distinguish between primary materials and secondary materials. The so-called main materials include the authoritative release of the Ministry of Education and the examination center, as well as the current political materials clearly stipulated in the examination syllabus (such as the report of the 16th National Congress of the Communist Party of China in 2003). Everything else is secondary, used to supplement the main material. Don't usurp the host's role or reverse your priorities.

The second step is to study the main materials. For example, when studying the report of the 16th National Congress of the Communist Party of China in 2003, we should carefully read the original text and study with the guidance of the Ministry of Education. This step is very similar to studying textbooks. At the same time, selectively look at some auxiliary materials. Note that no matter how famous the author of the reference book is, he is not writing college entrance examination questions, but also speculating on the thinking of the test center. Therefore, we must not be bound by reference books, and we must not replace the most important materials with reference books.

The third step is to summarize the core content of the main materials. This is an easy-to-miss step in college entrance examination review. For example, in the report of the 16th National Congress of the Communist Party of China, the core content is: material civilization, the core of which is to build a well-off society in an all-round way, including ownership, distribution system and management system; The core of political civilization is the concept of political civilization, the requirements of construction, the construction and leadership of the party. In practice, the summary of the core content should be more detailed. The above is the embodiment of the refining principle.

(2) Integration and implementation

Integrated implementation is a process of transforming hot spots into capabilities and effectively mastering them.

The first is mastery through a comprehensive study, that is, the summary of the previous step is integrated with the basic knowledge of the textbook. In other words, it is to "modify" the teaching materials for the hot spots of that year. The result of integration is in the chapter "Political Guidance" of this book.

The second is implementation, that is, mastering the content of integration through rote learning. Note that the final result of studying hot issues should be a comprehensive summary, not a pile of materials written or printed by others. The key is to extract knowledge and turn it into your own knowledge.

(3) Supplementary explanation of hot issues

First, pay attention to long-term hotspots. Issues such as environment, sovereignty, science and technology are fundamental to human development and are always hot spots. This long-term hot spot is the main content of the college entrance examination (see Examination Center's "Design of Examination Questions for Comprehensive Ability Test of Liberal Arts" in 2004). Our research focus should focus on these long-term problems. One is to master the basic knowledge and judgment basis (in textbooks), and the other is to understand and analyze the new manifestations of long-term hot spots (current politics).

Second, how to deal with the annual hot spots. First, don't recite and don't care about details. In recent years, the college entrance examination, the hot spots in those years have basically appeared as background materials, and there is no positive exam (this is completely different from the current affairs of the political college entrance examination in previous years), so as long as the face is familiar. Second, it should be analyzed in the context of long-term hot spots. For example, the United States does not sign the Kyoto Protocol, and the background is global environmental issues and development issues. Our focus is to master the basic knowledge of environmental issues and development issues, and use it to analyze American behavior. Don't talk about things, divorced from the macro background. The "humanistic care" that has been emphasized all the time now refers to these big backgrounds that are related to the future and destiny of mankind.

(2) Some suggestions

1. Step down and study the following.

(1) examination outline;

(2) Past college entrance examination questions (mainly in recent years, mainly literature).

2. About the allocation of review time and suggestions.

(1) Spend 50% of your time reviewing the comprehensive literature. Literature comprehensive review is easy to spread out too much and squeeze three main courses, which is not cost-effective in terms of scores.

(2) Seize the fragmentary time and memorize knowledge.

Second, history.

(A) the main points of historical review

1. Remember historical facts

History is the most emphasis on rote learning. Why? The content of historical memory mainly includes two parts, one is historical facts, and the other is analysis. Political rote learning is mainly about analysis, and there is little memory of facts, so it is far less difficult to remember history. Can't recite it? Let's analyze the history paper several times to see how many points are lost because of unclear memory. The answer is self-evident. In fact, unclear historical facts and careless examination of questions are the two major reasons for the loss of points in history. How to remember historical facts?

First, read carefully. Read one period at a time, including introduction, notes and illustrations. In the college entrance examination in 2002, there was a question about the geographical location of Congling, and the score rate was very low. In fact, the answer to "Pamirs and Karakorum Mountains" lies in the notes of ancient history textbooks. This enlightens us that we must study hard, especially the first round of review.

