When I came to class, my wife said to me, "If students want to learn math well, they should like, appreciate and be close to math, so that students can feel happy in math learning." I hope today's lecture will bring some happiness to the students.
First, what is mathematics?
1, the great revolutionary mentor Engels said: "Mathematics is a science that studies quantitative relations and spatial forms in the real world." Engels is a mentor of the world people's revolution who is as famous as Marx, but mathematics has added infinite glory to Engels' greatness.
What is mathematics? This is a problem that mathematicians are still thinking about. Mathematicians' language is simple. Listen to voices other than mathematics:
The musician said, "Mathematics is the most harmonious note in the world."
The PE teacher said, "Mathematics is gymnastics to train people's thinking."
The botanist said, "There is no flower more beautiful than mathematics."
The aesthetician said, "Where there is mathematics, there is real beauty."
The poet said, "Without mathematical thinking, any poem is nonsense."
Listen to the philosopher again and say, "Maybe you don't have to believe in God, but you must believe in mathematics. Everything in the world is changing, and only the theory of mathematics is eternal. "
All the nationalities in the world have their own languages, some of which are used by many nationalities. On the earth, no language can unify the earth, but mathematical language has become the * * * language of all nationalities in the world.
Mathematical language is a scientific language, which enables people to express problems clearly, accurately, concisely and clearly.
3. Mathematics has had the most profound influence on modern society. People may say that the invention of computers is of epoch-making significance. In fact, students don't know that the discoverer of computer is mathematician von Neumann.
The higher level of computer application depends on mathematics. It is like this. It is so simple that it never publicizes itself and silently contributes to mankind.
But gold always shines. In modern society, people generally realize that mathematics is a kind of cultural accomplishment. Without modern mathematics, there is no modernization, and the culture without modern mathematics is doomed to decline.
In the 1980s, the President of the United States signed a decree calling on "American citizens and the whole nation to improve their mathematical literacy." Shook the world. The reason for this is that the National Bureau of Statistics of the United States found that the fundamental reason for the slow development of national science and technology in the United States in the 1980 s was insufficient attention to mathematics.
Not long ago, US President Barack Obama emphasized this law in his State of the Union address.
Now, the whole world has this understanding: "The prosperity of a country lies in education, the foundation of education lies in science and technology, and the foundation of science lies in mathematics." High-tech is essentially mathematical technology.
Mathematics has become the foundation of natural science, which is the heartfelt feeling of physicists, chemists and biologists after their success. Marx said: "Only by successfully applying mathematics can a science be perfect."
In the social and economic field, it is found that most of the winners of the Nobel Prize in Economics are mathematicians or have experience in studying mathematics. Why? It is mathematics that teaches people how to think, and it is mathematics that teaches people how to innovate. This is mathematics, a subject that has changed and promoted the world.
Second, why do you study math?
1, mathematics is very interesting, like going deep into the world of mathematics.
(1) Two children in the neighborhood are fighting for size: two children in the neighborhood just entered primary school. One day, I asked them who was older and who was younger, and they answered truthfully. I asked them who is older, 1 or 2, and they all got the correct answer. When I asked him who was older, they argued, "I am older, I am older." "I am the second child, and two are older than one, so I am older."
After a hard struggle, when I told them to study math well, they knew the answer. They left with confusion.
(2) The story of the ghost witch: In the past, in rural areas, people often told such an experience: "On an opaque night, someone walked from one village to another nearby village for a night and did not arrive. At dawn, he found himself wandering around a cemetery all night. " This is called a ghost witch in the countryside, which is a terrible thing, but after learning the knowledge of circle, you will easily know the real answer.
2. Math is very useful: Some parents tell their children that if they don't learn math well, they will be cheated in the street, which is the basic requirement of life. Another way of saying this question is: "If you learn math well, you won't be cheated, and you won't be cheated."
You don't have to worry at all. People who learn mathematics well have completely entered a high-level realm, got rid of secular concepts and pursued the nobleness and perfection of mathematics.
A few years ago, social corruption in China became a serious social problem. Although the country has taken some measures, it cannot be completely solved. It has been suggested that popularizing mathematical knowledge among cadres in party member and improving their mathematical literacy can effectively prevent corruption.
In fact, people who study mathematics pursue nobleness and perfection, and through mathematical calculation, the price of corruption is heavy.
Young people like to dress themselves up. Do you know how to dress yourself according to your figure and personality? Mathematics can tell you.
If you are as thin and tall as bean sprouts, wear striped clothes if you want to dress stronger.
If you are a little fatter and want to dress thinner, wear vertical clothes.
If you want to show your youth and liveliness, you can wear oblique corrugated clothes, which really gives people the feeling of dynamic zone.
Looking around the world, World War I was a chemical war, World War II was a physical war, and modern war was a mathematical war.
