How to have a master in the family-Talking from the core literacy of high school mathematics

Category：education

2021-06-11

"Hope your child will become a dragon" must be the wish of many parents. Parents all want their children to be academic masters. Xueba [ xué bà ] refers to students who are good at learning and have high scores. People who study hard, study all the time, and can easily get high marks when everyone fails the exam. Can bear the pain and pressure that ordinary people can't bear. 2016 Beijing College Entrance Scholar, Beijing College Entrance Scholar, 120 points in Chinese, 120 points in mathematics, 120 points in English, 100 points in physics, 80 points in chemistry, and 40 points in physical education! The five subjects were all full marks, with a bare score of 580. Even the school principal was shocked and exclaimed: genius. In 2018, there was a report on the Internet that "Beijing's college entrance examination results are now full marks in all subjects". Jiang Haiyang, class 2, grade 3, junior high school, Beijing No. 12 Middle School, got a full score of 580 in all subjects. In 2016, Jiang Haiyang from Class 2, Grade 3, Junior High School, Beijing No. 12 got a perfect score of 580 in all subjects. In 2019, a parent asked a question on the Internet, "It is said that the mathematics of the college entrance examination is simple. When children practice, it is just careless to lose three or four points. Can the college entrance examination get full marks"? First, the mathematics of the college entrance examination can of course get full marks, and there are still many people with full marks. If it is said that among the three courses of Chinese, mathematics, and English, the subject that is most likely to get full marks, it must be mathematics. This is determined by the nature of the subject test. First of all, let's take a look at Chinese. The Chinese test has subjective questions, objective questions, and more importantly, the biggest composition question. For objective questions, there is a certain probability of being correct. Generally, objective questions are mainly filled in the blanks. If some teachers change the paper loosely, it is possible to get full marks by stepping on the points. But the composition test, if you want to get full marks, is very, very difficult. Has there ever been a perfect score in history? Yes, in both the college entrance examination and the college entrance examination, there are full scores of compositions, but every year in the college entrance examination, there are very few full score compositions. Those who can get full scores can basically make a sensation in the whole country, and the same is true for the college entrance examination. Therefore, the difficulty of getting a full score in the Chinese test is very high, and the probability is very low.Second, let's look at English. The structure of English test questions is similar to that of Chinese. The biggest obstacle to getting full marks in the test is composition, so the probability of getting full marks in the English test is relatively low. Finally, let's look at mathematics. The question types of the math test are very fixed and relatively simple. They are basically multiple-choice questions, fill-in-the-blank questions and answer questions. For multiple-choice questions and fill-in-the-blank questions, if there are no errors in the test paper, the answers are basically unique, and there will be no A. or the case of B. Math answer questions are different from subjective questions in other subjects. Although there may be many ways to solve the questions, the answer must be unique. Even if it is a proof question, the principle of the proof will not be too biased, which theoretically has the basis for full marks. Invisibly, this also increases the probability of a perfect score in the math test.

For students, only a small number of students can be considered top students, but most of them are middle-level students. Everyone is born with about the same IQ. Why is there so much difference in learning? Motivation, interest, methods, and perseverance can make you a scholar. China is also a country that attaches great importance to education. Many families save money for their children to go to good schools and take remedial classes. So how do scholars develop? Every candidate who is struggling to catch up on the road to study hopes that there will be a bright road under their feet, and that the final destination is the admission letter of the ideal university. But what can you do to get your grades up? This is a concern for both candidates and parents.

First, the characteristics of high school mathematics and the six core competencies

Mathematics is the word God used to write the universe - Galileo. "Math is the mother of all sciences", "Math is the gymnastics of thinking". It is a science that studies numbers and shapes based on the objective world. Compared with junior high school mathematics,

has an exponential increase in the difficulty of high school mathematics.For many students, high school mathematics is the most feared subject in the three years of high school. Many students with good grades in junior high school math have suffered big troubles in their first year of high school. It is conceivable that for those students who did not learn mathematics well in junior high school , high school mathematics textbooks are even more shocking as "books from heaven". So how has high school math changed? How can most students be at a loss?

Entering high school, you will find that it is very different from junior high school, with many subjects and broadened knowledge. Mathematics, in particular, develops from concrete to abstract. High school mathematics learning is a critical period in the middle school stage to link the past and the future. After many students enter high school, whether they can adapt to the study of high school mathematics is an urgent problem for high school students. In addition to the external environment such as learning environment, teaching content and teaching factors, students should change their ideas, increase their awareness and improve their methods. Compared with junior high school mathematics, high school mathematics has more content, is abstract and theoretical, so many students are very uncomfortable after entering high school. Especially in the first year of high school, after entering the school, the first thing you encounter in algebra is the function with strong theoretical value. Coupled with the three-dimensional geometry, the concept of space and the ability to imagine space cannot be established all at once. This makes some junior high school students. Students who are good at math find it difficult to adapt quickly. Combined with the characteristics of high school mathematics content, I will talk about the method of high school mathematics learning. High school mathematics courses are divided into compulsory courses, optional compulsory courses and elective courses. The content of high school mathematics curriculum highlights four main lines: function, geometry and algebra, probability and statistics, mathematical modeling activities and mathematical exploration activities, which run through compulsory, optional compulsory and elective courses. Mathematical culture is integrated into the curriculum content. The structure of high school mathematics curriculum is as follows:

1. Abstraction enhancement of high school mathematics knowledge

Mathematics is a science that studies quantitative relationships and spatial forms.Mathematics originates from the abstraction of the real world. Based on abstract structures, it understands and expresses the nature, relationships and laws of things in the real world through symbolic operations, formal reasoning, and model building. Mathematics is closely related to human life and social development. Mathematics is not only a tool for calculation and reasoning, but also a language for expression and communication. Mathematics carries ideas and culture, and is an important part of human civilization. Mathematics is an important foundation of natural sciences, and plays an increasingly important role in social sciences. The application of mathematics has penetrated into all aspects of modern society and people's daily life. With the rapid development of modern science and technology, especially computer science and artificial intelligence, people's ability to acquire and process data has been greatly improved. With the advent of the era of big data, people often need to The reflected information is processed digitally, which greatly expands the research field and application field of mathematics. Mathematics directly creates value for society and promotes the development of social productivity.

