What are the characteristics and changes of 20 12 college entrance examination notes compared with 20 1 1?

Compared with 20 1 1, the examination notes of arts and sciences of 20 12 have no change in proposition, paper structure, objectives and requirements, but some examples have been changed in the examination papers of 20 1 1. These newer and more vivid examples are also used to explain and illustrate the knowledge and ability requirements for candidates. In terms of examination content, compared with last year, the content and requirements of science mathematics have been adjusted, especially the selection of coordinate system, parameter equation and inequality, and some test sites required last year have been cancelled. The reference test paper changes greatly, but the question type and test paper structure remain unchanged.

What contents have been deleted from the "Contents and Requirements of Selected Tests" in this year's science examination notes? Why?

This year's "Examination Instructions" of science deleted some contents in "Examination Contents and Requirements". In "2. Coordinate system and parameter equation ",delete two small items: one is" understand the position and method of expressing spatial emphasis in coordinate system and spherical coordinate system, and compare it with the method of expressing point position in spatial rectangular coordinate system to understand their differences "; Another is "understanding the generation process of hypocycloid and involute, and deducing their parameter equations". In addition, in "3. In Selected Lectures on Inequality, we deleted "We will discuss rank inequality by vector recursion" and "We will prove Bernoulli inequality by mathematical induction".

Why do you want to delete these contents? I think it's because these contents are complicated, difficult to master and not widely used. Over the years, the college entrance examination has basically not been taken, and some even have not been taught. In the spirit of people-oriented and seeking truth from facts, it is better to delete it directly. Therefore, it is called "people-oriented, making things easy, seeking truth from facts, and simplifying the complex".

What changes have been made to the reference papers in this year's exam notes?

There are always ***2 1 minor problems in science papers, among which 13 are different from last year. There are always 22 small questions in liberal arts papers, 9 of which are different from last year. It embodies the propositional principles of the college entrance examination: paying attention to the times and practicality; Functions and derivatives, series, trigonometric functions, solid geometry, analytic geometry and probability statistics should account for a large proportion. It embodies the spirit of people-oriented and advancing with the times. Through the study of the sample questions of "Examination Instructions", we find that the main contents of the sample questions are still in the traditional chapters of traditional textbooks. The focus and difficulty of the exam are still in function, sequence, inequality, trigonometric function, solid geometry and plane analytic geometry, so basing on foundation has become the main theme of college entrance examination review. Therefore, "the meaning of each year is similar, and the topic of each year is different." "Based on the foundation, it should be changed, and it is still calm in the face of freshness."

How to understand the three levels of knowledge requirements in the exam instructions?

The "Test Instructions" of the college entrance examination mathematics points out that "the requirements for knowledge are three levels in turn: understanding, cognition and mastery." Candidates must first distinguish what is "understanding, understanding and mastering". In a plate, what needs to be understood and what needs to be understood? What do you need to master? In fact, the knowledge requirements are divided into three levels from low to high, namely "cognition/understanding/imitation", "understanding/logical judgment/discrimination/application" and "mastery/proof/discussion transfer". The requirements at the higher level include the objectives at the lower level.

For example, the knowledge requirements for "function" in the exam instructions are:

① Knowing the elements that make up a function, we can find the definition domain and value domain of some simple functions; Understand the concept of mapping.

② In the actual situation, appropriate methods (such as image method, list method and analysis method) will be selected according to different needs to express functions.

③ Understand the simple piecewise function and apply it simply.

④ Understand the monotonicity, maximum (minimum) value and geometric significance of the function; Combined with specific functions, understand the meaning of function parity.

⑤ Understand and study the properties of functions by using function images.

There is no requirement of "mastering" in this part, in which "understanding" is the lowest level requirement, and "knowing, calculating and understanding" are the same level requirements; The level of "understanding" is higher than "understanding", which requires it to be correctly expressed in mathematical language and can be compared and distinguished. It is particularly important to note that in ④, the requirement for monotonicity of functions is "understanding", while the requirement for parity is "understanding", which obviously requires higher monotonicity.

How to study and read the Examination Instructions carefully and thoroughly?

