The college entrance examination in 2009, as the first college entrance examination after the implementation of the new curriculum reform in Liaoning Province, has aroused great concern of the majority of middle school mathematics teachers. What information can be obtained from this test paper? What are the implications for middle school mathematics teaching? What's the impact on the math review of the 20 10 college entrance examination? Let's talk about some views in this regard, hoping to help colleagues.
1. Overview of test questions
In 2009, the mathematics examination paper of Liaoning college entrance examination basically implemented the guiding ideology, principles and examination requirements of the college entrance examination set by the National Unified Examination Outline for Enrollment of Ordinary Colleges and Universities in 2009 and the Examination Instructions of Liaoning Province. The liberal arts examination paper was integrated into the new curriculum reform concept, which better reflected the proposition idea of "emphasizing foundation, simplicity and highlighting characteristics" and truly realized the smooth transition between the college entrance examination paper and the traditional college entrance examination paper under the new curriculum reform. The layout structure of the whole volume of arts and sciences is reasonable, the test questions are based on the foundation, the backbone is highlighted, and the ability to conceive is there. In the proposition, we should face up to the differences of candidates in arts and sciences and reasonably design the difficulty coefficient of arts and sciences papers. After the examination, it is estimated that the difficulty coefficient of the liberal arts and science papers is about 0.6 and 0.5 respectively. The two test papers well reflect the reliability, gradient, validity and discrimination of the test questions, which is beneficial to social harmony and stability, talent selection in colleges and universities, quality education in middle schools and the cultivation of students' innovative spirit and practical ability. It points out the direction for the mathematics review of the 20 10 college entrance examination and plays a good guiding role in the mathematics teaching reform of the new curriculum in senior high schools.
2. Analysis of the main characteristics of the test questions
2. 1 Base on the foundation and highlight the backbone.
In 2009, Liaoning mathematics test questions focused on basic knowledge and skills, and most of them were not comprehensive. For example, 1-7 and 10 in science multiple-choice questions, 13, 14 and 16 in fill-in-the-blank questions, only 1~2 knowledge points are examined, and there is no overlap between the knowledge points; 17, 18 (1), 19 (1), 20 (1) and multiple-choice questions only examine basic knowledge and skills, accounting for about 65% of the whole volume. On the one hand, these questions highlight the guiding ideology of "smooth transition" in the examination syllabus, and on the other hand, they better implement the requirements of "acquiring the necessary basic knowledge and skills of mathematics" in the curriculum standards. This year's Liaoning college entrance examination questions about functions and derivatives, triangles and vectors, probability and statistics, series, inequalities, solid geometry, straight lines and conic curves account for about 70% of the whole paper, which better reflects the examination requirements of "the examination of basic mathematics knowledge should be comprehensive and focused, and the key knowledge supporting the subject knowledge system should maintain a high proportion to form the main body of the test paper".
2.2 focus on curriculum reform, attach importance to teaching materials.
In 2009, Liaoning Mathematics Examination Paper paid enough attention to the new content in curriculum reform. Algorithms, three views, geometric probability, statistical knowledge, event independence test, simple logical terms and other knowledge, as well as scientific space vectors, conditional probability and other knowledge are all reflected in the test paper. This year, about 14% of our province's science mathematics papers and 17% of our province's liberal arts papers were added. It can be said that the new content is basically fully covered, but considering that the new content must have a gradual adaptation process, the difficulty requirements for these contents are relatively low. In addition, a considerable number of questions in the test paper have prototypes in the teaching materials. For example, the sixth question of science and the eighth question of liberal arts are adapted from the second question of exercise B in the 2.3 geometric series part of compulsory 5 and the second question of exercise B in the basic relationship part of 1.2.2 trigonometric function in compulsory 4 respectively. 16 is transferred from exercise 2-2b in section 2.2 of 2- 1. The second question: "It is known that point A( 1, 1) is the left focus of the ellipse, which is the minimum and maximum value of any point on the ellipse". 17 is a triangular application problem, which consists of two sub-questions 1 and 2 in the application example part of compulsory 5. The multiple-choice question 12 comes from the classic problem in function: it is known as the solution of the equation, and its solution evolves.
