In 2009, the content of the examination paper for the CET-6 upgrade.

The entrance examination for the sixth grade is an important examination in the nine-year compulsory education stage, which plays a guiding role in primary and secondary education and teaching. According to the sixth grade teaching content stipulated in the nine-year compulsory education mathematics syllabus and the related contents of the textbooks used, it is mainly to evaluate whether the students have reached the basic teaching requirements stipulated in the syllabus in terms of knowledge and ability in this year. The examination method and structure, the types of questions used and the number of questions equipped, the score ratio of various types of questions, the examination content and its score ratio, and the requirements for the examination content are basically in line with the relevant provisions of the examination instructions. On the premise of maintaining overall stability, the test paper pays attention to the examination of basic knowledge and mathematical quality, designs test questions from the perspective of subject knowledge structure and internal relations, pays attention to the basics, comprehensiveness and application of test questions, and creates novel question situations and questioning methods. In the design of some test questions, the examination of ability is strengthened, and the examination of students' thinking quality, innovation consciousness and learning potential is highlighted.

First, the basic situation of the test paper:

1, test paper structure:

The full mark of the test paper is 100, and the test time is 60 minutes. Among them, fill-in-the-blank question 10, multiple-choice question 10, each small question is 2 points, * * 40 points, focusing on examining basic knowledge and skills, and seeing the big picture from small questions-examining the depth and breadth of students' understanding of the basic contents of mathematics, designing options based on students' common mistakes, encouraging students to think more and think more, applying what they have learned vividly, and reducing rote memorization. Answer 9 questions and get a score of ***60. While examining the basic knowledge and skills, we should also examine the ability of thinking, calculation and comprehensive application of mathematical knowledge to solve practical problems. The design of test questions fully embodies the idea of easy starting, deepening and changing. Among them, 2 open inquiry questions were designed, with ***4 points and 5 application questions, with *** 19 points.

2. Statistical results:

In 2003, the average score of the mathematics test paper in the sixth grade entrance examination was 70.48, the difficulty value was 0.7 1, the passing rate was 76.03%, and the excellent rate was 2 1. 1%.

See table 1 (sample size is 556) for the difficulty (sampling) distribution of test questions.

Table 1

Classification 0.4 below 0.4-0.7 above 0.7

The number of questions is 2, 5 and 22.

Score 12,10,78.

The above data show that most students have mastered the basic knowledge and skills of grade six and have the ability to continue their studies in grade seven.

Second, the main characteristics of the test questions:

On the one hand, junior high school students in 2003 paid attention to the mathematics syllabus and its teaching materials, emphasizing the examination of basic knowledge and skills. On the other hand, by designing questions and opening exploratory questions in a certain realistic situation, students can show different thinking and understanding of the problems, show different levels of ability, and more effectively examine students' thinking quality, learning potential and comprehensive quality. Its main features are as follows:

1, pay attention to the foundation

The basic knowledge, basic skills and basic mathematical thinking methods of middle school mathematics are the necessary mathematical qualities for students, and also the basic contents for students to go to society and further study in the future. Starting from the current nine-year compulsory education full-time junior high school mathematics syllabus and its teaching materials, the 2003 test questions not only focused on the examination of basic knowledge and skills, but also strengthened the examination of basic mathematics methods, mainly in three aspects:

(1) Make a comprehensive survey of the basic concepts, laws, formulas and basic mathematical methods of sixth grade mathematics.

In 2003, the examination questions covered almost all the knowledge points in the sixth grade algebra books (1) and (2), and examined the rational numbers, algebraic expressions, equations, inequalities and other related knowledge. See Table 2:

Table 2

Test the inequality of rational number integral equation.

Score 24 25 34 17

(Some test questions are comprehensive in content, and scores are assigned according to the grading standards. For example, the score of question 29 is 7, and according to the content and grading standard of the exam, the equation accounts for 3 and the inequality accounts for 4).

See Table 3 for the test statistics of each chapter in the test paper:

Table 3

Chapter (in the order of teaching materials) Number score of test questions

Chapter 1 Basic knowledge of algebra 9 2

Chapter II Rational Numbers 1, 2,3, 1 1,12,21,22

Chapter III Addition and subtraction of algebraic expressions 4, 15, 20, 23 10

The fourth chapter is the unary linear equation 5, 10, 18, 24,2816.

Chapter 5 Binary linear equations 8, 16, 26, 27, 29 18.

Chapter VI One-dimensional Linear Inequalities 6, 25, 28, 29 17

Chapter VII Multiplication and division of algebraic expressions 7, 13, 14, 15, 17, 19, 20, 27 15.

The above questions reflect the most basic and important contents in the textbook. Examining students' understanding and mastery of basic concepts and laws belongs to the category of basic knowledge and skills. The design of test questions is close to students, life, mathematics teaching practice, avoiding complicated calculation and focusing on key knowledge, which embodies the comprehensiveness and foundation of the examination.

(2) Pay attention to the examination of basic mathematical thinking methods.