Mathematics plays an irreplaceable role in the process of forming people's rational thinking, scientific spirit and promoting the development of personal intelligence. Mathematical literacy is the basic literacy that everyone should have in modern society. Mathematical education carries the functions of implementing the fundamental task of cultivating morality and developing quality education. Mathematics education helps students master the mathematical knowledge, skills, ideas and methods necessary for modern life and further study; improve students' mathematical literacy, guide students to observe the world with mathematical eyes, think about the world with mathematical thinking, and express the world with mathematical language; It promotes the development of students' thinking ability, practical ability and innovative consciousness, explores the law of changes in things, and enhances their sense of social responsibility; it plays a unique role in forming a correct outlook on life, values, and world outlook for students.

The high school mathematics course is the main course of ordinary senior high schools after the compulsory education stage, which is basic, selective and developmental. Compulsory courses are for all students and build a common foundation; optional compulsory courses and elective courses fully consider the different growth needs of students, and provide a variety of courses for students to choose independently; high school mathematics courses create conditions for students' sustainable development and lifelong learning.

2. The way of thinking transitions to a rational level. Junior high school mathematics: less knowledge, more flexible question types, and the effect of surprise learning is greater than that of high school. Some knowledge, such as linear function quadratic function probability, will be further extended in the high school curriculum. Factoring and other knowledge will exercise students' letter operation ability. Generally speaking, junior high school mathematics plays a fundamental role. The basic knowledge points of high school mathematics have increased and the depth has been strengthened. Many knowledge points are more abstract and difficult to understand, such as the periodic increase and decrease of functions, and solid geometry. It is necessary for children to understand the knowledge points and cultivate basic abilities in the daily learning process, otherwise it will cause great pressure to the senior three learning.

3. The overall volume of knowledge content has increased dramatically. One obvious difference between high school mathematics and junior high school mathematics is that the "quantity" of knowledge content has increased sharply, the amount of knowledge information received per unit time has increased a lot compared with junior high school mathematics, and the class hours for auxiliary practice and digestion have been reduced accordingly. The high school mathematics curriculum reflects the needs of social development, the characteristics of mathematics and students' cognitive laws, and develops students' core competencies in mathematics. Optimize the curriculum structure to provide students with a common foundation and diversified choices; highlight the main line of mathematics, highlight the inherent logic and thinking methods of mathematics; select curriculum content, handle the relationship between the core literacy of mathematics and knowledge and skills, and emphasize the relationship between mathematics and mathematics. The connection between life and other disciplines improves students' ability to apply mathematics to solve practical problems, and at the same time pays attention to the penetration of mathematical culture.High school mathematics teaching is guided by the development of students' core competencies in mathematics, creating appropriate teaching situations, inspiring students to think, and guiding students to grasp the essence of mathematics content. Promote independent thinking, independent study, cooperative communication and other learning methods, stimulate interest in learning mathematics, develop good study habits, and promote the development of students' practical ability and innovative consciousness. Pay attention to the in-depth integration of information technology and mathematics courses to improve the effectiveness of teaching. Constantly guide students to perceive the scientific value, application value, cultural value and customs value of mathematics.

In September 2016, "Chinese Students' Development of Core Literacy" was released. Since then, my country's educational guiding ideology has undergone a major change from teaching to educating people. The Ministry of Education's "Mathematics Curriculum Standard for Senior High Schools (2017 Edition)" pointed out that the core literacy of the subject is the concentrated expression of the value of educating people, and it is the correct value concept, necessary character and key ability that students gradually form through subject learning. The core literacy of mathematics is the concentrated expression of the objectives of the mathematics curriculum, and it is a comprehensive reflection of the thinking quality, key abilities, emotions, attitudes and values with the basic characteristics of mathematics. It is gradually formed and developed in the process of mathematics learning and application. The core competencies of mathematics include: mathematical abstraction, logical reasoning, mathematical modeling, intuitive imagination, mathematical operations and data analysis. These core competencies of mathematics are both relatively independent and inter-integrated, forming an organic whole. The essence of core literacy is the fundamental and leading element in the human literacy system. It is the "key literacy" in quality education, three-dimensional goals, all-round development, and comprehensive quality. Mathematical literacy is one of the necessary literacy for students. As far as mathematics is concerned, the core literacy of mathematics includes six aspects: mathematical abstraction, logical reasoning, mathematical modeling, mathematical operations, intuitive imagination, and data analysis. It also includes learning to learn, mathematical application, and innovative awareness.

Second, take core literacy as the guide to talk about how students can learn high school mathematics

The college entrance examination mathematics test paper presents a multi-level and high-quality examination of students' literacy ability, which not only requires students to have a solid foundation, but also requires students to have good mathematical thinking Quality, pioneering, reflective, and innovative thinking, able to flexibly use the knowledge learned to seek effective problem-solving ideas. It can be seen that the teaching of mathematics review courses for the college entrance examination in Fujian Province can no longer follow the traditional test-oriented teaching mode. It is necessary to pay attention to the development of students' literacy and ability, and take core literacy as the guide to improve students' thinking ability, and then review the course. achieve the expected learning effect. Candidates experience three realms of college entrance examination review: the first realm: do one question, know one question; the second realm: do one question, know a class of questions;

1. The required knowledge points are clearly understood. To learn mathematics well, we must first know what mathematics is and what it includes (high school mathematics content). When we look at high school mathematics macroscopically, there are two main modules: geometry and algebra. Geometry includes points, lines, surfaces, figures (triangles, quadrilaterals, ellipses, circles): there are rational numbers, fractions, integers, functions, etc. in algebra. Knowing the knowledge points corresponding to its general content, how to master each knowledge point, use it skillfully, and achieve the results we need is the ultimate goal.According to the content and requirements of the college entrance examination syllabus, it is necessary to centrally sort out the knowledge points required for high school mathematics, and use mind maps, pre-class warm-up and other forms to systematically divide the basic knowledge points, conceptual characteristics, image properties, etc., and refine them more concisely. The intuitive knowledge structure is convenient for further understanding in the review, strengthens the test site, and achieves the purpose of being clear at a glance and mastering all the knowledge points involved in the college entrance examination.