2.3 Pay attention to thinking methods and highlight the examination of thinking ability.
Mathematical thoughts and methods are abstractions and generalizations of mathematical knowledge at a higher level, which are contained in the process of occurrence, development and application of mathematical knowledge. Therefore, the examination of mathematical thinking method must be combined with the examination of mathematical knowledge, and the examination of mathematical knowledge, as a carrier, reflects the examinee's understanding and mastery of mathematical thinking method. In the examination of mathematical knowledge, the 2009 Liaoning Mathematics Examination Paper focuses on the examinee's understanding and mastery of mathematical thinking methods. Pay attention to the distribution of topic information in the whole test paper, consider using different methods from different angles, create various ways to solve problems, and effectively distinguish the thinking level of students at different levels. For example, the science test paper 12 examines the idea of combining numbers with shapes; 19 (2) and 2 1 (1) mainly examine the ideas of classified discussion; Questions 10 and 2 1 (2) Examine functions and equations, transformation and reduction. In the examination paper, reduction to absurdity, limit method and undetermined coefficient method are all reflected in different degrees. Question 20 of the liberal arts examination paper strengthens the examination and independence test of students' probability and statistics knowledge, and especially requires students' computing ability.
2.4 Pay attention to general methods and downplay skills.
In 2009, Liaoning mathematics examination paper highlighted conventional methods and general methods, but downplayed special skills, which better reflected the proposition orientation with knowledge as the carrier, methods as the support and ability as the examination purpose. The whole volume does not directly examine the declarative knowledge of pure memory, but focuses on the application ability of knowledge and the students' computing ability and reasoning ability. On the basis of basic method and general method, the gradient of the whole test paper from easy to difficult is well realized, and the pattern of low starting point, wide entrance and gradual deepening is realized. The new questions in the whole volume are not difficult and the questions are not strange. The questions are conventional but not difficult, which helps to test the candidates' understanding, mastery and application of mathematical knowledge, and is more conducive to top students to play their level, show their strength and distinguish and select.
2.5 Break the routine and bring forth the new.
An important idea of the new curriculum reform is to cultivate students' application consciousness and ability, and to cultivate students' ability of inquiry, discovery and creation. In 2009, the number of questions in Liaoning mathematics examination paper was large, reaching a certain depth. Such as 10 test algorithm; Science 13 exam statistics; Science questions 17 and liberal arts questions 18 examine the application of trigonometric functions; Science question 19 and liberal arts question 20 examine probability statistics; Science topic 17 examines students' ability to explore new problems by using what they have learned.
The new curriculum standard and syllabus have changed the requirements for some knowledge, for example, the new curriculum standard has improved the application requirements of sine and cosine theorem and increased the reduction to absurdity in the proof method. The change of these requirements leads to the change of proposition points of college entrance examination questions. In 2009, Liaoning Volume Theory (17) investigated trigonometric function knowledge, which changed from simplification, evaluation, image and essence of trigonometric function to practical application of trigonometry. Li (18) changed the examination of solid geometry knowledge from the proof of the relationship between parallelism and verticality and the solution of dihedral angle in the original solid geometry to the calculation of the angle between a straight line and a plane, and proved that two straight lines are non-planar straight lines by the inverse method. The paper (2 1) changes the investigation of function, derivative and inequality from cubic function to derivative of binomial product. At first glance, the examination of these questions seems a bit unexpected. If we re-examine the new curriculum standards, we think that these problems are inevitable in the curriculum reform. However, there are different voices on this issue: some teachers think that the unsuccessful test questions in the liberal arts and science papers are to prove that the two straight lines are different planes by reduction to absurdity, which fails to test the classical content of solid geometry advocated by the new curriculum reform. The proof of non-planar straight lines involved in this question is vague in the syllabus and examination instructions, so it is difficult for students and teachers to grasp it in place because there are many teaching contents and the class hours are tight. If all knowledge is required of students in this form, it will definitely increase their academic burden. Facing the new curriculum reform, teachers' biggest doubt is: how to grasp the classic content that is not mentioned or diluted in the new curriculum standard? The baton function of this problem in guiding middle school teaching is very worthy of our consideration and study. The first problem in science does not show the superiority of solving problems with space vectors. The exam of solid geometry is "wearing new shoes and taking the old road". In my opinion, the examination questions of solid geometry in arts and sciences in 2009 have a great influence on school teaching. The most direct consequence is that teachers will blindly carry out outward bound training, and students with poor math subjects will become more and more tired, which will affect their enthusiasm for learning math.