Nine-year compulsory education full-time junior high school mathematics syllabus classifies the mathematical ideas and methods embodied in junior high school mathematics as basic knowledge. The investigation of some basic mathematical thinking methods in 2003 reflected the requirements for students' mathematical quality. Questions 5, 10, 18, 27, and 28 examine the mathematical thought of the equation, questions 16, 12 examine the mathematical thought of the classified discussion, questions 17, and 25 examine the mathematical thought of the combination of numbers and shapes, and questions 650. The above questions account for 46 points.

(3) A considerable number of problems come from textbooks.

Nearly 80% of the papers are selected from the textbooks, algebra quality monitoring and review papers compiled by our teaching and research section. Some of the test questions are original in the reference materials, and some are adapted from examples and exercises that students are familiar with. For example, no. 1, 3,4,5,6,7, 10,1,12, 13, 14,/kloc-0. This practice fully embodies the proposition idea of paying attention to the foundation, which helps students to solve problems easily and will not go astray and get into trouble because they can't understand the questions. At the same time, teachers and students will be guided to attach importance to the basic role and demonstration role of teaching materials. Mathematics course is a "blueprint" for learning the basic knowledge of mathematics and forming basic skills, and it is also the examination basis stipulated in the examination instructions, which will surely play a correct guiding role in mathematics teaching in primary and secondary schools.

2. Outstanding ability

The examination of Grade 6-7 not only examines students' mastery of mathematical knowledge in Grade 6, but also examines students' mathematical ability in the process of applying mathematical knowledge and methods. Mathematical ability refers to thinking ability, calculating ability, spatial imagination ability and the ability to analyze and solve problems by using the learned mathematical knowledge. Mathematical thinking ability is the core of mathematical ability, and the ability to analyze and solve problems is a comprehensive ability compared with the first three, which embodies a higher level of thinking. The examination questions in 2003 were peaceful, fresh and approachable, but we saw the novelty in commonness, the cleverness in clumsiness and the strangeness in plainness. Students are required to organize, process and combine the information provided by the test questions with mathematical knowledge as the carrier, so as to find a solution to the problem. Students are required to be good at knowledge transfer and examine their comprehensive ability and mathematical quality with mathematical ability and thinking ability as the core. Mainly reflected in two aspects.

(1) put forward at the intersection of knowledge networks, put forward questions, and investigate the internal connection and synthesis of mathematics.

Solving this kind of test questions requires a certain comprehensive ability, and it is difficult to get a correct or satisfactory answer by one ability alone. For example, Question 29 is a combination of the knowledge of ternary linear equations in Chapter 5 and the knowledge of inequality groups in Chapter 6. Based on equations, this paper examines students' ability to transform equations into inequalities and solve problems by using mathematical ideas and methods. This test requires not only a certain calculation ability, but also a certain logical reasoning ability.

(2) There are many ways to solve the problem.

Through the difference of rationality and complexity of the solution, we can not only examine students' proficiency in mastering knowledge, but also better distinguish students with different ability levels, and also provide a space for students with different levels to show their mathematical talents. For example, the solution of the problem 15 can use the complete square formula or the reciprocal square difference formula; The solution of problem 20 can be constructed by collocation method, and the whole known condition can be substituted for evaluation, or the known condition can be converted into algebraic expressions with the same letters and substituted for evaluation together, or other deformation methods can be used. The solution to the problem of 2 1 is simpler by additive commutative law and the associative law than by direct calculation. Question 28

Solution: 1:A company works for x days, which is 2.1x+1.2 () ≤ 38.7;

Option 2: the company is established for x days, according to the meaning of the question: 42×+36 (1-) ≤ 38.7;

Solution 3: Let Company A complete the overall project of X, according to the meaning of the question:

42x+36 (1-x) ≤ 38.7, and the solution is x≤, so × 20 = 9;

Option 4: Let Company A construct for X days and Company B construct for Y days. According to the meaning of the question, draw a conclusion:

Option 5: set up the company for x days, according to the meaning of the question:

1.2x+2. 1x+ 1.2×≤38.7；

Question 29

Solution 1: From the meaning of the question:

∵x, y and z are nonnegative rational numbers.

∴ 0≤k≤2

Solution 2: According to the known conditions:

X=, z= into k = 3x+y-z to get k = 2-3y.

∵x, y and z are nonnegative rational numbers.

∴ 0≤y≤

From k = 2 to 3y

∴ 0≤ ≤

∴ 0≤k≤2

The different methods adopted from the answers to the above questions reflect the differences of students' abilities, that is, the differences of students' abilities are not only reflected in whether they can answer questions, but also in the choice of problem-solving speed and methods and strategies. Conversely, the advantages and disadvantages of methods and strategies restrict the speed of solving problems.

(3) Create new situations and examine the quality of mathematics.