2. Special analysis, key breakthroughs. The object of the topic is based on the hard and difficult knowledge points , high-frequency test points, and easily confusing and error-prone knowledge points based on the attention of mathematics test candidates. Identifying the key points from the level of subject knowledge and ability is an important phenomenon for the college entrance examination mathematics. A summary of the results formed from the research on the core issues. The topic analysis should pay attention to the guidance of ideas, clear identification and analysis, rigorous logic, and focus on the standardization and complete guidance of knowledge context and problem-solving ideas. Pay attention to analyze the characteristics and connections between knowledge points and various problem-solving methods, analyze the connection between the conditions in the questions and the obtained results, and flexibly link the basic theories learned with the problem-solving methods and skills, so as to achieve the learning effect of drawing inferences from others and drawing parallels by analogy. At the same time, students can quickly find the test questions they want through the compulsory knowledge points of the college entrance examination, with clear ideas and key points. The analysis method and analysis process of classic famous questions help students master and skillfully use mathematical thinking methods, hoping to achieve the effect of attracting others, so that students and candidates can draw inferences from one to the other, so as to sway freely in the examination.

3. Summary and improvement of mathematical problem-solving models

Mathematics has many knowledge points in the college entrance examination. What problem-solving models are there for students to do? The problem-solving model is a practical and efficient problem-solving method. It grasps the essential laws of disciplines, and extracts several disintegration models through in-depth analysis, induction and summarization of the essential laws of disciplines. Help students solve ever-changing test questions.For example, the teacher teaches you additions such as 50+21, etc., but the problem is endless, but you have mastered the method model. You can also do complex addition of multiple digits. , The so-called model is like building a building. First, according to the overall requirements of the design, the first step is to build a frame, and then carry out detailed construction. Xueba always has a framework for doing questions. Poor students have a dagger in the east and a dagger in the west. The progress is slow and there is no pattern. What is a frame? It is the baton of mathematics in the college entrance examination, and it is the most important modules in high school mathematics. Philosophically speaking, it also includes several important points and difficulties of several important modules. A "model" is actually the simplest form of graphics. It is extracted from the most basic and core knowledge points in the discipline. Its problem-solving principle is to master simple knowledge modules, and to solve various complex problems by applying these simple knowledge modules. When building and improving problem-solving models, students must collect and organize the things to be investigated. They are not random, but have rules to follow, and they form the model. The problem-solving steps of "grasp the question type, set the model, and produce the result" realize the use of limited modules to solve the ever-changing test questions, making the problem-solving from difficult to easy and complicated to simple. Specifically, it is "find the law: take three to one, build a model; use the law: draw inferences from one case, set a model."

high school mathematics problem-solving models mainly include: Model 1: Element and Set Model; Model 2: Function Property Model; Model 3: Fractional Function Model; Model 4: Abstract Function Model; Model 5: Function Application Model; Model 6: Equal area transformation model; Model 7: Equal volume transformation model; Model 8: Line-plane parallel transformation model; Model 9: Vertical transformation model; Model 10: Normal vector and symmetry model; Model 11: A circle and Miller problem model; Model 12: Conditional structure model; Model 13: Cyclic structure model; Model 14: Classical and geometrical models; Model 15: Angle model; Model 16: Trigonometric function model; Model 17: Vector model; Model 18: Edge and angle mutual solution Triangle model; Model 19: The problem model of reducing to arithmetic sequence to solve recursive sequence; Model 20: Constructor model to solve inequality problem; Model 21: The most value model in analytic geometry

4. What questions to brush, how many Questions, to what extent?

brushing questions is a method of quickly contacting a large number of questions in a short period of time, understanding the meaning of the questions and answers in the shortest time possible, and then answering them. It focuses on the number of questions rather than the quality of completion. There are usually not many original questions in the exam, but the methods and ideas are similar. When the number of questions reaches a certain level, there will be a kind of inertia to do the questions. When you see similar questions in the exam, you will be more or less in your mind. There will be some ideas and ideas (at least the brain will not be empty). Brushing questions is an effective and unavoidable review method for college entrance examination mathematics. Why do we need to brush questions? Brushing questions can make us familiar with the proposition ideas of college entrance examination mathematics, can Let us be proficient in using various formulas of mathematics, which can improve our operation speed, so our college entrance examination mathematics starts from brushing questions and ends. The process of brushing questions is undoubtedly effective, but we are most afraid of blind brushing.Blind brushing and efficient brushing are the essential difference between scumbags and scumbags. This difference helps scumbags have more time to review English and physics classes, while scumbags can only seek to improve their own level. In the long run, the academic bully will become stronger and stronger, and the more competitive advantages will be accumulated.

Actively brush the questions, but also actively organize them, and organize the things that you think are important: set traps, answer templates, knowledge loopholes, extracurricular extensions, test-taking skills, etc. in the book, and read through the fragmentary time and before the exam. It will be helpful of. After sorting, you will also find exam questions. The first form of

brushing questions is not only to do the questions well, that is to say, the questions are completely made by oneself, it is not enough to achieve this level, but also to master the questions that you can do, Practice makes perfect, which is very meaningful for developing "number sense". The second form of brushing questions is naturally aimed at those questions that cannot be done. After reading the answers, questions that are not well grasped. In the high school stage, there is a name called "wrong question book". The third form of question brushing can be called the "group coaching method", which is a deformation of the memory screen under the form of group learning, that is, two or three people work together as coaches for each other, and divide the questions that everyone does not know into. There are three groups of questions. One person is responsible for looking at the answers for each group of questions. They come to be the coaches of the other two people. They are allowed to ask questions, and the coaches give hints. The questions are solved by this process. Improve, very beneficial.