2.6 The differences in liberal arts and science topics have increased.
According to the actual situation of students of arts and sciences in Liaoning Province, compared with previous years, the number of mathematical questions used in arts and sciences decreased in 2009. Among them, the number of questions used by liberal arts * * * is 9, including liberal arts 15, science 18, science 17, liberal arts and science 18 (2), liberal arts 22 and science 20, and the rest are multiple-choice questions. As can be seen from the above statistical results, the difficulty of liberal arts test questions varies greatly. The whole volume 13 questions, arts and sciences use different questions. Among the questions of liberal arts, liberal arts is less difficult than science, which is conducive to stimulating the enthusiasm of liberal arts students in learning mathematics and promoting their all-round development.
In short, on the basis of examining the basic knowledge, the test questions pay attention to the examination of mathematical thinking methods, the examination of mathematical ability, the reasonable control of comprehensive degree, and multi-angle and multi-level attention. However, there are also some shortcomings in the test paper. For example, in the science examination paper, the two three-dimensional geometry sub-questions are all about the volume of the geometry, and the two series sub-questions are related to the sum of the first items of the series, which is slightly monotonous when examining these two aspects of knowledge.
3.09 College Entrance Examination Mathematics Teaching Enlightenment
3. 1 Pay attention to the new contents in the curriculum reform.
The new content in the new curriculum reform not only increases the material and broadens the space for the college entrance examination proposition, but also provides the background and ideas for innovative questions. We should pay more attention to new content in our study. In 2009, the examination of the new contents of Liaoning mathematics volume was relatively simple and incomplete. With the deepening of curriculum reform, new content and traditional content will be gradually integrated, mainly in the organic combination of algorithm, sequence, function and inequality; The organic combination of geometric probability and knowledge such as function, equation, inequality, analytic geometry and solid geometry; Analogical reasoning combines geometry, sequence and other knowledge. There will be new changes in the intensity and difficulty of the new content of the college entrance examination questions, and we should be prepared in this aspect psychologically and in action.
3.2 The review of knowledge points leaves no blank.
In 2009, the title 18 (ii) of Liaoning Volume Science (title 19 (ii) of liberal arts) proved that two straight lines are different planes by reduction to absurdity. In the process of marking papers, we found that 90% of the students could not get full marks, and most of them could only get 2 points. Until now, some teachers and students are still surprised by the emergence of this problem. There are many reasons, but we analyze that the fundamental reason is that many teachers only pay attention to the review of the principle of reduction to absurdity in the review of senior three, and do not emphasize the concept of out-of-plane straight line enough, which leads to students not reaching contradictory conclusions. So don't review any knowledge points, and don't underestimate them. When reviewing, the coverage of basic knowledge points must be comprehensive and systematic. In order to prevent students from forgetting, teachers can arrange these non-main knowledge in a planned way during the second and third review.
3.3 Strengthen students' computing ability, pay attention to the synthesis of knowledge, and cultivate students' inquiry ability.
This year, candidates in Liaoning Province generally feel that the math test questions are not difficult, but the amount of calculation is large. One of the basic concepts of the new curriculum is to "cultivate students' awareness of mathematical application", and the application of mathematics is finally realized through operational solution, which requires students to have solid operational solution ability. The introduction of algorithm and the deletion of the second definition of quadratic curve are all related to strengthening students' computing ability. Whether from the perspective of examination or student development, the cultivation of computing ability should run through the review. In actual training, we should also avoid tedious and artificial skilled operation.