Teachers should study the exam instructions and candidates should read them carefully. Candidates should pay special attention to the solution of the example and a short paragraph after the solution. Through the explanation of this passage, candidates can understand the difficulty of knowledge questions, how the ability is tested, and how the thinking method permeates the problem-solving ideas, which can help candidates better understand the characteristics and methods of the college entrance examination and train more pertinently. After reading through the exam instructions, we should emphasize the training of mathematical thinking in the review. Now some candidates are doing problems, and a lot of knowledge is listed. The narrative is specious and self-righteous, but it is actually chaotic. This is precisely the evil result of asking the sea tactics. In order to deal with problems about the ocean, we are exhausted and mechanically copy and swallow dates. As a result, the students' mathematical quality can not be improved, and their thinking and reasoning abilities are poor, which can not meet the needs of universities and society.

In addition, candidates should also regard reference papers as simulation papers. After a round of review, they will spend two hours doing a "simulation test" for themselves, simulating the structure of college entrance examination papers, experiencing the examination methods of reference papers, and learning how to allocate time reasonably in the examination.

What do you think is the strategy of reviewing for the next college entrance examination?

In the limited time of the next college entrance examination review, how to make our review fully effective and efficient is a problem that every examinee, teacher and parent should seriously reflect on. In view of the new ideas, new trends and new methods of the new curriculum college entrance examination, our review strategy, I think, is the following 16-character policy: people-oriented, book-oriented, based on the foundation, seeking truth from facts and understanding books.

How to understand the idea of "people-oriented" in the college entrance examination proposition?

The college entrance examination questions should fully respect students' differences in learning mathematics, and strive to make students with different ways of thinking get scientific evaluation. The design of the whole paper should be reasonable and pay attention to the overall effect.

People-oriented is to take care of all aspects, so that good students can also have room to play, so that poor students can also have a successful experience, so that ordinary students can get ideal scores through hard work. For example, the 20 1 1 Fujian college entrance examination paper is challenging for good students. Science 10, 15, 20, liberal arts 12, 16, 22 are all relatively innovative in this paper.

For poor students, there are many questions to examine basic concepts, basic operations and basic methods, such as science 1, 2, 3, 4, 5, 6, 1 1, 12, 13 and/kloc-0. Wenke 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 17, 18 are also subtopics. For middle school students, they also have their own advantages. In addition, science 8, 9, 18, 19, liberal arts 0,1,15, 19, 20, 2 1 etc. They are all intermediate questions, which are beneficial to middle school students.

20 1 1 The college entrance examination paper is made on the basis of understanding students' learning situation, which is undoubtedly beneficial to middle school mathematics teaching and quality education. In our opinion, the general trend of the proposition of the 20 12 college entrance examination in Fujian Province should be based on ordinary students, so that both good students and poor students have their own space, so as not to deviate from the people-oriented thought.

How to implement the guiding ideology of people-oriented in college entrance examination review?

Taking trigonometric function review as an example, based on the propositional characteristics of trigonometric function test questions and the different situations of candidates, trigonometric function should vary from person to person, so as to teach students in accordance with their aptitude and prepare for exams effectively, and have different preparation goals and knowledge and ability guidance for students at different levels.

1. For candidates who don't have high requirements for math scores, such as sports and art, they should pay attention to "guiding excavation, finding the right entrance and scoring as much as possible" when preparing for the exam. For them, the content of trigonometric function is the most important point, but we can't expect them to get high marks. When reviewing for preparation, teachers should not simply tell students how to solve problems, but should guide students how to dig out the conditions for solving problems and find the entrance to solving problems (although it is very simple for students at other levels), so that they can realize the importance of memorizing trigonometric functions of special angles, the basic properties of sine functions, trigonometric functions of the same angle and sine and cosine theorems for solving problems in the first step, and try to solve problems with relevant knowledge points.

2. For secondary school students, we should pay attention to "meeting and completing, strictly standardizing and striving for full marks" when preparing for the exam. Most students can find the solution quickly when solving trigonometric function problems, but there are mistakes due to nonstandard problem solving, imprecise thinking and careless calculation, such as multiple solutions or missing solutions due to ignoring the angle range, formula errors of trigonometric identity deformation (including induced formula, trigonometric function relationship with the same angle and sine and cosine formula of sum and difference of two angles) and numerical calculation errors. For these students, the emphasis should be on error analysis. First, we should emphasize the standardization of problem-solving steps, second, we should emphasize the standardization of writing, and third, we should ask students to develop the good habit of serious, accurate and fast calculation, so as to be comprehensive and strict, and strive for full marks.