5. Hua said: "The universe is big, the particles are tiny, the speed of rockets, the sophistication of chemical industry, the change of the earth, the mystery of creatures, the complexity of daily use and so on. And there are important contributions of mathematics everywhere, and even some problems are the only way out. "
Third, how to learn high school mathematics well
1, the transition from junior high school to senior high school
After entering high school, students' grades will change greatly, and so will every student. The leaders of our school attach great importance to this. During the military training, students did a thorough examination, and before they entered high school, their scores were quite different from those in the senior high school entrance examination. The former 100 students retired to 800, and the former 1000 students entered the former 65400.
The school is actively exploring this reason. First, students passed the intense senior high school entrance examination and got the ideal No.1 middle school. Some students have the idea of relaxing, and the knowledge of junior high school is forgotten without review and consolidation.
Second, the senior high school entrance examination paper is a level test, and the score can't fully represent the intelligence level, especially the senior high school entrance examination math paper, which is very easy, and even middle school students get full marks.
After a period of high school, grade differentiation becomes prominent. Some students scored very well in the senior high school entrance examination, and their scores declined seriously. Even students and parents are puzzled: "How good is junior high school? What's the matter now? "
This phenomenon is common not only in our school, but also in middle schools all over the country, including national key middle schools.
The fundamental reason is the huge contrast between junior high school and senior high school. Let's make a comparison between junior high school and senior high school:
(1) knowledge difference:
Junior high school: the content is small, shallow, narrow and constant, and the number of questions is small and simple. You can exercise it repeatedly and even recite it to get high marks.
High school: knowledge, depth and breadth; There are many variables and problems, so there is no time to go into them.
(2) differences in teaching methods:
Junior high school: small classroom capacity, slow speech, few examples and repeated imitation.
Senior high school: the classroom is large in capacity, complex in knowledge, fast in speed, with many questions and few repetitions.
(3) Differences in learning methods:
Junior high school: poor self-study ability, teaching, passive learning and repeated practice.
High school: independent exploration, active learning and extensive knowledge acquisition.
2. Skills and methods of high school mathematics learning.
At present, what students have to solve is the technology and method of mathematics learning in senior high school. The following points deserve attention:
(1) From passively accepting knowledge to actively exploring, actively adapt to the teaching methods of senior high school math teachers. Some people say that when you can't change the environment, change yourself actively.
(2) From rote learning and imitation to a deep understanding of concepts and theories.
(3) From simple problem solving to induction and practice of mathematical thinking methods. High school mathematics is rich in mathematical ideas and methods, which is our guide to mathematics learning. What is thought, thought is thought, what is method, and method is the practice of carrying out thought. For example, if a person wants to cross the river, thinking is crossing the river, and the method is how to cross the river. ...
(4) preview before class, write down the questions you don't understand, study and discuss the written questions, and go to class with questions, so as to have a clear purpose, increase attention and improve the class effect.
(5) Take math notes, write down what is not in the textbook, the teacher's deeper understanding of the concept, the extra-curricular knowledge added and deepened for the college entrance examination, and some important conclusions.
(6) Do more math, and the effective way to learn math well is to "do math".
At the relatively elementary stage, we should do more exercises on the basis of understanding the basic contents of mathematics, including doing some difficult and enlightening topics independently.
Because we know that exercises only give conditions and conclusions, or even only conditions and questions, then the process of solving problems is actually a process of re-creation, and difficult exercises often require repeated thinking for a period of time, which can naturally cultivate innovative ability, and repeated thinking for a period of time can exercise students' persistence and cultivate your perseverance and indomitable spirit.
Ye Jianying, a strategist and thinker in China, wrote a poem to students: "You are not afraid of fortifications when you attack a city, and you are not afraid of difficulties when you attack a book. If there are obstacles in science, efforts can be passed. "
However, we should also pay attention to the fact that "good" questions contribute to a deeper understanding and mastery of the course content and thinking methods, which is a natural basic problem in learning. Questions should be thoughtful and open, not artificial biased and strange questions.
At present, most of the materials are based on economic interests, regardless of gradual progress, difficulty, bias and strangeness. This mainly caters to some students' pursuit of difficult concepts, which is not conducive to a deeper understanding of concepts.
To learn mathematics, we should understand the basic ideas of mathematics on the basis of mastering basic knowledge and skills. Mastering mathematical thinking methods and spiritual essence, we can deduce ever-changing vivid conclusions from a few formulas and theories, showing infinite power, which is precisely the constant reaction in mathematics.
3. Open channels to solve problems.
Hua, a mathematician in China, put it well: "The problem is the core of mathematics." If you don't stop, you will have a good life. Solving problems has become the basis of learning mathematics well, and it is also what students are most concerned about. How to deal with the problem, what are the methods to solve the problem (how to make the channels to solve the problem smooth).
For the problems in mathematics learning, we can set up an error correction file for the problems, which is the most precious thing for you to learn mathematics and is worth cherishing.
How to record it? First, write down the wrong questions or questions in chapters; The second is to write down the process of making mistakes; The third is to find and analyze the root of the error; The fourth is to give the correct answer. After the establishment, you can often go home and have a look, but you are not afraid of trouble. Success belongs to the persevering.