This year is the third college entrance examination after the curriculum reform in Ningxia and Hainan. The difficulty of the test questions is obviously increased, and the comprehensiveness is also improved. It is particularly noteworthy that the original title of science question 17 is like this: "In order to measure the distance between two mountain tops M and N, the plane will measure at two points A and B along the horizontal direction. A, B, M and N are on the same vertical plane (as shown in the schematic diagram), and the measurable data of this plane include depression angle and the distance between A and B. Please design a scheme, including: ①. ② Write out the steps of calculating the distance between m and n with words and formulas. "
This is an open test with realistic background, which examines students' ability to apply what they have learned and highlights the basic requirement of "thinking with ability" in the college entrance examination proposition. From this point of view, the way and thinking of proposition in Liaoning Province will also change greatly in the future. Therefore, when reviewing, we should not only gradually cultivate students' ability to solve practical and comprehensive problems, but also increase the training of students in mathematical modeling, exploration and exploration.
3.4 improve the utilization of teaching materials
Textbooks are the carrier of mathematical knowledge and mathematical thinking methods, and also the basis of teaching, and should be the source of college entrance examination questions. In fact, the college entrance examination proposition attaches great importance to the role of textbook exercises and the role of textbooks as the fundamental source of test questions. Studying NMET's math test questions, it is found that a certain number of test questions are customized through deformation, reorganization, extension and expansion based on textbook exercises every year. In 2009, a considerable number of questions in Liaoning Paper came from textbooks, which not only effectively examined the basic knowledge of mathematics, but also provided a good guiding role for teachers in "preparing lessons, teaching, tutoring, correcting, proposing and evaluating". Therefore, in the college entrance examination review, we should go back to the textbook and have a deep understanding of the textbook. Textbooks are the foundation, and textbooks are the source of college entrance examination questions.
3.5 Pay attention to "high background, elementary solution"
No matter the requirement of "selecting freshmen from colleges and universities" or the unique charm of "highly educated" problem. There are often some questions from the background of high mathematics in the college entrance examination. For example, 2 1 (2) of Liaoning Volume in 2009 is actually the Lagrange mean value theorem in advanced mathematics. In recent years, some problems have appeared in the background of higher mathematics, such as finding the general term formula of recursive sequence by using fixed points, the principle of delimitation, the concavity and convexity of functions, etc. For these problems, I think it only creates a situation, and students are not required to use the tools in the university to solve these problems, nor are teachers required to tell students too much about advanced mathematics. In preparing for the exam, we should focus on the transformation of problems and the methods of using elementary mathematics knowledge to deal with problems.
3.6 Strengthen the discussion of new curriculum standards
The new curriculum reform has brought new vitality to the college entrance examination. In order to fully prepare for the college entrance examination, teachers must strengthen the discussion on the new curriculum standards, deeply understand the changes in the knowledge structure of new textbooks and the changes in the ability requirements of the new curriculum standards, so as to better grasp and adapt to the college entrance examination.
Second, senior three review preparation strategies
First of all, let's review the basic experience of college entrance examination.
The first keyword: timetable
Usually called three rounds of review:
The first round of review, the basic ability to pass (mid-July-end of February). Read textbooks to systematize knowledge and improve application ability.
The second round of review, comprehensive ability breakthrough (early March to mid-May). Strengthen the main content, grasp the knowledge connection and improve the actual combat ability through problem-solving training.
The third round of review will improve the application ability (from mid-May to the end of May). Use simulation questions, master the rules, strengthen memory and enter the examination state through exams and lectures.
The second keyword: road map
What is the audit procedure? This procedure is to emphasize the foundation, starting from the foundation, from the foundation to the ability; It is to emphasize textbooks, start from textbooks, and integrate on the basis of integrating textbook content. According to this procedure, almost everyone who talks about the college entrance examination is unanimous: rely on the outline, innovate and live; Based on teaching materials, pay attention to "double basics"; Highlight the main content and emphasize the general method; Attach importance to thinking methods and improve thinking quality. Moreover, we all know what the main content is and what the thinking method is.