3. For top students, we should pay attention to "preparing for exams should be excellent, improving efficiency and ensuring full marks". For top students, the content of trigonometric function is relatively simple, and the goal should be "no perfect score is unqualified", with special emphasis on the optimization and accuracy of calculation methods to improve the efficiency of problem solving. Only through such strict requirements can they change their carelessness and not lose a point in this content exam.

Why should the college entrance examination review be based on this?

Why should we use this as a basis to apply an old saying: "The book has its own examination questions, its own problem-solving skills, and its own words are like jade".

1, the book has its own test questions.

Over the years, especially in 20 1 1 year, it can be clearly seen that many questions come from textbooks and are processed from textbook examples or exercises, while some questions are almost copied from typical examples or exercises in textbooks.

2. The book has its own problem-solving skills.

Textbooks are the basic growth point of problem-solving ability. For example, reading ability can only be cultivated through reading, and textbooks are the basic materials to cultivate reading ability. College entrance examination review is exam-oriented teaching. One purpose of exam-oriented teaching is to form some models and print them in candidates' minds to ensure rapid extraction in corresponding situations. This is correct. The problem is that when we boil everything down to problem-based teaching and summarize various methods into each kind of topic, it will inevitably blur some basic things of mathematics, even the context and essence of mathematics.

Of course, some important conclusions and basic methods are indispensable for the joint entrance examination of mathematics. Some conclusions are named properties, theorems or formulas, while others are just examples or exercises. These conclusions themselves or generalizations are often hidden by certain situations and become unique entrance examination questions. Only by being familiar with the textbook can we quickly identify its prototype and simplify the thinking process. When solving objective problems, the workload will be reduced because of these conclusions; When solving problems, it is also the basis for exploring the thinking of solving problems and making reasonable reasoning. Moreover, some important mathematical ideas and the examinee's intuitive understanding of knowledge are all implicit in the textbook.

3, the book has its own words like jade.

The important task of college entrance examination review is to organize knowledge and make it systematic. Such as knowledge block diagram and knowledge list, the question is, how do they get it? Of course, teachers can tell these directly to candidates, but can what they hear directly be internalized into the cognitive structure of candidates? The best way is to let the candidates get it independently. These golden words are hidden in the textbook. This is actually a process of revisiting learning experiences and textbooks, and it is also a process of reading textbooks from thick to thin.

Mathematics college entrance examination also needs to standardize the answer. So, who will demonstrate? Which theorems can't be directly applied, which processes can't be omitted, which expressions can't be arbitrary, and which symbols can't be recognized can and can only be based on textbooks. The expression of solving problems should be based on textbooks. The omission of key steps, the abuse of symbols, the randomness of language and the generalization of graphic methods in many review materials are not desirable, and should be standardized through teaching materials and need to be thoroughly cleaned up.

The difficulty of trigonometric identity transformation is reduced, why is the score rate of candidates still not high?

Trigonometric identity transformation, the complexity of the test questions has been significantly reduced compared with before, while the candidates' answers have become more and more unsatisfactory as the test questions become simpler. This somewhat puzzling fact tells us that the trend of simplifying test questions leads to the simple application of simulation questions. The test questions are simple and understandable, and the simulation questions should be simple. The problem is not here, but the simplicity of the simulation questions makes candidates ignore the process of deriving the trigonometric formula, which should not be ignored. Only on this basis can we make up for this deficiency.

Triangle was not difficult, why didn't you get high marks?

I don't understand the basic concepts, and the special angular radian is very confused.

The angle range cannot be determined, and the symbol is difficult to break positive or negative.

Three changes and three uses are not flexible enough to remember important formulas.

The vein is not clear, how to deal with it mechanically?

Two transformations of the same image have less number, shape and phase assistance.

The oblique triangle solution without conditional selection is wrong.

Candidates are advised to grasp the basics, reflect and summarize, and learn more.

How to understand the return textbook?

Returning to textbooks is by no means "hot leftovers", but through "returning", we can constantly clarify and grasp the mathematical knowledge structure, constantly form and improve our understanding of mathematical thinking methods, and constantly improve our comprehensive application ability. The regression textbook can be summarized in four words: combing, developing, editing and changing.

(1) combing-combing knowledge and sorting out the mess. What are the important concepts? There are several important theorems (formulas).