Some students, the path to solve the problem is very single, leading to a large backlog of problems, and finally formed a stubborn disease, which is difficult to solve.
To solve the problem, we must open a number of roads, so that the road to solve the problem is unimpeded. There is a drug advertisement that says well: "The general rule does not hurt, but the pain will not work."
At present, what solutions do we have?
(1) independently study or search for information, so as to deeply solve problems and cultivate and exercise the ability to learn mathematics.
(2) Ask the teacher, because the time between classes is short, the time for the teacher to answer questions is limited, but the teacher will summarize and explain things through several students' questions, and there may be your questions, so don't be shy to ask questions (for example).
In order to make it easier for students to ask questions, I have now designed a "student math question and answer paper", which students can use freely, so the ability to solve problems is greatly improved.
(3) Students help each other, which is a relatively broad avenue. Students spend a long time together, have similar thinking levels and are easy to communicate with. To make good use of this channel actively, we must establish a good relationship with our classmates and help each other.
(4) actively explore new ways to solve problems, only unexpected, not impossible. The channel is opened and the problem is solved. How can there be no progress? Achievement belongs only to you, and victory belongs only to you.
People have created mathematics, and mathematics will certainly create a new you.
Marx said: "Only when a science can successfully use mathematics can it get real development." In all previous scientific and technological revolutions, mathematics mostly played a leading and pillar role.
We can't ask decision makers to know a lot of mathematics, but at least we should always think about whether there are any mathematical problems in our work that need to be consulted by mathematicians.
Because mathematics is the resource of scientific and technological innovation, it is a universally applicable technology that empowers people.
I. World Power and Mathematical Power
Mathematical strength often affects national strength, and a world power must be a mathematical power. Mathematics is very important for the development of a country, and developed countries often regard maintaining the leading position of mathematics as their strategic demand. 17-/kloc-Britain, France, and later Germany in the 0/9th century are both European and mathematical powers. /kloc-In the 7th century, Newton invented calculus in England, and used calculus to study many problems of mechanics and celestial motion. This is a mathematical revolution, from which Britain has led the trend of mathematics.
France has a good tradition of mathematical culture and has always maintained its position as a powerful mathematical country. /kloc-In the 0/9th century, Germany and France competed fiercely in mathematics. At the beginning of the 20th century, Gottingen, Germany, became the center of mathematics in the world.
Russian mathematics rose from19th century and became one of the world's mathematical powers in the 20th century in the former Soviet Union. In particular, the Soviet Union successfully launched the first artificial earth satellite in 1958, which shocked the whole world. John, then president of the United States? Kennedy is determined to catch up with the Soviet Union in space technology. He learned that one of the reasons why the Soviet Union successfully launched satellites was that the Soviet Union was in the leading position in related mathematics fields in the world. In addition, the Soviet Union's emphasis on basic science education (including mathematics education) is also an important reason for its strong basic science research strength, so it ordered to vigorously develop mathematics.
Before World War II, the United States was just a new country, which lagged behind Europe in mathematics, but today it has become the only mathematical superpower. Before the war, the German Nazis expelled Judah, and a large number of European Jewish mathematicians were forced to immigrate to the United States, which greatly enhanced the mathematical strength of the United States and made great contributions to the United States' victory over World War II and the promotion of post-war economic strength. After the Soviet Union launched the first artificial earth satellite, the United States strengthened its investment in mathematics research and education, making the United States, which has a good foundation in applying mathematics in science and technology, industry and commerce, and military departments, quickly become a mathematical power. After the disintegration of the Soviet Union and Eastern Europe, the United States absorbed a large number of outstanding mathematicians.
Second, mathematics and its basic characteristics
Mathematics is a subject that "studies quantitative relations and spatial forms" (namely "number" and "shape"). Generally speaking, mathematics is divided into pure mathematics and applied mathematics according to the source of the problem. It is pure mathematics (also called basic mathematics) that studies the problems raised by itself (such as Goldbach conjecture); It is applied mathematics that studies mathematical problems from the real world. By establishing mathematical "model", the object of mathematical research is expanded on the basis of "number" and "shape". Various relationships, such as language, program, DNA sequencing, election and animal behavior, can all be the objects of mathematical research. Mathematics has become a formal science.
The boundary between pure mathematics and applied mathematics is sometimes not so obvious. On the one hand, because there are many objects in pure mathematics, the source comes from solving external problems (such as astronomy, mechanics, physics, etc.). ); On the other hand, in order to study mathematical problems raised from the outside world (such as molecular motion, network, dynamic system, information transmission, etc. ), sometimes we need to look at them from a more abstract and pure point of view to solve them.
The basic characteristics of mathematics are:
One is highly abstract and logical.
The second is the universality of application and the accuracy of description.
It is the language and tool of all kinds of science and technology, and the concepts, formulas and theories of mathematics have penetrated into textbooks and research documents of other disciplines. Many mathematical methods are written into software, some are sold as commodities, and some are made into chips, which are installed in hundreds of millions of computers and various advanced devices and become the core of high-tech products.
Third, the diversity and internal unity of the research objects.