The third key word: policy
The college entrance examination requires us to study the examination syllabus, national examination questions and independent examination questions in recent years to understand the trend of curriculum reform and development, from which we can make various conjectures about the future examination questions: although we can't say that certain questions will definitely appear in the 20 10 test paper, we can speculate that certain questions may appear in the 20 10 test paper. The emergence of a specific problem is accidental, but the emergence of a certain kind of problem is regular. It is based on the examination syllabus, previous examination questions and the concept of curriculum reform that we can deeply understand the four principles of the college entrance examination proposition: designing examination questions at the intersection of knowledge around key contents, strengthening the examination of thinking methods, and not simply pursuing coverage.
The fourth keyword: the source of the test questions.
(1) Textbooks are the basic source of test questions and the main basis of college entrance examination propositions. Most test questions are the result of combination, processing and development on the basis of textbook topics.
(2) The previous college entrance examination questions have become new college entrance examination questions for reference, and there are precedents to follow. In the prediction of test questions, the most frequently used keyword is stability and innovation under the premise of stability. Emphasize stability, that is, admit that propositions are naturally developed and will not mutate, and propositions cannot cut off history, such as the development history of applied problems, the evolution history of multiple-choice questions and the interaction history of multiple disciplines. Over the years, the test questions present a kind of regularity, and its development and change track will give us a lot of enlightenment. This is especially true as a provincial independent proposition. As long as we imagine ourselves as a proposer and put ourselves in the other's shoes a little, this truth is very clear.
(3) Some classic questions that students usually study may be adapted into college entrance examination questions. Classic questions are not only rooted in our teachers' minds, but also familiar to the members of the college entrance examination proposition group. These questions may become college entrance examination questions with a little treatment.
(4) The basic ideas and problems of advanced mathematics provide the background for the life system of college entrance examination questions. There are two basic reasons for this. First, the college entrance examination questions should examine students' potential for further studies. The basic ideas and problems of advanced mathematics can be a good material to examine the potential. Second, the background of the proposer. University teachers are absolutely dominant among the members of the proposition group, and it is impossible for them not to be influenced by their own academic background and interest when making propositions.
These four sources enlighten us on how to develop the resources of college entrance examination review courses. Under the guidance of the examination syllabus, this paper explores from four aspects: teaching materials, curriculum standards and related resources, previous college entrance examination questions, and the connecting zone between elementary and advanced mathematics.
Next, combined with my own practice in the review process of senior three, I will communicate with you on the specific arrangements for the three rounds of review of the college entrance examination.
First round of review
(1). Content integration of mathematical knowledge.
Part I: Set and Logic
Part II: Inequality.
Part III: Functions and derivatives.
Part IV: Preface.
The fifth part: trigonometric function and trigonometric solution.
Part VI: Vector and Analytic Geometry.
Part VII: Solid Geometry (Literature and Theory)
Part VIII: Probability and Statistics (Literature and Theory)
Part IX: Algorithm
Part X: Reasoning and Proof
Part 1 1: plural part
Part XII: Select the part of the exam
Features: Break the boundaries between modules, and arrange review according to the order between knowledge sections, so that students can easily master the knowledge system.
(B) A round of review to solve several key problems
1. Emphasize the foundation and strengthen the specification.
We can't organize review according to the difficulty of the last two questions in the college entrance examination, especially a round of review. Emphasize that we should pay attention to the foundation and be down-to-earth in the review process. The so-called knowledge base, I think, is "familiar with the basic knowledge; Skilled in basic skills; Understand the basic ideas; We must master the basic methods. "
2. Strengthen training (consolidate tactics) and summarize.
Senior three review is a process to familiarize students with the vague knowledge forgotten by senior one and senior two, and to apply this knowledge to solve problems. In this process, students should be familiar with and consolidate this knowledge by doing a certain amount of exercises, so as to achieve a profound understanding of the knowledge. In this process, it is not enough to just do the questions. We should learn to sum up while doing the questions, and finally turn the knowledge and methods into our own things. Only in this way can we achieve the purpose of review.
