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What are the characteristics and changes of the 2012 College Entrance Examination Mathematics "Examination Instructions" compared with 2011?

Compared with 2011, the 2012 "Examination Instructions" for Arts and Sciences has not changed in terms of proposition ideas, test paper structure, goals and requirements, etc. However, some sample questions have been changed to 2011 local college entrance examination papers. questions that appear in the test. These newer and more vivid examples are also used to explain and illustrate the knowledge and ability requirements of candidates. In terms of exam content, compared with last year, the content and requirements of the science and mathematics elective exams have been adjusted. In particular, some test points required last year have been cancelled, such as coordinate systems and parametric equations, and inequalities. The reference test paper has undergone major changes, but the question types and test paper structure remain unchanged.

What contents have been deleted from the "Exam Selection Contents and Requirements" of this year's science "Examination Instructions"? Why?

This year’s "Examination Instructions" for science subjects has deleted some content in the "Examination Contents and Requirements". In "2. Coordinate systems and parametric equations", two small items were deleted: one is "Understand the position and method of expressing spatial points in the coordinate system and spherical coordinate system, and the method of expressing the position of points in the space rectangular coordinate system Compare and understand their differences"; another one is "Understand the generation process of cycloids and involutes, and be able to derive their parametric equations." In addition, in "3. Selected Lectures on Inequality", "can use vector recursion method to discuss ordering inequalities" and "can use mathematical induction to prove Bernoulli's inequality" are deleted.

Why should we delete this content? I think it’s because these contents are complex, difficult, difficult to master, and not widely used. They have rarely been tested in college entrance examinations in various places over the years, and some even do not teach them. In the spirit of people-oriented and seeking truth from facts, it would be better to delete them directly. . Therefore, it is said that "it is people-oriented to determine difficulty and ease, and to seek truth from facts and eliminate redundancy."

What changes are there in this year’s "Examination Instructions" reference test papers?

The science test paper has a total of 21 questions, 13 of which are different from last year. The liberal arts test paper has a total of 22 questions, 9 of which are different from last year. It embodies the proposition principles of the college entrance examination: focusing on contemporary and practical aspects; functions and derivatives, sequence, trigonometric functions, solid geometry, analytic geometry, probability and statistics should occupy a larger proportion. It embodies the spirit of people-oriented and advancing with the times. Through research on the sample questions of the "Examination Instructions", we found that the main content of the sample questions is still in the traditional chapters of traditional textbooks. The key and difficult points in the exam are still functions, sequences, inequalities, trigonometric functions, solid geometry and plane analytic geometry, so focusing on the basics has become the main theme of college entrance examination review. Therefore, it is said that "the meaning is similar every year, but the questions are different every year", "based on the basics and adapt to changes, and still calmly face the freshness."

Three knowledge requirements in the "Examination Instructions" How to understand levels?

The "Examination Instructions" of the College Entrance Examination Mathematics points out that "the requirements for knowledge are three levels of understanding, understanding and mastering." Candidates must first distinguish what "understanding, understanding and mastering" are. In a section, what do you need to know and what do you need to understand? What else needs to be mastered? In fact, here it is said that the knowledge requirements are divided into three levels from low to high, namely "know/understand/imitate", "understand/logical judgment/judgment/application", "master/prove/discuss transfer", and the higher level The hierarchical requirements of the first level include the hierarchical goals of the lower level.

For example, the knowledge requirements for "function" in the "Exam Instructions" are:

① Understand the elements that constitute a function, and be able to find the definition domain and value range of some simple functions; understand mapping concept.

②In actual situations, appropriate methods (such as image method, list method, and analytical method) will be selected to represent functions according to different needs.

③Understand simple piecewise functions and be able to apply them simply.

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

⑤Be able to use function images to understand and study the properties of functions.