Due to the limited study time and energy of students, the key to improving grades is to use the time reasonably and effectively to "evaluate the questions effectively". The premise of brushing the questions is to have a good grasp of the basic knowledge of the textbook, and then accumulate certain problem-solving skills through a certain amount of question-type exercises.

brushing questions, not mathematics, focusing on thinking training and question understanding, this is a long-term "self-cultivation" process. Problems evolve from basic questions. Only by fully mastering the basic knowledge can we develop ideas, use skills proficiently, make big questions and difficult problems, and open up the "grade" with other candidates. When brushing the questions, you can choose some difficult exercises according to your own mathematics scores. It is best to have analytic real questions for the middle and high school entrance examinations. point of purpose.

In summary, the key to brushing questions is not how many questions you have done, but how many effective question types you can “brush”, that is, whether to choose appropriate questions according to your own grades and knowledge. Although the questions of each set of real questions are diverse, the types are roughly similar, and the knowledge points are similar. Therefore, during the problem solving process and after solving the problem, you should pay attention to "covering the paper and introspection", summarize the problem solving steps, and summarize the connection between the knowledge points. Apply it, find the way of thinking of "the key point of breaking the question", and master the answering skills. It is simply to brush the whole set of test papers. Instead, you should first find a few sets of questions and focus on brushing your weak questions in a targeted manner. For example, brushing questions of moderate difficulty or above, brushing reading comprehension and task-based reading questions, etc. It's just a rough look and an intuitive judgment on whether you can quickly find an idea. If you can't find a solution to the problem, take it seriously. In particular, it should be noted that the way of brushing questions in each subject is different. The best method is like "strike iron", analyzing one's own "shortcomings", "according to the situation and selecting questions" is the premise of "writing questions" condition.

5. Have your own Xueba notes.

Xueba’s notes are mainly divided into three types: (class notes, wrong questions, and at least 100 standard and classic title notes) A record formed after knowledge points are recorded in a notebook. It is very important for reviewing the knowledge that has been learned, and it is very important for overcoming the limitations of memory and knowledge storage in the mind. The process of taking notes is the process of selecting and condensing information, which is conducive to exercising thinking, improving the ability to capture important information, and improving the concentration of information. processing capacity. In order to make good lecture notes, the students’ thought process must be consistent with the teacher’s thought process, and distractions that are not related to lectures must be discarded. Thoughts cannot be slipped away, and the content of the notes should pay attention to the key points, difficulties, doubts, and new ideas. The lecture notes can be used in your own words. Use key words and clue sentences, outline the territory records.

Class notes can help us clarify the thinking of listening to the class, grasp the key points of listening to the class, and provide convenience for future review. More importantly, it can make us pay close attention to the learning and deeply understand the content of the teacher, so as to facilitate the review in the future. Improve learning efficiency. Remembering outlines, thinking, key points, difficulties, supplements, summaries and perceptions are the important contents of class notes. The real function of ordinary notes is to organize ideas when taking notes, that is, to reflect the connection between different knowledge points and the classification of different knowledge in the same topic. For example, Sichuan cuisine is a general knowledge, and Gongpao Chicken is a branch of it. According to scientists' research, fragmented knowledge can be extracted more quickly and efficiently only when it forms chunks in the brain. The second function is to trigger thinking when reviewing. These two functions are actually saying that taking notes is more valuable, after all, understanding the class is the biggest.

In summary, taking notes in class requires listening, seeing, thinking, and manual. On the premise of comprehension, the acquired knowledge information goes through the process of "selection-processing-induction-concentration-feedback" through the brain's thinking, and then record it with the focus. There are various methods of recording, we can gradually find out the method that suits us in learning, and finally achieve the effect of promoting our learning and improving the learning effect.

Wrong question book: "wrong question book", also called "wrong book", "error correction book", "error correction book", "wrong question set". It means that in the process of learning, students organize their own homework, exercises, and wrong questions in the test paper into a book, which is easy to find out the weak links in their own learning, so that the learning focus is highlighted, the learning is more targeted, and the learning is improved. Efficiency to improve academic performance workbook. In the process of using the "wrong question book", some students not only sorted out the exercises that they did wrong, but also sorted out the "problem-prone questions", "difficult questions", "typical questions", "good questions", etc. , known as the "good book". The core value of the error book is reflected in three aspects:

First, the collection of learning problems: it is a collection of students' learning problems, which is a collection of students' learning problems. In fact, it is to completely record the students' lost points, and the establishment of the wrong question book provides specific directions for solving problems. The second is to focus on the learning objectives: the wrong question book makes the students' learning objectives more concentrated, and the learning focus is more clear. If you catch the wrong question, you will grasp the key problem of losing points in learning. If students can focus on the wrong question book, focus on solving the problem, and solve the wrong question, the loss of points will be reduced, and the score will naturally improve.The third is to develop study habits: collecting and sorting out wrong questions is a continuous process in itself. During this process, students continuously sort out and summarize the wrong questions in their own learning. Understanding, on the other hand, long-term persistence and unconsciously will develop a good habit of reviewing and summarizing in time. The formation of habits is an extremely important manifestation of learning ability.