Open the textbook, you can relive the course of learning and recall the plot of learning. For example, when reading textbooks carefully, we should form several kinds of consciousness: empty set consciousness, domain priority consciousness, consciousness of discussing whether the common ratio is 1, consciousness of discussing discriminant (especially in the key equations obtained by solving straight lines and conic curves simultaneously), etc. When understanding concepts, we must chew slowly and pay attention to details. For example, the definition of slope: only when the inclination angle is not 90, the tangent of the inclination angle is called the slope of this straight line, which is often forgotten by many candidates.

(2) hair-find the law and develop thinking. Reproduce the formation and development process of key knowledge, especially the mathematical thinking method produced in this process, and refine it. When reviewing each topic, be sure to contact the corresponding part of the textbook. We should not only understand the knowledge and methods provided by textbooks, but also understand the theorem, formula, derivation process and solution process of examples, and reveal the connection and transformation between examples and exercises.

In the process of review and training, we will accumulate a lot of experience and methods to solve problems, including some regular things. Attention should be paid to discovering the basis of these experiences, methods and laws from textbooks.

(3) Weaving-Weaving the network to seek integration. Clear up the knowledge structure before and after, initially establish the framework of the whole knowledge system, consciously strengthen the horizontal and vertical connection of knowledge, and form a preliminary network.

It is necessary to thoroughly understand and grasp the mathematical ideas, methods and essence contained in the teaching materials, refine the commonness and methods in the teaching materials, and strengthen the summary and application, string them into lines, form chains, stretch them into beautiful necklaces, and make them "sublimate".

(4) change-change the angle and change the training. We should thoroughly understand the typical examples and exercises in the textbook, and be good at studying the variant questions of the textbook from the perspective of connection. Pay attention to expanding the training function of the topic by changing the way of asking questions, increasing or decreasing the changing factors and extending the popularization as necessary. Nowadays, teaching materials are generally routine solutions, so we should think about the functions of selection, filling in the blanks, inquiry and so on, and explain them from the aspects of background, reality and source.

Every year, there are some "familiar questions" in the college entrance examination questions, which are actually "variant questions" of some exercises with rich connotations. Considering a changeable question can cultivate the flexibility and adaptability of candidates' thinking. The proposer of the college entrance examination is only allowed to bring the current teaching materials, but not any teaching materials, which shows that it is of great significance to study the examples (learning) of teaching materials.

Why should college entrance examination review be based on foundation?

Every question in the college entrance examination is a basic question, 80% is a pure basic question, and 20% is a basic question shrouded in smoke bombs. The so-called problem is to add more or less deceptive camouflage to the basic questions and dig some traps. Students who can't learn blindly do difficult problems, and the foundation will never be good; Students who can learn encounter problems, see the essence through the phenomenon, and the clouds disappear.

The secret of the success of the "tumbler" in the math exam is not to get all the difficult questions right in each exam, but to get all the basic questions right in the middle class. The contest between experts lies in details and foundation. The thinking of college entrance examination proposition experts when conceiving college entrance examination questions is often to make a big fuss about the transplantation and adaptation of basic content and the intersection between basic content. Every year, after dissecting the mathematical finale of the college entrance examination, it is branded with the shadow of the basic content, which can be linked to the basic knowledge test center.

The basic knowledge of mathematics is the bottleneck of improving the mathematics score in the college entrance examination. Only by combing the knowledge into a net and having a deep understanding of the basic knowledge of mathematics can we break through this bottleneck, gradually form basic skills and improve our ability. Just like Lao Tzu said, "Everything is difficult for a willing mind.".

In the college entrance examination review, many students understand it as soon as they listen, but they will do it at first sight, but they will make mistakes when they do it, and they will paste when they take the exam. What is the reason?

This is because it has not reached its due level of thinking. Because learning has three levels of ability: first, "understanding", as long as the teacher explains clearly, the topic is chosen properly, and the students participate seriously, there is generally no problem, which is the lower level of thinking; The second is "meeting", that is, being able to imitate on the basis of understanding, which needs to be reflected in appropriate practice, and thinking has reached a higher level; The third is "enlightenment". When we realize the truth of solving problems, we can sum up the rules of solving problems, and we can flexibly apply them to other problems, so as to grasp the thinking method of solving problems in essence. This is the height of thinking and the goal we pursue. The ancients said, "The way to teach lies in degree, and the way to learn lies in enlightenment.".

Without paying attention to the essence of mathematics, being interested in superficial phenomena, doing a large number of simulated test papers and repeating exercises, it is impossible to improve the quality of mathematics. In the review of college entrance examination, only by strengthening the internal connection of mathematics knowledge, grasping the essence of mathematics, emphasizing the understanding and application of concepts and the cultivation of thinking ability can we really improve our mathematics quality. In the review of college entrance examination, we should achieve "three natures", that is, a deep understanding, comprehensive mastery and application of knowledge.