In this section, there is no requirement for "mastery", among which "understanding" is the lowest level requirement, and "being able to ask and calculate" and "understanding" are requirements at the same level; "understanding" The level is higher than "understanding" and requires the ability to express correctly in mathematical language, and to be able to compare and distinguish. Pay special attention to ④. The requirement for the monotonicity of the function is "understanding", while the requirement for parity is "understanding". Obviously, the requirement for monotonicity is higher.

How to study, carefully read the "Exam Instructions" and understand the "Exam Instructions" thoroughly?

For the "Examination Instructions", teachers must study it and candidates must read it carefully. Candidates should pay particular attention to the solution to the example problem and the short text following the solution. Through the explanation of this paragraph, candidates can understand the difficulty of knowledge questions, how ability is tested, and how thinking methods penetrate into problem-solving ideas. This can help candidates better understand the characteristics of propositions in the college entrance examination. and methods to carry out training in a more targeted manner. Thoroughly understand the "Examination Instructions" and emphasize the training of mathematical thinking during review. Nowadays, some candidates list a lot of knowledge when answering questions, and the descriptions are specious. They think they are right, but in fact they are in chaos.

This is exactly the evil result of the tactics of overcoming the sea of ??questions, struggling to deal with the sea of ??questions, copying by rote, and swallowing the truth. The result of this is: the mathematical quality of the candidates cannot be improved, and the candidates' thinking and reasoning skills are very poor, and they cannot adapt to university and society. needs.

In addition, candidates should also regard the reference test paper as a simulation paper. After a round of review, spend 2 hours on a "mock test" for themselves to simulate the structure of the college entrance examination paper and experience Refer to the examination method of the test paper and learn how to allocate time reasonably during the examination.

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

In the limited time for the next college entrance examination review, how to make our review fully effective and efficient is a question that each of our candidates, teachers and parents should seriously reflect on. In response to the new concepts, new trends and prescriptive methods of the new curriculum college entrance examination questions, our review strategy, I think, is the following sixteen-character policy: people-oriented, based on the foundation, based on the basics, seeking truth and understanding the foundation.

How do you understand the concept of "people-oriented" in the college entrance examination question?

The college entrance examination questions should fully respect the differences among students in learning mathematics, and strive to enable students with different thinking styles to receive scientific evaluation. The design of the entire test paper should be reasonable and focus on the overall effect.

Putting people first means taking care of all aspects, allowing good students to have room to perform, allowing poor students to have a successful experience, and allowing average students to get ideal scores after hard work. For example, for good students in the 2011 Fujian Provincial College Entrance Examination, questions 10, 15, and 20 in science and questions 12, 16, and 22 in liberal arts are challenging questions, and they are the more innovative ones in this examination paper. The test questions are prepared for good students. Of course, average students can also solve such questions if they work hard.

For poor students, there are many questions that test basic concepts, basic operations, and basic methods, such as Science 1, 2, 3, 4, 5, 6, 11, 12, 13, 14, and 16 , 17, 21, etc. are all easy questions. Liberal Arts 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 17, 18 are also given points. For intermediate students, there is room for improvement. For example, question 7 in science (question 11 in liberal arts) can be solved directly using the geometric theorem, or it can be divided into ellipses and hyperbolas. Different thinking can lead to different paths, which can reflect Depending on the students' differences, for example, there are many ways to approach question 9 in liberal arts. Also, questions 8, 9, 18, and 19 for science subjects, questions 0, 11, 15, 19, 20, 21, etc. for liberal arts subjects are mid-range questions, which are conducive to the performance of middle-level students.

The 2011 College Entrance Examination Papers were formulated on the basis of understanding students’ learning conditions, which is undoubtedly beneficial to middle school mathematics teaching and the implementation of quality education. We believe that the general tendency of the 2012 Fujian Province College Entrance Examination Mathematics test papers should be more focused on average students, and allow both good and poor students their own space. In this way, we will not deviate from the people-oriented approach.