Second, start summing up. Be sure to devote yourself to writing, because reading and writing feel completely different. The exam is writing, not reading. Especially in the first round of review, I'd rather be verbose and write a complete summary. The following is a general format for analyzing historical events, which should be chosen in specific operations:

The name of 1. and its meaning (for example, early reform thoughts, reform thoughts)

2. Background

(1) Reasons (inevitability of things happening): main reasons (major contradictions), secondary reasons (minor contradictions), root causes (major social contradictions), specific reasons (concrete manifestations of root causes), direct reasons, indirect reasons and fuses.

(2) Conditions (possibility of things happening): politics, economy, class, ideology, times and others.

(3) Purpose (the reason and conditions are objective, but the purpose is subjective)

3. Process: strength, leadership, stage and stage characteristics, etc.

4. Meaning: nature, function, influence, characteristics (extremely important! Features = differences = test sites), experience and lessons

Third, pay attention to the characteristics. The characteristic is the difference. For example, the feature of Agricultural Administration Encyclopedia is mainly to introduce western water conservancy technology. The characteristic is the test center, so we should attach great importance to it, especially the characteristics of the times, which is often the hidden background of the answer.

Fourth, recite it regularly. Reading-writing-reciting is a complete chain, and we should recite it in a planned and step-by-step way at ordinary times. For example, recite a chapter a week, or synchronize with the teacher's review. Don't recite before the exam, it is very unstable; Don't recite anything in the exam, it's not systematic.

contact

High school history is characterized by paying attention to cause and effect, analyzing the relevance of knowledge and opposing rote memorization of isolated knowledge points. In fact, the process of setting questions is the process of establishing new contacts; The process of doing the problem is the process of analyzing the connection. There are two main steps to grasp the connection:

First, vertical and horizontal integration. On the one hand, we should pay attention to vertical contact (time contact), on the other hand, we should pay attention to horizontal contact (such as regional contact). Pay special attention to the causal link, which is the core of all links.

Second, weave the network. Vertical and horizontal integration, warp and weft crisscross, become a knowledge network.

3. Strengthen the examination of problems

In recent years, the college entrance examination, more and more emphasis has been placed on obtaining information from topics (especially material questions), combining textbook knowledge and forming answers with * * *. In this way, the importance of examining questions is highlighted. Pay attention to three points when examining the questions:

First, accuracy. Answer whatever you ask, don't answer irrelevant questions. Ask more questions about a big problem, not only for big problems, but also for every problem; There are many multiple-choice questions in a group, and it is necessary to examine not only the stem of each question, but also the total stem.

Second, all. Answer whatever you ask, don't miss it. Every sentence in the stem (especially the material question) generally contains at least one information point, and every point on the answer has a score.

Third, pay attention to "hints". In recent years, the comprehensive college entrance examination answer is often "both unexpected and reasonable", and these points have been lost. For example, the national college entrance examination in 2002 examined the changes in the sovereignty of the brigade. If we only examine the questions according to the above requirements, we will lose some points, such as "not respecting China's territorial sovereignty" and "trading China's sovereignty and interests behind China's back". These points come from the "moral" of the topic: the main idea of this topic is sovereignty, so we should answer questions around this point. This score is not easy to get, but if you think about the macro theme of each question when you do it (instead of just focusing on the topic), you will hopefully get a score.

(b) Discrimination against misconceptions

One, you can't do it. Memorizing knowledge points by taking notes is never systematic enough, which will split the connection. Doing problems is a good method, but it should not be abused.

Second, don't make random contact. Focus on mastering the basic knowledge network and don't have too many topics (the scope of this year's exam has been greatly reduced, and many topics have become unsystematic and should be abandoned).

(2) About the book "Historical Guidance"

1. Content

(1) grasp vertically, sort out historical clues and summarize the characteristics of the times;

(2) Grasping horizontally, explaining historical topics and demonstrating summary methods;

(3) Auxiliary materials, giving historical chronology and detailed knowledge summary to help you remember.

Due to the limitation of space, this book does not include exercises, but only summarizes and demonstrates many similar problems without enumerating them one by one. I hope readers can supplement their own exercises and establish their own relatively complete summary system.

Third, politics.