The situation and form of the test questions are innovative, which reflects the examination of ability and innovative consciousness and the teaching concept of the new curriculum standards. Mathematical ability is the concrete embodiment of mathematical quality, and mathematical ability is embodied by solving problems. Whether the exact information can be obtained from the conditions or conclusions of the topic, whether the information related to the topic can be extracted from the memory system, whether the information extracted by both parties can be organically combined, whether the problem-solving action sequence can be organized, and whether the reasoning and operation can be successfully completed in the process of implementing the problem-solving sequence are all manifestations of mathematical ability, which can be specifically melted into computing ability, logical reasoning ability, spatial imagination ability and problem-solving ability. Mathematical literacy sometimes highlights mathematical consciousness, that is, thinking and dealing with problems by mathematical methods. For example, question 8 examines the concept of binary linear equation and its solution in an open form. The problem design is novel, the solution is not unique, and it has rich divergent thinking. This question has no obstacles in the knowledge background, but it has changed the original unique answering mode in an open form, thus examining the flexibility and innovation of students' thinking. Question 9 examines the knowledge of algebra in the form of inquiry. The background of this question is the calendar of June 2003. It is required to find out the relationship between three adjacent numbers in any vertical column, express the middle number with letters, and find the algebra of the sum of these three numbers. By solving this problem, the students' abilities of observation, experiment, comparison, conjecture, analysis, synthesis, abstraction, generalization and inquiry are examined, and the students' thinking ability is well examined. The ability test in 2003 reflected the requirements for mathematics quality.

3. Emphasize application

Strengthen the examination of application consciousness and improve students' ability to use mathematics. The examination questions in 2003 added the examination of applied questions. Through the examination of practical problems, students are guided to start from practical problems familiar in life and production, and the practical problems are abstracted into mathematical problems through analysis, so as to cultivate the ability of analyzing and solving problems and gradually form the consciousness of applied mathematics. For example, 1 examines the meaning of positive and negative numbers in the context of daily life, and 10 examines the bank savings problem closely related to economic life in solving practical problems. 18 questions take the postal exhibition as the background to examine the application problems of solving equations. Question 23 takes the green lawn as the background to examine algebraic formulas and algebraic operations. Question 28: Based on the current Shanghai Road widening and reconstruction project in our district, the equations and inequalities for solving practical problems are investigated. These problems reflect the examination of students' comprehensive quality.

Third, enlightenment and thinking

1, basic knowledge is fundamental.

Mastering basic knowledge and skills is the key to successful answer. In teaching, we should pay attention to the deepening of knowledge, especially the internal relationship between knowledge, and establish a good knowledge structure, so as to better have the ability to process, summarize, refine and reorganize basic knowledge, find the best way to solve problems and optimize the problem-solving process. Teachers should conscientiously implement every teaching link, pay attention to the formation and development of knowledge, and not just memorize conclusions, let alone blindly copy them by rote. The question 18 in 2003 is the original title in the textbook, and only the numbers are changed. The original question requires the calculation of the class size and the total number of stamps, while the question only requires the calculation of the total number of stamps. However, a large proportion of students practice according to the original question, and there is a serious mistake that the set unknowns do not match the listed equations. Question 23 is also the original title in the textbook, but neither teachers nor students pay enough attention to it, and the textbook resources are not fully utilized, resulting in more students losing points. Some students don't have basic mathematical knowledge, such as the formula for calculating the perimeter of a rectangle. In teaching, teachers should cultivate students' basic methods of learning mathematics, strengthen the infiltration of mathematical thinking methods, and summarize common problem-solving methods. Such as the elimination method, special value method and exhaustive method commonly used to solve multiple-choice questions.

2. Improving mathematical ability is the core.

Mathematical ability can be gradually formed in the process of learning mathematical knowledge. In the process of mathematics teaching, it is very important to consciously stimulate students' thinking process and enhance the interaction between teaching and learning. Teachers should follow students' thinking track, overcome blindness, improve their consciousness, avoid a large number of mechanical repetition of tactical exercises, select exercises, pay attention to analysis, attach importance to problem-solving process, sum up laws, and improve their mathematical ability in the process of knowledge accumulation, systematization and networking. At the same time, we should pay attention to reflection after solving problems, study different thinking levels in the process of solving mathematical problems, and constantly sum up experience. In daily teaching, teachers should pay more attention to the application of mathematical knowledge as a kind of consciousness to cultivate students, so that the cultivation of ability can be truly implemented. In teaching, teachers should strengthen the cultivation of students' reading ability and enhance students' understanding of symbolic language, graphic language and tabular language of mathematics, so as to correctly examine the conditions and requirements of questions, which is also one of the factors that affect the answers to questions.

3. Cultivating innovative consciousness is the key.

Taking certain knowledge as the carrier, paying attention to cultivating students' innovative consciousness and spirit and improving citizens' mathematical ability and quality are the requirements of basic mathematics education in the era of knowledge economy. Paying attention to the development of innovative potential, innovative consciousness and innovative spirit in teaching and cultivating students' practical ability has become the mainstream of classroom teaching. Teachers should update their educational concepts and guide teaching with the educational concepts of new curriculum standards, so that our mathematics teachers can be transformed from teachers to scholars, thus improving the level of mathematics teaching in our region.

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