Mathematics is a subject with strong logical thinking. Unlike other liberal arts, it is basically the same as other science studies, focusing on understanding. The understanding of mathematics is most important in the classroom. Each teacher may have different ways of teaching mathematics, but the knowledge points are similar. In the classroom, the understanding of the knowledge and the problem-solving methods taught by the teacher must follow the teacher's ideas, and even you have to run in front of the teacher. Come to the class, get twice the result with half the effort. If you want to learn mathematics well, you must learn a variety of methods to solve problems. Only when you practice in ordinary times, ask yourself, whether this problem is a problem and there are other better ways to solve it, learn to draw inferences from one case, and master all kinds of solutions. Question method, in the exam, you can easily use the simplest method to solve the question, at least not be exhausted. There is no one who will never encounter difficulties on the road of learning. Everyone has made mistakes, but it is not terrible to make a mistake once, but it is terrible to make the same mistake next time. The main purpose of this step is to establish the overall framework of mathematics and master the method of converting the question stem into mathematical language.During this long and tedious process, I accumulated a large number of wrong questions and recorded the wrong questions in the wrong book (at this stage, I often did not write the answer to this question in the wrong book) , so that I can have a very clear understanding of the common test sites of mathematics, and at the same time, I can also grasp the corresponding relationship between the stem text and the mathematical language. For example, in analytic geometry, I can write the corresponding mathematical Express. There are often many kinds of such correspondences, so it takes a lot of practice to quickly determine which mathematical expression can be used more easily under the given conditions. My favorite book in high school is the set of wrong math problems, which not only accumulates the problems that I often make mistakes in, but also learns from the mistakes of others. To learn mathematics, you don't need to memorize by rote, and you don't need to engage in tactics. Only by fully integrating the knowledge of mathematics textbooks and teachers into your own knowledge system, it is possible to get high scores in the mathematics test, and even get a full score in the final test.

standard notes on classic titles: follows the changing trend of the college entrance examination, captures the latest college entrance examination information from all over the country, carefully divides and filters various types of questions, and selects the most typical example questions. These sample questions are novel and practical, and can represent the hottest and most important types of examinations in the content of the college entrance examination. Effectively improve students' problem-solving ability, focus on exploring problem-solving skills, and help students see through the traps carefully designed by the propositioner, so as to achieve the purpose of teaching people how to fish.High School Mathematics Curriculum Standards (Experiment)" takes "embodies the cultural value of mathematics" as one of the basic concepts of the curriculum, and clearly points out in the teaching suggestions: "Mathematics is an important part of human culture, the product of human social progress, and the The driving force for promoting social development. In teaching, students should be guided to initially understand the interaction between mathematical science and human social development, to realize the scientific value, application value, humanistic value of mathematics, and broaden their horizons...".

The classic mathematical title is Goldbach's conjecture. More than two hundred years ago, there was a German mathematician named Goldbach. He found that every even number not less than 6 can be written as the sum of two prime numbers (also called prime numbers), abbreviated as "1+1".例如：

　　6＝3＋3　　　　 100＝3＋97　　　　　　 1000＝3＋997

　　8＝3＋5　　　　 102＝5＋97　　　　　　 1002＝5＋997……

　　12＝5＋7　　　　104＝7＋97　　　　　　 1004＝7＋997

哥德巴赫对许多偶数进行了检验，都说明这个推断是正确的. In the future, some people have carried out a large number of checks on even numbers, starting from 6 and counting to 330 million numbers one by one, all showing that Goldbach's discovery is correct. However, natural numbers are infinite. Is this assertion correct for all natural numbers? It must be proved theoretically, and Goldbach himself could not prove it. In 1742, he wrote to Euler, a famous mathematician at the time, asking him to help prove it. Later Euler wrote back: "He thinks that the question raised by Goldbach is right, but he has no way to prove it. Because it cannot be proved, it cannot become a law, so it can only be said to be a conjecture, and people put Goldbach forward. The problem is called "Goldbach's conjecture." Since then, Goldbach's conjecture has become a world-famous problem.Some people call it "the jewel in the crown", it is like a peak in mathematics. Who can climb this peak? For more than 200 years, many mathematicians have tried to prove this conjecture. Chinese mathematician Chen Jingrun has made a breakthrough in the study of "Goldbach's conjecture" and is in a leading position in the world. The results of his famous paper "The table of large prime numbers is the sum of a prime number and the product of no more than two prime numbers" is called "Chen's Theorem" by the international mathematical community.

"Hope your child will become a dragon" must be the wish of many parents. Parents all want their children to be academic masters. Xueba [ xué bà ] refers to students who are good at learning and have high scores. People who study hard, study all the time, and can easily get high marks when everyone fails the exam. Can bear the pain and pressure that ordinary people can't bear. 2016 Beijing College Entrance Scholar, Beijing College Entrance Scholar, 120 points in Chinese, 120 points in mathematics, 120 points in English, 100 points in physics, 80 points in chemistry, and 40 points in physical education! The five subjects were all full marks, with a bare score of 580. Even the school principal was shocked and exclaimed: genius. In 2018, there was a report on the Internet that "Beijing's college entrance examination results are now full marks in all subjects". Jiang Haiyang, class 2, grade 3, junior high school, Beijing No. 12 Middle School, got a full score of 580 in all subjects. In 2016, Jiang Haiyang from Class 2, Grade 3, Junior High School, Beijing No. 12 got a perfect score of 580 in all subjects. In 2019, a parent asked a question on the Internet, "It is said that the mathematics of the college entrance examination is simple. When children practice, it is just careless to lose three or four points. Can the college entrance examination get full marks"? First, the mathematics of the college entrance examination can of course get full marks, and there are still many people with full marks. If it is said that among the three courses of Chinese, mathematics, and English, the subject that is most likely to get full marks, it must be mathematics. This is determined by the nature of the subject test. First of all, let's take a look at Chinese. The Chinese test has subjective questions, objective questions, and more importantly, the biggest composition question. For objective questions, there is a certain probability of being correct. Generally, objective questions are mainly filled in the blanks. If some teachers change the paper loosely, it is possible to get full marks by stepping on the points. But the composition test, if you want to get full marks, is very, very difficult. Has there ever been a perfect score in history? Yes, in both the college entrance examination and the college entrance examination, there are full scores of compositions, but every year in the college entrance examination, there are very few full score compositions. Those who can get full scores can basically make a sensation in the whole country, and the same is true for the college entrance examination. Therefore, the difficulty of getting a full score in the Chinese test is very high, and the probability is very low. Second,Let's look at English. The structure of English test questions is similar to that of Chinese. The biggest obstacle to getting full marks in the test is composition, so the probability of getting full marks in the English test is relatively low. Finally, let's look at mathematics. The question types of the math test are very fixed and relatively simple. They are basically multiple-choice questions, fill-in-the-blank questions and answer questions. For multiple-choice questions and fill-in-the-blank questions, if there are no errors in the test paper, the answers are basically unique, and there will be no A. or the case of B. Math answer questions are different from subjective questions in other subjects. Although there may be many ways to solve the questions, the answer must be unique. Even if it is a proof question, the principle of the proof will not be too biased, which theoretically has the basis for full marks. Invisibly, this also increases the probability of a perfect score in the math test.