3. Teachers should handle the relationship between teaching and practice.
Students can't just practice in the review class of senior three, but the teacher should talk about it. What should we talk about? How can I put it? In my opinion, teachers should first understand what students lack, and speak according to the needs of students, rather than explain aimlessly. In the process of speaking, we should focus on clarifying concepts, summarizing methods and teaching thinking. Explain complex and difficult problems in accurate and concise language.
When talking about knowledge, we should talk about connection (horizontal, vertical, internal and external);
When talking about methods, we should talk about ideas (principles, how to think);
When talking about results, we should talk about process (not only paying attention to answers, but also paying attention to sources and processes);
To explain the problem process, we must talk about the thinking process (how did you come up with it? );
When talking about exercises, we should talk about changes;
Talk about success and failure;
In short, quantity is more important than quality.
4. Prepare exercise books suitable for students.
Appropriate is the best. At present, there are too many reference materials for the first round of review in senior three. Let me choose which one for the students. Your own students know best, and teachers make their own exercise books according to the students' situation. Yucai senior three students use Yucai learning plan, which is divided into one round and two rounds. The first round of topics is based on basics, routines and classics, which need to be completed by each student. The biggest advantage of the Yucai study plan is that it doesn't give students answers and requires students to do each question by themselves. I always think that personal experience is the most effective way to solve problems. At present, many reference books on the market give too detailed answers, which leads students to rely too much on answers and is not conducive to students' study.
5. Be clear and unambiguous about knowledge.
Teachers who teach new curriculum standard textbooks must be familiar with the phrase "knowledge spirals up", which makes students unclear about the overall context of high school mathematics knowledge. Therefore, a very important part of senior three review is to help students build a knowledge network and form a good knowledge structure and experience system. It is helpful for students to remember and understand knowledge and facilitate the transfer and application of knowledge.
6. Grasp the key points and pay attention to commonness and the implementation of commonness.
Research on the behavior of 1) function: domain, range, analytical formula, monotonicity, parity, inverse function, image, maximum (minimum) value.
2) Inequality: Grasp the nature of the foundation-inequality, grasp the key point-the solution of inequality, break through the difficulty-the proof of inequality, and pay attention to the instrumental role of inequality.
3) Two basic series and mathematical induction: through appropriate transformation, pay attention to some arithmetic progression or geometric progression, and pay attention to the synthesis of series.
4) Line-plane relationship in solid geometry: emphasize the parallel and vertical relationship and several angles and distances. Pay attention to the positional relationship between straight line and surface in the context of polyhedron and rotator.
5) Conic curve in analytic geometry: focus on curves and equations, and master the common solutions of curve equations. The relationship between straight line and conic curve, such as intersection point, chord length, chord midpoint, symmetry, range, etc. Pay attention to solving analytic geometry related problems with vectors in the new curriculum examination paper.
6) Plane vector: First, do the addition and subtraction, real number and cross product (number multiplication) of the vector; The second is to do well the coordinate operation and application of vectors; The third is to do a good job of vector product (point multiplication or inner product) and its application.
7) Image, property and trigonometric transformation of trigonometric function: implement basic requirements and master general methods.
8) plural: the requirements have been lowered, so don't go beyond them. Master basic requirements and common methods.
9) The review of probability and statistics should focus on the foundation.
Pay attention to the mutual transformation and flexible application of quadratic function, quadratic equation and quadratic inequality.
7. Infiltrate mathematical thinking methods
1) transformation and regression thought: simplification, familiarity and harmony.
2) Thought of functions and equations: important viewpoints and methods.
3) The idea of classified discussion: no repetition, no omission.
4) The idea of combining numbers with shapes: judge shapes according to numbers, and discuss numbers according to shapes. And teach students to be good at using numbers, symbols, formulas and graphics (images) to represent a mathematical object.
It is necessary to help students establish a strong sense of combining numbers and shapes through their usual study, so that students can have strong ability of classified discussion.
