202 1 Comments on the Difficulty of Mathematics Test Paper in Beijing Senior High School Entrance Examination

Mathematics discipline has determined the proposition of facing all students, taking students as the center, realizing the function of horizontal examination and giving consideration to the function of choice.

202 1 Beijing Senior High School Entrance Examination Paper Comment The system of mathematics examination questions is based on the compulsory education mathematics curriculum standard (20 1 1 version), adheres to the guiding principle of striving for progress while maintaining stability, implements the fundamental task of cultivating people in Lide, achieves "three stresses" and "four tests" in content and ability examination, and pays attention to giving full play to educational functions. At the same time, combining with the teaching practice in middle schools, focusing on the main knowledge, core competence, basic mathematical ideas and basic activity experience, we should highlight the nature of the subject, examine mathematical thinking, further guide teaching to return to the classroom and teaching materials, and realize the benign interaction between teaching and examination.

First, combine the characteristics of the subject and give play to the role of educating people.

Function, to implement the fundamental task of Lide Shu Ren.

Mathematics combines the characteristics of its own subject, selects suitable materials, naturally integrates the socialist core values into the examination questions, and exerts the educational function of the examination questions.

For example, in the second question, with the background of poverty alleviation through education, this paper introduces the situation that the central government invested a total of special subsidy funds for "comprehensively improving the basic conditions for running schools with weak compulsory education in poverty-stricken areas" from 20 14 to 20 18, so that students can intuitively feel that the improvement of the learning environment cannot be separated from the national policy guarantee and financial input.

For example, in question 20, according to the method of determining the east-west direction in Huai Nan Zi Tian Zi Xun, it is expounded that in ancient China, the in-depth study of astronomy and other aspects began very early, which shows the wisdom of our ancient people. Taking mathematical culture as the carrier, we can guide students to use their own mathematical knowledge to solve simple practical problems and achieve the goal of educating people with mathematical culture.

Second, based on the "four basics", examine the backbone,

Reflective thinking, apply what you have learned.

The characteristics and overall style of 202 1 mathematics test paper remain stable. The overall design of the test paper is based on the "four basics" (basic knowledge, basic skills, basic ideas and basic activity experience), which examines the understanding of the nature of knowledge, students' mathematical thinking, and students' ability to think about problems from a mathematical perspective and solve practical problems with mathematical knowledge.

1. Pay attention to the requirements of "four basics" and embody the mathematical foundation.

The examination paper design and test paper design pay attention to the examination of the basic knowledge of three knowledge blocks (number and algebra, figure and geometry, statistics and probability), and highlight the examination of basic skills, basic ideas and basic activity experience in the examination process.

For example, ruler drawing requires students not only to master the procedures and steps of skill operation, but also to understand the mathematical principles contained in it. In question 20, students should first draw accurately according to the requirements of the topic, then explain the drawing principle of ruler drawing by using the mathematical principles they have mastered, and complete the proof.

2. Pay attention to the process of knowledge formation and realize the subject thought.

One of the important goals of mathematics learning is to let students experience the process of knowledge formation, development and application, accumulate activity experience, understand the essence of knowledge and comprehend mathematical thoughts. For example, in statistics teaching, students have to go through a complete statistical process, extract information from data and use this information to explain problems. This year's special topic on statistics focuses on the analysis of data and the interpretation of information provided in data on the basis of investigating the collection, arrangement and description of data, and examines students' understanding of the meaning of median, the role of median and average in analyzing data distribution and the overall understanding of sample estimation, reflecting students' awareness and ability to obtain effective information and conduct quantitative analysis. Guiding teaching should pay attention to the essence of mathematical problems, so that students can deepen their understanding and application of statistical ideas and methods on the basis of accumulating experience in statistical activities.

Another example is the eighth question, with the background of "the length and area of two adjacent sides of a rectangle", the examination function is a mathematical model to study movement and change. It comes from and serves the reality, abstracts the related concepts of function from practical problems, and uses the knowledge of function to solve practical problems. More importantly, from the two angles of figure and quantity and their relationship, it highlights that the essential feature of function is to reflect the connection and change between things. This is not only the main line of function teaching, but also the main line of function learning. Let students deepen their understanding of function concepts and thinking methods in the process of modeling and solving practical problems.