First, the characteristics of high school mathematics and the six core competencies

has an exponential increase in the difficulty of high school mathematics. For many students,High school mathematics is the most feared subject in the three years of high school. Many students who did well in mathematics in junior high school fell into trouble in their first year of high school. It is conceivable that for those students who did not learn mathematics well in junior high school, high school mathematics textbooks are even more important. Surprised as "Book of Heaven". So how has high school math changed? How can most students be at a loss?

1. Abstraction enhancement of high school mathematics knowledge

Mathematics is a science that studies quantitative relationships and spatial forms. Mathematics stems from the abstraction of the real world,Based on abstract structures, through symbolic operations, formal reasoning, model construction, etc., to understand and express the nature, relationships and laws of things in the real world. Mathematics is closely related to human life and social development. Mathematics is not only a tool for calculation and reasoning, but also a language for expression and communication. Mathematics carries ideas and culture, and is an important part of human civilization. Mathematics is an important foundation of natural sciences, and plays an increasingly important role in social sciences. The application of mathematics has penetrated into all aspects of modern society and people's daily life. With the rapid development of modern science and technology, especially computer science and artificial intelligence, people's ability to acquire and process data has been greatly improved. With the advent of the era of big data, people often need to The reflected information is processed digitally, which greatly expands the research field and application field of mathematics. Mathematics directly creates value for society and promotes the development of social productivity.

The high school mathematics course is the main course of ordinary senior high schools after the compulsory education stage.It is fundamental, selective and developmental. Compulsory courses are for all students and build a common foundation; optional compulsory courses and elective courses fully consider the different growth needs of students, and provide a variety of courses for students to choose independently; high school mathematics courses create conditions for students' sustainable development and lifelong learning.

3. The overall volume of knowledge content has increased dramatically. One obvious difference between high school mathematics and junior high school mathematics is that the "quantity" of knowledge content has increased sharply, the amount of knowledge information received per unit time has increased a lot compared with junior high school mathematics, and the class hours for auxiliary practice and digestion have been reduced accordingly. The high school mathematics curriculum reflects the needs of social development, the characteristics of mathematics and students' cognitive laws, and develops students' core competencies in mathematics. Optimize the curriculum structure to provide students with a common foundation and diversified choices; highlight the main line of mathematics, highlight the inherent logic and thinking methods of mathematics; select curriculum content, handle the relationship between the core literacy of mathematics and knowledge and skills, and emphasize the relationship between mathematics and mathematics. The connection between life and other disciplines improves students' ability to apply mathematics to solve practical problems, and at the same time pays attention to the penetration of mathematical culture. High school mathematics teaching is guided by the development of students' core competencies in mathematics, creating a suitable teaching situation,Inspire students to think and guide students to grasp the essence of mathematical content. Promote independent thinking, independent study, cooperative communication and other learning methods, stimulate interest in learning mathematics, develop good study habits, and promote the development of students' practical ability and innovative consciousness. Pay attention to the in-depth integration of information technology and mathematics courses to improve the effectiveness of teaching. Constantly guide students to perceive the scientific value, application value, cultural value and customs value of mathematics.

In September 2016, "Chinese Students' Development of Core Literacy" was released. Since then, my country's educational guiding ideology has undergone a major change from teaching to educating people. The Ministry of Education's "Mathematics Curriculum Standard for Senior High Schools (2017 Edition)" pointed out that the core literacy of the subject is the concentrated expression of the value of educating people, and it is the correct value concept, necessary character and key ability that students gradually form through subject learning. The core literacy of mathematics is the concentrated expression of the objectives of the mathematics curriculum, and it is a comprehensive reflection of the thinking quality, key abilities, emotions, attitudes and values with the basic characteristics of mathematics. It is gradually formed and developed in the process of mathematics learning and application. The core competencies of mathematics include: mathematical abstraction, logical reasoning, mathematical modeling, intuitive imagination, mathematical operations and data analysis. These core competencies of mathematics are both relatively independent and inter-integrated, forming an organic whole. The essence of core literacy is the fundamental and leading element in the human literacy system. It is the "key literacy" in quality education, three-dimensional goals, all-round development, and comprehensive quality. Mathematical literacy is one of the necessary literacy for students. As far as mathematics is concerned, the core literacy of mathematics includes six aspects: mathematical abstraction, logical reasoning, mathematical modeling, mathematical operations, intuitive imagination, and data analysis.It also includes learning to learn, mathematical application, and innovation.

Second, take core literacy as the guide to talk about how students can learn high school mathematics

1. The required knowledge points are clearly understood. To learn mathematics well, we must first know what mathematics is and what it includes (high school mathematics content). When we look at high school mathematics macroscopically, there are two main modules: geometry and algebra. Geometry includes points, lines, surfaces, figures (triangles, quadrilaterals, ellipses, circles): there are rational numbers, fractions, integers, functions, etc. in algebra. Knowing the knowledge points corresponding to its general content, how to master each knowledge point, use it skillfully, and achieve the results we need is the ultimate goal. According to the content and requirements of the college entrance examination syllabus, it is necessary to centrally sort out the knowledge points required for high school mathematics, and use mind maps, pre-class warm-up and other forms to systematically divide the basic knowledge points, conceptual characteristics, image properties, etc., and refine them more concisely. Intuitive knowledge structure, easy for further understanding in review,Strengthen the test site, to achieve the purpose of being clear at a glance and mastering all the knowledge points involved in the college entrance examination.