(A) the main points of political review

1. Pay attention to the method

Due to the discipline characteristics of politics, we should pay attention to some special methods when studying:

First, the universality and particularity of contradictions are combined. All chapters of Economic Common Sense (except the first chapter) focus on general economic principles first, and then advance to the particularity of Socialism with Chinese characteristics's market economy. Each chapter of Political Common Sense first talks about the general principles of political science, and then advances to the particularity of Socialism with Chinese characteristics's political theory. When learning, we must distinguish between universality and particularity, and make clear the relationship between them.

Second, the combination of world outlook and methodology. Philosophical common sense expounds a principle, that is, first talk about the world outlook, and then talk about methodology. When studying, we must not confuse the two, but make clear the corresponding relationship. (See the summary of the section "Political Orientation-Spiritual Civilization" in this book)

Third, the combination of primary and secondary, highlighting the key points. By doing the questions, we can find that the content of the political review is very concentrated, and these are the key points. Focusing on mastering key knowledge can get twice the result with half the effort.

Focus on hot spots

Please refer to "(1) summary, main points and misunderstandings-3" for this question. Handle the relationship between hot spots and knowledge. "

3. Pay attention to problem-solving ideas

The remarkable characteristics of political questions are clear questions and relatively fixed ideas. For example, as soon as we see environmental problems, we have the following philosophical thinking, and answering questions is rarely out of the circle. This kind of thing should be summarized more. I suggest that you use only one authoritative exercise book (such as "Compilation of College Entrance Examination Questions in the Last Five Years" and "Compilation of College Entrance Examination Questions in the Ten Years") to thoroughly understand each question and summarize the routines of each question.

Materialism: recognizing the objectivity of nature is the basic premise for people to consciously deal with the relationship between man and nature.

Dialectics: connection: dealing with the relationship between economic development and environmental protection; Development: sustainable development strategy; Contradiction: look at the influence of human beings on nature in two ways; Quantitative change: moderate development.

Epistemology: giving play to the unity of subjective initiative and respecting the law;

Values: Establish correct ecological values.

(2) About the book Political Guidance

In view of the difficulty of hot learning, this chapter gives the integration result of hot issues and basic knowledge, which is the final result of hot learning. If possible, I hope you can do it yourself; If time does not allow, you can also use the summary in this chapter directly. In addition, attention should be paid to adding new hot spots (for example, the current Theory of Three Represents Theory Learning Outline is very important).

Fourth, geography.

(A) geography review points

1. Pay attention to analysis and synthesis.

The remarkable feature of geography in senior high school is that it emphasizes the memory of knowledge and transits to the analysis and synthesis of knowledge. There are many causal analysis, especially the analysis of multi-factor interaction. For example, the geographical topic in 2002, the reason why Balkhash Lake is half light and half salty, is the result of the interaction of climate and runoff. The cause of the 10 degree isotherm was investigated in the 2003 national volume geography topic, which was the result of the interaction between latitude and topography. It can be seen that the continuity of college entrance examination questions! We must pay attention to research and contact, pay attention to comprehensive analysis, and don't get caught up in complex philosophy.

2. Pay attention to the combination and transformation of graphics and text.

Geography in senior high school is different from politics and history by combining pictures and texts. Image problem has been a hot topic in recent years because it can comprehensively examine students' ability to obtain information, convert information and analyze information. Several points should be paid attention to in learning image problems well:

First, study the common images carefully. Including charts in textbooks (statistical charts, schematic diagrams, landscape maps, etc.). ) and common charts in workbooks. For example, the basic form of terminator diagram is available in books, but there are many variations in exercise books, so we should master them one by one.

Second, master the method of analyzing images. There are few pictures in the college entrance examination, but there is a general method to analyze the images. For example, line charts must pay attention to coordinate names, trends, intersections and numerical levels. You should ask your teacher more about this matter.

Third, learn to draw. In the college entrance examination of 200 1, the general situation of painting was examined, and it appeared again in the college entrance examination of spring 2003, so painting can not be ignored. In particular, I will draw some difficult maps, such as section maps and isoline maps.

Pay attention to "pick it up"

The remarkable feature of geography review in senior high school is to pick up knowledge again after a year of suspension from high school. It is suggested to read through the textbooks in the summer vacation of senior two, summarize them in detail and review the exercise books and exam notes of senior one. Through self-study to complete the first review, thus winning the initiative of senior three.