09 National Volume 1
This year's college entrance examination mathematics may present the following characteristics:
First, the overall difficulty of the test paper is moderate. The question type is also more conventional, because it is a key goal of college entrance examination mathematics to examine a student's ability and level of mastering basic knowledge. Therefore, the investigation of basic knowledge and basic skills in the college entrance examination mathematics questions accounts for a high proportion every year, and will also maintain the necessary depth. So we can see from the test paper that the topic covers a wide range. It involves all the knowledge points of high school mathematics, and the content is very comprehensive and basic. Judging from the examination questions, I think at least the candidates will not feel nervous after getting the examination paper, so the answers will be smoother, even if there are one or two questions on the examination paper, it will not cause great psychological pressure, so this is also in line with the trend of our current college entrance examination curriculum reform, that is, focusing on basic knowledge. Moreover, judging from our daily teaching and answering questions in the college entrance examination, students' mistakes are mainly due to the lack of flexible thinking methods and keen observation, and it is precisely because the problems occur on the basis of basic knowledge that they are somewhat lacking in mastery.
In addition, the test questions can still be grasped from the overall height and the height of the subject knowledge structure, and an important direction for designing test questions and measuring an examination outline is whether an orderly and networked knowledge structure can be formed. When designing the topics of the national volume and the Beijing volume, good consideration was given. This is the first feature, the difficulty is moderate, and the question type is more conventional. Most of the topics involved in the test paper are reviewed in the mock exam, which has a certain stabilizing effect on students' minds.
The second feature is that the examination questions still focus on mathematical thinking methods, and there is nothing technical. There are no strange questions in the proposition reflected in the test paper, and the amount of calculation is relatively low. There is no complicated operation, which will be good for candidates to play in the examination room. Moreover, there are some problems in the national paper, such as the serial number of 2 1 question, which reduces the difficulty of the test questions through multi-level questions. It embodies the humanistic care for candidates and also conforms to the direction of current curriculum reform and teaching reform.
The third feature is that because the college entrance examination is a selective examination after all, students' mathematical ability and their potential should also be highlighted. As far as our mathematics is concerned, we should basically examine four abilities. The first is computing ability, the second is thinking ability, the third is spatial imagination, and the fourth is the ability to analyze and solve problems. The four abilities seen in these two papers have been comprehensively investigated, and they are all in place. Speaking of the potential of the students under investigation, we just said that this matter is moderately difficult, but there are some difficult or big thinking problems behind the multiple-choice questions and fill-in-the-blank questions. This kind of problem is rarely encountered in the simulation of preparing for the exam in senior three, or in the textbook examples. The topic design is relatively novel, which is conducive to examining a student's real mathematical literacy and his improvisation level, so that students can really be selected.
The previous questions were moderately difficult. Will it weaken the discriminating test paper? In fact, I don't think so, because the college entrance examination not only examines a student's mastery of basic knowledge, or judges the correctness of a candidate's answer from the test paper, but also examines the quality of the candidate's answer. If the students with better thinking level and higher mathematical quality can answer questions faster and have better accuracy in the examination room, but what benefits does this bring? It frees up time for solving difficult problems later, so it has some advantages over other students in the total score of mathematics.
Another feature is that this year's topic description is relatively concise from the perspective of the national volume and the Beijing volume, because mathematics reading is also a difficult stage and an obstacle for students. Sometimes the topic description is long, and many new terms are used in it, which will also cause certain difficulties for students. Judging from this year's topic, this situation does not appear, it is relatively simple, and students can easily read the topic and text. It turns out that the topics in Beijing are long and difficult for students to understand. There have been some changes in this aspect this year, so the topic is designed more exquisitely with the original paper, so these two questions should be said to be very good.
In terms of examination questions, this year's exam results should be slightly higher than last year. Of course, it also depends on the performance of candidates in the examination room. Although the examination questions are relatively basic, I found that some students' mistakes mainly lie in basic knowledge, so we suggest candidates review or master basic knowledge.
Compared with this year's test paper, there is little change. For example, in the structure of test papers, both Beijing test papers and national test papers have remained relatively stable for several years. The other is that the content of the survey has not changed much. It reflects that the examination papers of both the examination center of the Ministry of Education and Beijing are stable, thus playing a good guiding and guiding role in senior high school mathematics teaching and avoiding ups and downs. Provide opportunities for future review and teaching materials.