3. Summary and improvement of mathematical problem-solving models

Mathematics has many knowledge points in the college entrance examination. What problem-solving models are there for students to do? The problem-solving model is a practical and efficient problem-solving method. It grasps the essential laws of disciplines, and extracts several disintegration models through in-depth analysis, induction and summarization of the essential laws of disciplines. Help students solve ever-changing test questions. For example, the teacher teaches you additions such as 50+21, etc., but the problem is endless, but you have mastered the method model. You can also do complex addition of multiple digits. , the so-called model is like building a building. First, according to the overall requirements of the design, the first step is to build a frame.Then proceed to detail construction. Xueba always has a framework for doing questions. Poor students have a dagger in the east and a dagger in the west. The progress is slow and there is no pattern. What is a frame? It is the baton of mathematics in the college entrance examination, and it is the most important modules in high school mathematics. Philosophically speaking, it also includes several important points and difficulties of several important modules. A "model" is actually the simplest form of graphics. It is extracted from the most basic and core knowledge points in the discipline. Its problem-solving principle is to master simple knowledge modules, and to solve various complex problems by applying these simple knowledge modules. When building and improving problem-solving models, students must collect and organize the things to be investigated. They are not random, but have rules to follow, and they form the model. The problem-solving steps of "grasp the question type, set the model, and produce the result" realize the use of limited modules to solve the ever-changing test questions, making the problem-solving from difficult to easy and complicated to simple. Specifically, it is "find the law: take three to one, build a model; use the law: draw inferences from one case,Set of models. "

4. What questions to brush, how many Questions, to what extent?

brushing questions is a method of quickly contacting a large number of questions in a short period of time, understanding the meaning of the questions and answers in the shortest time possible, and then answering them. It focuses on the number of questions rather than the quality of completion. There are usually not many original questions in the exam, but the methods and ideas are similar. When the number of questions reaches a certain level, there will be a kind of inertia to do the questions. When you see similar questions in the exam, you will be more or less in your mind. There will be some ideas and ideas (at least the brain will not be empty). Brushing questions is an effective and unavoidable review method for college entrance examination mathematics. Why do we need to brush questions? Brushing questions can make us familiar with the proposition ideas of college entrance examination mathematics, can Let us be proficient in using various formulas of mathematics, which can improve our operation speed, so our college entrance examination mathematics starts from brushing questions and ends. Brushing questions is undoubtedly effective, but we are most afraid of blind brushing. Blind brushing and having Efficient brushing is the essential difference between a scumbag and a scholar.This difference helps the learner to have more time to review English and physics courses, while the scumbag can only seek to improve his own level. In the long run, the learner will become stronger and stronger, and the more competitive advantages will be accumulated.

brushing questions, not mathematics, focusing on thinking training and question understanding,This is a long-term "self-cultivation" process. Problems evolve from basic questions. Only by fully mastering the basic knowledge can we develop ideas, use skills proficiently, make big questions and difficult problems, and open up the "grade" with other candidates. When brushing the questions, you can choose some difficult exercises according to your own mathematics scores. It is best to have analytic real questions for the middle and high school entrance examinations. point of purpose.

5. Have your own Xueba notes.

Xueba’s notes are mainly divided into three types: (class notes, wrong questions, and at least 100 standard and classic title notes)

class notes: notes are a permanent and systematic record.It is a record formed after recording knowledge points in a notebook in the process of learning knowledge. It is very important for reviewing the knowledge that has been learned, and it is very important for overcoming the limitations of memory and knowledge storage in the mind. The process of taking notes is the process of selecting and condensing information, which is conducive to exercising thinking, improving the ability to capture important information, and improving the concentration of information. processing capacity. In order to make good lecture notes, the students’ thought process must be consistent with the teacher’s thought process, and distractions that are not related to lectures must be discarded. Thoughts cannot be slipped away, and the content of the notes should pay attention to the key points, difficulties, doubts, and new ideas. The lecture notes can be used in your own words. Use key words and clue sentences, outline the territory records.

In summary, taking notes in class requires listening, seeing, thinking, and manual. On the premise of understanding, the acquired knowledge and information can be thought through the brain,After the process of "selection-processing-induction-concentration-feedback", they were recorded by hand in a focused manner. There are various methods of recording, we can gradually find out the method that suits us in learning, and finally achieve the effect of promoting our learning and improving the learning effect.

First, the collection of learning problems: it is a collection of students' learning problems, which is a collection of students' learning problems. In fact, it is to completely record the students' lost points, and the establishment of the wrong question book provides specific directions for solving problems. The second is to focus on the learning objectives: the wrong question book makes the students' learning objectives more concentrated, and the learning focus is more clear. If you catch the wrong question, you will grasp the key problem of losing points in learning. If students can focus on the wrong question book, focus on solving the problem, and solve the wrong question, the loss of points will be reduced, and the score will naturally improve. The third is to develop study habits: collecting and sorting out wrong questions is a continuous process in itself. During this process, students continuously sort out and summarize the wrong questions in their own learning. understand,On the other hand, if you persist for a long time without knowing it, you will develop a good habit of reviewing and summarizing in time. The formation of habits is an extremely important manifestation of learning ability.