3. Pay attention to the quality of thinking and give full play to the value of teaching materials.

The examination of mathematical thinking is mainly reflected in the process of students' understanding and understanding of mathematics. At the same time, the examination of mathematical thinking is not empty, but based on the design of teaching materials, and teaching is carried out on the basis of fully understanding and excavating teaching materials, so as to examine students' thinking quality.

For example, in question 22, this question mainly examines students' thinking process from the special to the general, from the intuitive to the abstract, and from the perceptual to the rational from the perspective of movement change, combined with functional images. For example, 26 questions, combined with the symmetry of quadratic function images, analyze the characteristics of function images that meet the conditions and explore the scope of symmetry axis. The design ideas of these questions all come from classroom teaching and textbooks.

For example, in the 27 questions, the test focuses on students' drawing conclusions through operation, observation and guess in the process of solving a comprehensive problem, and then proving the conclusions through deductive reasoning. Test students' ability to find, ask, analyze and solve problems in math activities such as guessing and testing. The topic explores the internal relationship of knowledge in the textbook from the perspective of movement change and graphic change, and to some extent, it synthesizes basic knowledge and methods, enriches the background of the test questions, provides students with opportunities to think from multiple angles, and also provides students with a stage to show themselves. The idea of life system of test questions originates from teaching materials, which guides teaching to think about the relationship between test questions and teaching materials.

For example, in question 28, with one of the key knowledge of students' learning-rotation as the main background, we examine students' mathematical literacy. The test questions are transformed into carriers by circles and rotations, and the "related line segments" are defined. Firstly, the special "related line segment" is studied, then the characteristics of a kind of "related line segment" are studied, and then the "related line segment" and related parameters are studied from the "positive" and "negative" angles in combination with the movement changes of graphics, showing the general process of learning new knowledge. This kind of test is not limited to the examination of knowledge itself, but by creating suitable situations, taking practical operation, exploration and discovery, and proving conjecture as the main line of activities, so that students can experience the general process of exploring and solving problems in mathematical activities and accumulate experience, which is the embodiment of mathematical literacy.

4. Pay attention to practical ability and reflect application value.

There are many problems related to quantity in real life. By establishing a mathematical model and solving it by mathematical methods, the application value of mathematics is reflected. Such as 16, with the background of "processing time of two production lines", this paper examines students' ability to analyze and solve practical problems by using what they have learned, so that students can develop the habit of observing the world with mathematical eyes and solving problems with mathematical knowledge in daily life, stimulate students' interest in learning mathematics and realize the application value of mathematics.

Third, deepen the reform of examination content,

Positive guidance teaching,

Reduce students' excessive academic burden

1. Take the curriculum standards as the key link, dig or select materials from the teaching materials, and further guide the teaching to return to the classroom and return to the teaching materials.

According to the knowledge and ability requirements of the curriculum standards, the 28th question is ranked, and the problem is "not exceeding the standard", so as to guide classroom teaching to implement teaching closely according to the requirements of the curriculum standards. According to the statement of the textbook, the design and questioning of the 28th question conforms to the psychological characteristics of students, and the question "does not dig a hole" further guides the classroom to return to the textbook. From the point of view of the number of questions, about 70% of the questions in question 28 come from textbooks, among which questions 4, 6, 8 and 13 are examples of textbooks or exercises after class.

2. The examination questions pay attention to the examination of main knowledge and key abilities, strengthen the examination of mathematical thinking, and further guide the classroom to return to the essence of the subject.

Questions 8, 16, 23, and 25-28 in the test paper are all based on the main knowledge, to investigate the accumulated activity experience, as well as the understanding of the nature of knowledge and the perception of mathematical thought in the process of knowledge formation, development and application. "Mechanical brush" is invalid for these problems, so we should pay attention to the essence of knowledge and the flexible use of thinking methods when guiding classroom teaching.