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

Take the review of trigonometric functions as an example. Based on the propositional characteristics of the trigonometric functions college entrance examination questions and the various situations of the candidates, trigonometric functions should be different from person to person, so as to teach students in accordance with their aptitude and effectively prepare for the exam, so as to prepare students at different levels. There should be different preparation goals and knowledge positioning.

1. For candidates who do not have high requirements for mathematics scores such as sports and art, the review preparation should focus on "guiding the excavation, finding the entrance, and scoring as much as possible." For them, the content of trigonometric functions is one of their most important scoring points, but they cannot expect high scores. When reviewing and preparing for exams, teachers should not simply tell them how to solve the problem, but should guide students how to explore the problem conditions and find the entrance to the problem (although it is very simple for students at other levels), so that they can memorize the trigonometric functions of special angles. Values, basic properties of sine functions, congruent trigonometric functions, sine and cosine theorems, etc. play an important role in the first step of solving the problem. Try to use relevant knowledge points to try to solve the problem.

2. For middle school students, when preparing for the exam, the review should focus on "knowing and being comprehensive, strictly standardizing, and striving for full marks." Most students can quickly find the solution when solving trigonometric function problems. However, due to insufficient standardization of problem solving, insufficient thinking and careful calculation, they make mistakes, such as neglecting the range of angles and resulting in multiple or missing solutions. Trigonometric identity deformation (including induction formulas, trigonometric function relations of same angles and sine and cosine formulas of the sum and difference of two angles) formula errors, as well as numerical calculation errors. For this group of students, the focus should be on the analysis of error causes. First, it is necessary to emphasize the standardization of problem-solving steps. Secondly, it is necessary to emphasize the standardization of writing. Thirdly, students are required to develop good habits of careful, accurate and fast calculation. Earnestly meet the requirements and be thorough, strictly standardize, and strive for full marks.

3. For top students, when reviewing for exams, we should focus on “knowing how to be good, improving efficiency, and ensuring full marks.” For top students, the content of trigonometric functions is relatively simple, so they should set the goal of "failure to pass without full marks", with special emphasis on the optimization and accuracy of calculation methods to improve problem-solving efficiency. Only through such strict requirements can they be prompted to change their carelessness and not lose a single point in this content test.

Why should we focus on the basics when reviewing for the college entrance examination?

Why should we be book-oriented? To paraphrase an old saying: "The book has its own test questions, the book has its own problem-solving techniques, and the book has its own words like jade."

1. The book has its own test questions

It can be clearly seen from the mathematics test questions of college entrance examinations across the country over the years, especially in 2011, that many test questions are derived from textbooks. Examples or exercises are processed, and some questions are almost copies of typical examples or exercises in textbooks in terms of question types.

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 growth point for cultivating reading ability. The basic material of ability. College entrance examination review is exam-oriented teaching. One purpose of exam-oriented teaching is to form some models and imprint them in the minds of candidates to ensure rapid extraction in corresponding situations. This is right. The problem is that when we boil everything down to the teaching of question types and focus on the various methods summarized into each type of question, we will inevitably obscure some basic things in mathematics, even the ins and outs of mathematics and the essence of mathematics.

Of course, some important conclusions and basic methods are indispensable for the mathematics college entrance examination. Some conclusions are named properties, theorems or formulas, and some conclusions are just examples or exercises. These conclusions themselves or their extensions are often A certain situation is hidden and becomes a unique college entrance examination question. Only by being familiar with the textbook can you quickly identify its prototype and simplify the thinking process. When solving objective problems, these conclusions will reduce the workload; when solving problems, they are also the basis for exploring problem-solving ideas and making reasonable reasoning. In addition, some important mathematical ideas and candidates' intuitive understanding of knowledge are implicit in the textbooks.