Mathematics is a subject with strong logical thinking. Unlike other liberal arts, it is basically the same as other science studies, focusing on understanding. The understanding of mathematics is most important in the classroom. Each teacher may have different ways of teaching mathematics, but the knowledge points are similar. In the classroom, the understanding of the knowledge and the problem-solving methods taught by the teacher must follow the teacher's ideas, and even you have to run in front of the teacher. Come to the class, get twice the result with half the effort. If you want to learn mathematics well, you must learn a variety of methods to solve problems. Only when you practice in ordinary times, ask yourself, whether this problem is a problem and there are other better ways to solve it, learn to draw inferences from one case, and master all kinds of solutions. Question method, in the exam, you can easily use the simplest method to solve the question, at least not be exhausted. There is no one who will never encounter difficulties on the road of learning. Everyone has made mistakes, but it is not terrible to make a mistake once, but it is terrible to make the same mistake next time. The main purpose of this step is to establish the overall framework of mathematics and master the method of converting the question stem into mathematical language. During this long and tedious process, I accumulated a large number of wrong questions and recorded the wrong questions in the wrong book (at this stage, I often did not write the answer to this question in the wrong book) , so that I can have a very clear understanding of the common test sites of mathematics, and at the same time, I can also grasp the corresponding relationship between the stem text and the mathematical language. For example, in analytic geometry, I can write the corresponding mathematical Express. There are often many kinds of such correspondence,Therefore, it takes a lot of practice to quickly judge which mathematical expression can be used more easily under the given conditions. My favorite book in high school is the set of wrong math problems, which not only accumulates the problems that I often make mistakes in, but also learns from the mistakes of others. To learn mathematics, you don't need to memorize by rote, and you don't need to engage in tactics. Only by fully integrating the knowledge of mathematics textbooks and teachers into your own knowledge system, it is possible to get high scores in the mathematics test, and even get a full score in the final test.

standard notes on classic titles: follows the changing trend of the college entrance examination, captures the latest college entrance examination information from all over the country, carefully divides and filters various types of questions, and selects the most typical example questions. These sample questions are novel and practical, and can represent the hottest and most important types of examinations in the content of the college entrance examination. Effectively improve students' problem-solving ability, focus on exploring problem-solving skills, and help students see through the traps carefully designed by the propositioner, so as to achieve the purpose of teaching people how to fish. High School Mathematics Curriculum Standards (Experiment)" takes "embodies the cultural value of mathematics" as one of the basic concepts of the curriculum, and clearly points out in the teaching suggestions: "Mathematics is an important part of human culture, the product of human social progress, and the The driving force for promoting social development. In teaching, students should be guided to initially understand the interaction between mathematical science and human social development, to realize the scientific value, application value, humanistic value of mathematics, and broaden their horizons...".

　　6＝3＋3　　　　 100＝3＋97　　　　　　 1000＝3＋997

　　8＝3＋5　　　　 102＝5＋97　　　　　　 1002＝5＋997……

　　12＝5＋7　　　　104＝7＋97　　　　　　 1004＝7＋997

哥德巴赫对许多偶数进行了检验，都说明这个推断是正确的. In the future, some people have carried out a large number of checks on even numbers, starting from 6 and counting to 330 million numbers one by one, all showing that Goldbach's discovery is correct. However, natural numbers are infinite. Is this assertion correct for all natural numbers? It must be proved theoretically, and Goldbach himself could not prove it. In 1742, he wrote to Euler, a famous mathematician at the time, asking him to help prove it. Later Euler wrote back: "He thinks that the question raised by Goldbach is right, but he has no way to prove it. Because it cannot be proved, it cannot become a law, so it can only be said to be a conjecture, and people put Goldbach forward. The problem is called "Goldbach's conjecture". Since then, Goldbach's conjecture has become a world-famous problem. Some people call it "the jewel in the crown", it is like a peak in mathematics. Who can climb to the top? What about this peak? For more than 200 years, many mathematicians have tried to prove this conjecture. Chinese mathematician Chen Jingrun has made breakthroughs in the study of "Goldbach's conjecture" and is in a leading position in the world. The results of the famous paper "The table of large prime numbers is the sum of a prime number and the product of no more than two prime numbers" is called "Chen's Theorem" by the international mathematical community.

German mathematician Hilbert (Hilbert, D.) in The International Congress of Mathematicians in Paris in 1900 eloquently pointed out: "As long as a branch of science can raise a large number of questions, it is full of vitality,The lack of problems heralds the demise or end of independent development.

Just as every human endeavor pursues a definite goal, mathematical research needs its own problems. It is through the solution of these problems that the researcher trains his steely The will and strength of the people, to discover new methods and new ideas, and to reach a wider and freer realm.” The history of mathematics is the history of mathematical problem solving. Ancient mathematics, such as Egyptian papyrus, Babylonian clay tablets, and later Ancient Chinese classics, Indian and Arabic mathematics books exist in the form of problems, and the classical mathematical theory formed later is actually the logical arrangement of the results of solving mathematical problems. Contemporary American mathematician Halmos, P. R. ) said: "Problems are the heart of mathematics." Without problems, there would be no mathematics, and without problems, there would be no development of mathematics. The items collected in this column (mathematical titles and conjectures) have the following characteristics in terms of selection criteria: 1. In the history of mathematics development, especially in the establishment process of the corresponding branch of mathematics, it has had a profound impact, at least on issues that have a certain role. For example, Fermat's last theorem, Model's conjecture, Kirkman's girl problem, Greek Albert's mathematical problems, etc. 2. Problems that have certain value for future research and development of mathematics. For example, the Poincaré conjecture, the Riemann conjecture, the continuum hypothesis, etc. 3. Some popular topics in the mathematics community. For example, the 3.z+1 problem. Hungarian mathematician Erdos (Erdos, P.) said about this problem: "Mathematics has not been developed enough to solve such a problem."

Reference:

[1] Huang Xiaoyan .Core literacy-oriented teaching strategies of junior high school mathematics review course[J]. Journal of Guangxi Institute of Education,2017 (04): 168-173.

[2]Fang Chaoping Thinking First - Comprehensively Improve Learning Ability Education Science Press Isbn 978 7 5191 1636 1

[3] Wu Xiaomei's core literacy-oriented lesson preparation Tianjin Publishing and Media Group Isbn 978- 7-5309-8175-7

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