3. The design and questioning of the test questions are in line with the teaching practice and students' psychological characteristics. There is no "no wonder" in the test questions, which guides the teaching to "run in no hurry"

No.28 of the whole volume has neither the questions with scattered knowledge in senior high school nor the questions adapted from junior high school mathematics competitions. It examines not profound learning knowledge and unconventional problem-solving skills in competitions, but the solidity of basic knowledge, the thickness of accumulated experience in effective mathematical activities, the depth of understanding the essence of mathematics and the perception of mathematical thoughts. Guide teaching to return to normal classroom teaching that conforms to students' cognitive characteristics and discipline development law, create a good educational ecology for middle school students to "reduce their burdens", promote the in-depth implementation of quality education, and help students grow up healthily.

In a word, the 20021Beijing Junior High School Proficiency Test Paper is aimed at all students and student-centered, which consolidates the achievements of the content reform of the senior high school entrance examination in recent years, actively explores the new mode of the junior high school academic proficiency test reform, adheres to the general principle of striving for progress while maintaining stability, gives full play to the educational function of the test questions, persists in creating new scenarios that meet the characteristics of students, examines the subject knowledge, core competence and basic ideas, and examines the ability to find, analyze and solve problems.

202 1 Beijing Junior High School Academic Level Examination

Evaluation of mathematics test questions

The 20021year Beijing Junior High School Level Examination Mathematics Paper (hereinafter referred to as "Beijing Paper") is based on the Compulsory Education Mathematics Curriculum Standard (20 1 1 Edition) (hereinafter referred to as "Curriculum Standard"), which not only realizes the function of level examination, but also embodies the function of selection, and conforms to the "two tests". Beijing Paper remains stable in the aspects of paper structure, question distribution and score setting, which embodies the characteristics of "striving for progress while being stable, giving priority to being stable".

First, according to the "Curriculum Standards"

Highlight the characteristics of mathematics curriculum

According to the requirements of "Curriculum Standards", Beijing Volume creates situations based on the topics or contents of textbooks that students are familiar with, which is conducive to reducing students' excessive academic burden. For example, the problem of "the sum of polygons" in the fourth question, the problem of "tossing two coins" in the sixth question, and the problem of "enterprise production line processing" in the first question 16.

Beijing paper guides students to pay attention to real social life and solve problems by mathematical methods. For example, question 25, with the background of "postal enterprise income", examines students' reading of statistical chart information and their interpretation and application of statistical data. Question 20. The background is to study the method of determining the east-west direction recorded in Huainanzi Astronomical Training. Students feel the charm of mathematical culture while reading analytical reasoning, and show the educational and scientific value of mathematics.

Second, comprehensively check the "four basics"

Implement the requirements of academic level

Beijing Volume closely follows the curriculum standards and teaching materials, and pays attention to the examination of basic knowledge, basic skills, basic ideas and basic activity experience. The score design of each knowledge field meets the requirements of curriculum standards, and the creation of most topics is closely related to teaching materials. The gradient design is meticulous and reasonable, which conforms to the cognitive law and level of junior high school students and embodies the requirements of junior high school academic level examination. Compared with the Beijing Volume in 2020, it has remained stable in the types of questions and questions.

Questions 2, 3, 4, 9 and 10 examine the basic concepts and properties. 8, 12, 23( 1) and 26( 1) examine the concepts, images and properties of the three functions in junior high school, highlighting the examination of the main knowledge, not only examining the basic knowledge, but also paying attention to the integrity of knowledge and the relationship between knowledge. 1 1, 18, 19 realize the examination of computing power with different knowledge as the carrier. Question 23: With the help of function images, the critical state in motion changes is found, which embodies the thinking method of combining numbers and shapes.

Most of the topics in Beijing Paper are presented in familiar forms, with a low starting point and easy understanding, which provides a direction for students' thinking. For example, Question 25 is similar to Question 25 of 20 18, and Questions 26 (1) and 27 (1) are also basic questions, which provide different opportunities for different students to show.

Compared with the Beijing Volume in 2020, the types of function inquiry are reduced, the types of quadratic equation in one variable are adjusted from fill-in-the-blank questions to solution questions, and the fill-in-the-blank questions increase the examination of the solutions of fractional equations. It fully embodies the basic, comprehensive and comprehensive nature of knowledge examination.

Third, pay attention to the depth of thinking.