3. There are words in the book like jade

The important task of reviewing for the college entrance examination is to sort out the knowledge and make the knowledge into a system. For example, knowledge block diagrams and knowledge lists. The question is, why do they get them? 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 obtain these good words on their own. These good words are hidden in the textbooks. This is actually a process of reviewing the learning experience and the textbooks, and it is also a process of reading the textbooks from thick to thin.

For the Mathematics College Entrance Examination, standardized answers are required. So, who will demonstrate? Which theorems cannot be directly applied, which processes cannot be omitted, which expressions cannot be arbitrary, and which symbols are not recognized, these can and can only be based on textbooks. Regarding the expression of problem solving, the textbook should be used as the standard. The omission of key steps, the misuse of symbols, the arbitrariness of language and the generalization of diagramming methods in many review materials are all undesirable. They should be standardized through textbooks and corrected through textbooks.

The difficulty of trigonometric identity transformation has been reduced. Why is the score rate of candidates still not high?

For trigonometric identity transformation, the complexity of the test questions has been significantly reduced compared to before, but the candidates’ answers have become increasingly unsatisfactory as the test questions have become simpler. This is somewhat puzzling. Tell us, because the trend of simplifying test questions has led to the simple application of simulation questions. If the test questions are simple, then of course the simulation questions should also be simple. This is understandable. The problem is not here, but that the simplicity of the simulation questions makes candidates ignore the process of deriving trigonometric formulas. This process should not be ignored. Only by focusing on the basics can we make up for this lack.

Triangle is not difficult, so why don’t you get high scores?

I don’t understand the basic concepts, and I am confused about special angles and radians.

The angle range cannot be determined, and the sign is difficult to determine whether it is positive or negative.

Three changes and three uses are inflexible, and important formulas cannot be remembered.

How to deal with it if you don’t know the ins and outs and apply it mechanically?

Identity image transformation, less use of numbers and shapes as assistance.

The theorem is not selected according to the conditions, and the solution of the oblique triangle is wrong.

I advise candidates to grasp the basics, reflect and summarize more.

How to understand the return textbook?

Returning to textbooks is by no means "burning leftovers", but through "returning" to continuously clarify and grasp the structure of mathematical knowledge, constantly form and improve the understanding of mathematical thinking methods, and constantly To improve comprehensive application ability, returning to textbooks can be summarized in four words: comb, hair, braid, and change.

(1) Comb - sort out knowledge and clarify the clues. What are the important concepts teased out? How many important theorems (formulas) are there?

Opening the textbook can relive the learning process and recall the learning plot. For example, when reading the textbook carefully, you need to form several kinds of awareness: empty set awareness, definition domain priority awareness, discussion of whether the common ratio is 1, and discussion of discriminant expressions (especially when the straight line and conic section are solved simultaneously. key equations), etc.; when understanding concepts, be sure to be precise and pay attention to details. For example, the definition of slope: only when the inclination angle of a straight line is not 90°, the tangent of its inclination angle is called the slope of the straight line. Many candidates often forget this.

(2) Discover - discover patterns and develop thinking. Reproduce the formation and development process of key knowledge, especially the mathematical thinking methods produced in this process, and refine them. When reviewing each topic, you must contact the corresponding part in the textbook. It is necessary not only to understand the knowledge and methods provided in the textbook, but also to understand the theorems, formulas, derivation processes and solution processes of examples, and to reveal the connections and transformations between examples and exercises.

In the process of review and training, we will accumulate a lot of problem-solving experience and methods, including some regularities. We should pay attention to exploring the basis of these experiences, methods and regularities from the textbooks.

(3) Editing - weaving networks and seeking intersections. Clarify the knowledge structure before and after, establish a preliminary framework for the entire knowledge system, and consciously strengthen the horizontal and vertical connections of knowledge to form a preliminary network.

It is necessary to deeply and penetratingly understand and grasp the mathematical ideas, mathematical methods and mathematical essence contained in the teaching materials, refine the generality and general methods in the teaching materials, and strengthen the summary and application to string them together. , to form a chain, and the variations are elevated, and the scattered pearls are strung into exquisite necklaces, so that they can be "sublimated".