Why should math review pay attention to the cultivation of memory?

Because of the characteristics of mathematics itself, students generally attach importance to strengthening the ability of calculation, logical reasoning, thinking, spatial imagination, observation, calculation, analysis and modeling, while ignoring the open cultivation of their own memory. Some students even exclude memory from the quality category, focusing only on knowledge learning and ignoring the mastery of memory methods. When learning mathematics, not only formulas need to be memorized, but also definitions, axioms, theorems and properties in mathematics need to be memorized on the basis of understanding, as well as common problem-solving methods and skills. There are some typical examples and exercises that are very important in themselves. Further refining these examples and exercises can be a very important "second-hand conclusion". Familiarity with these conclusions is of great benefit to candidates to improve the speed of solving problems.

There are many ways to improve memory:

For example, the solution set of one-dimensional linear inequality: "The same big, the same small, the big and the small are sandwiched together, and the big and the small cannot be solved."

For another example, many students can't remember the parallel judgment of line and plane and the theorem of nature, so they might as well fill in the lyrics with the farewell soundtrack:

"Out-of-plane, straight lines, parallel lines, you can deduce that straight lines are parallel to this plane.

A straight line, a parallel plane, and an intersecting line as a plane can be used to derive the intersecting line between the plane and the parallel line. "

How to improve the quality of review?

In your usual study, you must have come across many small conclusions. Although these small conclusions are lower than theorem formulas, they greatly enrich the original theorems and formulas and are very useful. Therefore, you should carefully collect and memorize more than 80 books in the order of the textbook catalogue.

When reviewing mathematics in college entrance examination, we should not simply repeat what we have learned, but sort out the basic knowledge as a whole according to the logical structure of mathematics and the internal relationship between knowledge. It is also necessary to connect the scattered knowledge, thinking methods and problem-solving rules of each unit with mathematics, condense them into essence, store them in the brain and use them in the exam in time, so as to master them integrally, systematically and online. As Pan Changjiang famously said, "All that is condensed is the essence".

How to overcome the phenomenon of "meeting but not right, right but not complete, all but not excellent, excellent but not beautiful" in mathematics review of college entrance examination?

"Meeting but not right, right but not complete, all but not excellent, excellent but not beautiful" is a common phenomenon in college entrance examination, which is mainly caused by candidates' weak ability to examine questions, careless problem solving and irregular writing. Therefore, it is necessary to cultivate a scientific and rigorous learning attitude, be good at paying attention to learning details, learn to accurately express mathematical concepts and principles, and standardize writing algorithms, reasoning, symbols, etc. Peacetime training is the basis to ensure a long score in the college entrance examination. Every mathematics test paper of NMET must have a considerable number of original questions, which embodies NMET's requirements and proposition ideas and condenses the experience and wisdom of the proposer. This kind of questions are unfamiliar in situation, novel in form and exquisite in structure, so it is impossible for them to devote themselves to problem-solving activities calmly and smartly, and it is impossible to spend too much time and energy deliberately seeking simplicity and novelty. The hope of success depends entirely on the accumulation of knowledge, skills, thinking and psychology in peacetime, that is, well-trained in peacetime. To be well-trained at ordinary times, we must do the following four things:

1, to do a good job in standardization training, we must pay close attention to the "three merits", that is, drawing, calculating and judging.

2. Pay attention to the exposure of the thinking process.

3. Pay close attention to the cultivation of normative consciousness.

4. Pay attention to the compensation training after error correction.

Because of the time, today's interview will be over. Thank you very much, Mr. Zhou. At the end of the program, please ask the teacher to say a few words to the candidates. Tomorrow, Liang Jingdang, a senior history teacher in Fuzhou Senior Middle School, will log on to this website. Candidates and parents are welcome to ask questions enthusiastically.

The goal of high school mathematics curriculum is: "to understand the basic mathematical concepts, the essence of mathematical conclusions, the background of concepts, and to apply the mathematical ideas and methods contained in them." This is not only the goal of the course, but also the goal of the college entrance examination proposition, and it is also the goal of our college entrance examination review. Therefore, people-oriented, people-oriented, based on the basic, seeking truth from facts, is the foundation of our senior three review success.