Reflect the function of test paper selection

Beijing paper focuses on examining the breadth of thinking, and the design of test questions reflects the ability to understand, analyze and solve problems with high quality. Based on the main knowledge of the subject, Beijing volume pays attention to the examination of the nature of the subject, which embodies the function of selecting volumes.

16 creates a realistic situation of a production line processing the same raw material, examines students' reading comprehension ability of mathematical conditions described by words and symbols, and their ability to extract, process and process information in the topic, establishes an appropriate mathematical model, encourages students to analyze and solve practical problems with diversified methods and different mathematical models, and examines model thinking and application consciousness.

Question 26 comes from textbooks and classroom teaching. Through the investigation of the concept, image and basic properties of quadratic function, students are guided to combine the symmetry of quadratic function image and use the method of combining numbers and shapes to reason, focusing on the ability of students to think and reason by using the main knowledge and learning experience accumulated in junior and middle schools. Students can choose different methods through in-depth analysis of problems, which reasonably reduces the amount of calculation, reflects the requirements for students' ability and literacy, and realizes the function of selecting test questions.

Question 27 continues the style of the previous Beijing Paper, and examines students' recognition, analysis and refinement of basic geometric figures and their properties in the question situation. By drawing, observing and analyzing the whole process of graphic movement change, we can guess and explore the relationship and law between the number of geometric figures contained in it, so as to examine students' geometric intuition, cognition of common auxiliary lines in basic graphics, and their ability to master general methods and logical reasoning.

As a characteristic test question that Beijing has always adhered to, 28 questions adhere to the process examination of concept learning. It takes the rotation, one of the key knowledge for students to learn, as the main background, defines the "related line segment", and takes practical operation, exploration and discovery, and proof of conjecture as the main line of activities, so that students can experience the general process of learning and researching new knowledge, and then study the characteristics of a kind of "related line segment" from the special situation, explore and solve problems, and learn experience on the spot.

Compared with 2020, the examination questions No.26, No.27 and No.28 remain stable in the examination direction and method, and pay attention to the depth of thinking, which embodies the function of examination paper selection.

Fourth, pay attention to the creation of situations.

Realize the educational function

Beijing Volume further enriches the choice of test questions, creates rich realistic cultural situations, designs test questions with students' personal life and social life as the background, embodies various applications of mathematics, bridges the gap between the content of mathematical knowledge and asking questions, and guides students to truly feel the application value of mathematics in the process of solving problems with mathematical knowledge. Question 6 is based on the coin toss experiment that students are very familiar with, and examines students' understanding of the meaning of probability and the method of finding probability by enumeration; Question 8 continues the proposition of Beijing Volume in 2020, selects the problem situation in the textbook, studies the relationship between two adjacent sides, areas and one side of a rectangle with a certain circumference, and examines the students' mastery of the function model. 16 is based on the distribution and processing business problems in industrial production, guiding students to solve problems with model thinking, and students need to make rational analysis and judgment on the basis of understanding the meaning of the questions; Question 25 takes the income problem of postal enterprises in two cities as the background, and investigates the statistical significance of average and median. The concept of data analysis such as estimating population with samples also enhances students' ability to analyze and solve practical problems.

Beijing Volume fully implements the fundamental task of moral education, embodies the correct orientation of educating people, promotes and promotes students' all-round development and healthy growth, and develops quality education. The second question is based on education in poverty alleviation, examining the knowledge of scientific notation, guiding candidates to cherish the motherland, pay attention to society, cultivate patriotism, love the party and love socialism, and consciously shoulder the mission of fighting for the great rejuvenation of the Chinese nation. Question 20: It is an inevitable requirement of socialist core values education in the new period to use the method of determining the east-west direction by using the shadow of a pole recorded in Huainan Xun, to design ruler drawing and simple geometric reasoning, and to realize education and cultural education, and to enhance cultural self-confidence.

Beijing Volume 202 1 embodies the characteristics of smooth transition in proposition, strengthens the proportion of basic questions, maintains the depth of thinking of difficult questions, and grasps the proposition orientation properly. Test questions play a very good role in creating situations, selecting materials and guiding values. The examination questions are combined with the development trend of the country, with the development of Beijing, and closely linked with the content of the teaching materials. Guiding students to apply what they have learned in new problems and situations has played a good guiding role in classroom teaching.