(4) Change - change the angle and train in different ways. Complete the typical examples and exercises in the textbook, and be good at studying variations of the textbook questions from a connected perspective. Pay attention to expanding the training function of textbook topics by changing the way they are asked, adding or reducing changing factors, and making necessary extensions and promotions. Current textbooks generally deal with conventional answer questions, which should be considered in terms of question functions such as selection, fill-in-the-blank, and exploration, and should be explained from aspects such as background, reality, and sources.

There are some "déjà vu questions" in the college entrance examination questions every year. These "déjà vu questions" are actually "variant questions". For some exercises with rich connotations, considering the variety of questions in one question can cultivate the candidates' thinking flexibility and various adaptability. College entrance examination test takers are only allowed to bring current textbooks and adapt them from them, but cannot bring any teaching aids. This shows that studying the examples (exercises) of the textbooks is of great significance.

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

Every question in the college entrance examination is a basic question, 80% are pure basic questions, and 20% are basic questions shrouded in smoke bombs. The so-called difficult questions are more or less confusing disguises and traps added to the basic questions. Students who can't learn will never get a good foundation if they blindly solve difficult problems; students who can learn will never get a good foundation if they encounter difficult problems and see the essence through the phenomenon.

The secret to success in math exams is not to get all the difficult questions right in every exam, but to do all the basic and mid-range questions flawlessly. The competition between masters lies in details and fundamentals. The idea of ????conceiving college entrance examination questions is often to transplant and adapt the intersection between the basic content and the basic content, and to make a big fuss about the integration of threads. Every year, the final problem of mathematics in the college entrance examination is dissected layer by layer, and the shadow of the basic content is imprinted on it, and it can all be linked to the basic knowledge test points.

Basic knowledge of mathematics is the bottleneck for improving mathematics scores in the college entrance examination. Only by sorting out knowledge to form a network and having a deep understanding of basic mathematics knowledge can we break through this bottleneck, gradually form basic skills, and achieve improvement in abilities. . As Lao Tzu said: "The difficult things in the world are made easy, and the great things in the world are made small."

In the college entrance examination review, many students understand it as soon as they listen and read it, but they make mistakes as soon as they do it and are confused when they take the test. What's the reason?

This is because the level of thinking has not been reached. Since there are three levels of ability in learning: the first is "understanding", as long as the teacher explains clearly, the questions are selected appropriately, and the students are serious about it, there is generally no problem. This is the lower level of thinking; the second is "knowing", which is the basis of understanding. Being able to imitate needs to be reflected in the appropriate amount of practice. Relatively speaking, the thinking has reached a higher level; the third is "enlightenment", which requires understanding the principles of solving problems, being able to summarize the rules of problem-solving, and being able to flexibly apply it to solve problems. For other problems, we must essentially grasp the thinking method to solve the problem. This is a high level of thinking and the goal we pursue. As the ancients said: "The way to teach lies in degree, and the way to learn lies in enlightenment."

If you do not pay attention to the essence of mathematics, you are only interested in superficial phenomena, and you cannot improve your mathematical quality by blindly doing a large number of mock tests and practicing repeatedly. In the college entrance examination review, only by strengthening the inner connection of mathematical knowledge, grasping the essence of mathematics, emphasizing the understanding and application of concepts, and emphasizing the cultivation of thinking ability can we truly improve our mathematical quality. In the college entrance examination review, we should achieve the "three qualities", that is, the profound understanding of knowledge, the comprehensive mastery, and the flexibility of application, so that we can form a comprehensive knowledge system.

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

Due to the characteristics of the mathematics subject itself, students generally focus on strengthening their calculation, logical reasoning, thinking, spatial imagination, observation, operation, analysis, modeling and other abilities, but neglect the open cultivation of their own memory. , Some students even exclude memory from the category of quality and only pay attention to the learning of knowledge and not the mastery of memory methods. When learning mathematics, not only formulas need to be memorized, but also definitions, axioms, theorems, properties, etc. in mathematics need to be memorized on the basis of understanding. Common problem-solving methods and techniques also need to be memorized. There are also some typical examples and exercises, which are also very important in themselves. If these examples and exercises are further refined, they can become very important "second-hand conclusions." Being familiar with these conclusions will be of great benefit to candidates in improving their problem-solving speed.

There are many ways to improve memory:

For example, the solution set of linear inequalities of one variable: "The same big and small, the same small and big, big and small can't be solved." .

Another example is the judgment of line-surface parallelism and the property theorem. Many students cannot remember it. You might as well fill in the lyrics with the music score of "Farewell":

"Outside the plane, there is a straight line. If a line is parallel to a plane, the straight line can be deduced to be parallel to the plane.

A straight line is parallel to the plane. If a plane is drawn through the line, the intersecting line can be deduced to be parallel to the straight line."

How to improve the quality of review?

In your daily study, you must have encountered a large number of small conclusions. Although these small conclusions have a lower status than theorems and formulas, they have greatly enriched the original theorems and formulas and are very useful, so You should collect them carefully according to the order of the textbook catalog and memorize more than 80 of them.

When reviewing mathematics for the college entrance examination, you should not simply repeat the mathematical knowledge you have learned, but organize the basic knowledge as a whole according to the logical structure of mathematics and the internal connections between knowledge. It is also necessary to mathematically connect the local and scattered knowledge of each unit, the thinking methods of problem-solving, and the rules of problem-solving that have been learned in daily life, and condense them into essence, store them in the brain, and use them in a timely manner in the exam. In this way, we can grasp knowledge, ideas and methods as a whole, systematically and online. The law of learning is "connection helps understanding" and "connection helps memory". As Pan Changjiang famously said: "What is concentrated is the essence."

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

"Knowing but not right, right but not complete, complete but not excellent, excellent but not beautiful" is a common phenomenon in the college entrance examination. This is mainly due to the candidates' weak ability to review questions, carelessness in problem solving, and lack of standard writing. caused by. Therefore, in daily training, we must 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., which are the basis for ensuring long scores in the college entrance examination. Each college entrance examination mathematics test paper must have a considerable number of original questions that reflect the college entrance examination requirements and proposition concepts, and condense the experience and wisdom of the questioners. Such questions have unfamiliar situations, novel forms, and exquisite structures. It is impossible for them to devote themselves to it calmly and freely. In problem-solving activities, it is impossible to spend too much time and energy on deliberately seeking simplicity and innovation. The hope of success depends entirely on the usual accumulation of knowledge, skills, thinking, psychology, etc., that is, usual training. To achieve "usual training", the following four points must be achieved:

< p>1. To do a good job in standardized training, we must pay close attention to the "three skills", namely drawing skills, calculating skills, and reviewing skills.

2. Pay attention to the exposure of thinking processes.

3. Pay close attention to the development of normative awareness.

4. Pay attention to compensation training after error correction.

Due to time constraints, today’s interview is almost over. Thank you very much, Teacher Zhou, for asking the teacher to say a few words to the candidates at the end of the program. The guest on the website tomorrow is Liang Jingdang, a senior teacher of history at Fuzhou Senior High School. Candidates and parents are welcome to ask questions

The goal of the high school mathematics curriculum is: "Understand basic mathematical concepts, the essence of mathematical conclusions, and understand concepts background, and apply and appreciate the mathematical ideas and methods contained therein." This is not only the goal of the course, but also the goal of the college entrance examination questions, and it is also the goal of our college entrance examination review. Therefore, putting people first, taking the foundation as the foundation, basing ourselves on the basics, seeking truth and understanding the foundation are the foundation for the success of our senior year review.