Hua, a famous mathematician, said: "The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical engineering, the change of the earth, and there are many biological mysteries, and mathematics is everywhere." Especially in 2 1 century, the application of mathematics is everywhere. Then, how can we lay a good foundation in mathematics from an early age, and what kind of classroom teaching is suitable for the new generation of students? I think in class, students should start learning.
In the activity class, under the guidance of the teacher, we divide into groups, measure, piece together, cut and calculate by ourselves, explore the laws found, and master mathematical knowledge. This not only cultivates the practical ability, but also improves the thinking ability, which gives us a preliminary taste of the success of mathematicians in studying problems and doubles our interest in mathematics.
For example, when we were in the class of "Calculation of parallelogram area", the teacher asked us to divide into several groups and distribute some small pieces of paper of parallelogram, so that students could discuss with each other how to cut and paste the parallelogram into a figure with which we can calculate the area. Everyone had a heated discussion. Some students found that they could cut right-angled triangles and right-angled trapeziums along the height of parallelograms with scissors, and then put them together to become rectangles. Some students also found that two right-angled trapezoids can be cut from any height of a parallelogram and can still be spliced into rectangles of the same size. Through observation and thinking, students realize that the "length" and "width" of the spliced rectangle are the "bottom" and "height" of the original parallelogram respectively. So, everyone finally found the parallelogram area formula: S=ah. The teacher asked the students to play poker, so that everyone could quickly understand and master the calculation law of division with remainder and learn knowledge in relaxed and happy activities.
Every time I do math olympiad, I always pick up a problem to do it, because I think it will be done quickly. However, doing math olympiad today, a problem changed my view. It is not necessarily right to do it quickly, but mainly to do it right.
Today, I made a question that puzzled me. I tried to think for hours, but I couldn't figure it out. So I had to obediently look at the basic refining and let it help me analyze. The question is this: How many odd numbers are there in the square of 33333333333? The analysis is as follows: the square of 3333333333 is 33333× 33333333. Because there are too many numbers in this multiplication formula, the calculation is complicated. We can simplify it by transformation, that is, one factor is tripled and the other factor is tripled. The product remains the same. The problem turned into finding 99999999999×1111111= (65438 × 1 1 1 1 1 1 1 1 1 1= 1 1 1 1 1 1 / Kloc-0/11100000000-1111/kloc-0. In this problem, we can also multiply two numbers with fewer digits to find the odd number in the product. That is, 3×3=9→ the product has 1 odd numbers. 33×33= 1089→ There are two odd numbers in the product.
From the previous calculation, it is easy to find that the product consists of four numbers: 1, 0, 8 and 9. The number of 1 and 8 is the same, which is less than the number of 3 in a factor 1, and 0 and 9 are after 1 and 8 respectively. The number of odd numbers in a product is the same as the number of 3 in a factor. It can be deduced that the product of the original problem is:111110888889, and there are10 odd numbers in the product.
After finishing this problem, I know I can't do math and Olympics quickly. I need to know how to do it. In a word, I think it is very popular for us primary school students to have math classes in the form of activity classes. In class, every student is curious about the process of exploring knowledge and eager to find a solution to the problem through his own experimental activities. In learning, we fully realize the happiness and pride of the host who is learning. I hope teachers can take more math classes in the form of activity classes.
Fan Wener:
Mathematicization of various sciences
What exactly is mathematics? We say that mathematics is a science that studies the relationship between spatial form and quantity in the real world. It is widely used in modern life and production, and is an essential basic tool for studying and studying modern science and technology.
Like other sciences, mathematics has its past, present and future. We know its past in order to understand its present and future. The development of modern mathematics is extremely rapid. In recent 30 years, the new mathematical theory has surpassed the sum of 18 and 19 th century theories. It is estimated that it will take less than 10 years for each "doubling" of future mathematical achievements.
An obvious trend in the development of modern mathematics is that all sciences are going through the process of mathematization.
For example, physics has long been regarded as inseparable from mathematics. In colleges and universities, it is also a well-known fact that students of mathematics department should study general physics and students of physics department should study advanced mathematics.
Another example is chemistry. We should use mathematics to quantitatively study chemical reactions. We should take the concentration and temperature of the substances involved in the reaction as variables, express their changing laws with equations, and study the chemical reaction through the "stable solution" of the equations. Not only basic mathematics should be applied here, but also "frontier" and "developing" mathematics should be applied.
For example, biology should study the periodic movement of heartbeat, blood circulation and pulse. This movement can be expressed by an equation. By finding the "periodic solution" of the equation and studying the appearance and maintenance of this solution, we can grasp the above biological phenomena. This shows that biology has developed from qualitative research to quantitative research in recent years, and it also needs to apply "developing" mathematics. This has made great achievements in biology.
When it comes to demography, it is not enough just to add, subtract, multiply and divide. When we talk about population growth, we often say what the birth rate is and what the death rate is. So the birth rate minus the death rate is the annual population growth rate? No, in fact, people are constantly born, and the number of births is related to the original base. So is death. This situation is called "dynamic" in modern mathematics. It can't be simply treated by addition, subtraction, multiplication and division, but described by complex "differential equations". Study such problems, equations, data, function curves, computers, etc. Both are indispensable. Finally, it can be clear how each family can have only one child, how to have only two children, and so on.
As for water conservancy, we should consider the storm at sea, water pollution and port design. We also use equations to describe these problems, and then input the data into the computer to find out their solutions, and then compare them with the actual observation results to serve the actual situation. Very advanced mathematics is needed here.
When it comes to exams, students often think that exams are used to check students' learning quality. In fact, the examination methods (oral examination, written examination, etc. ) and the quality of the test paper itself is not the same. Modern educational statistics and educational metrology test the examination quality through quantitative indicators such as validity, difficulty, discrimination and reliability. Only qualified exams can effectively test students' learning quality.
As for literature, art and sports, mathematics is essential. We can see from CCTV's literary and art grand prix program that when an actor is graded, it is often "to remove a highest score" and then "to remove a lowest score". Then, the average score of the remaining scores is calculated as the actor's score. Statistically speaking, "the highest score" and "the lowest score" have the lowest credibility, so they are removed.
Mr. Guan, a famous mathematician in China, said: "There are various inventions in mathematics, and I think there are at least three: one is to solve classic problems, which is a great job; First, put forward new concepts, new methods and new theories. In fact, it is this kind of person who has played a greater role in history and is famous in history; Another is to apply the original theory to a brand-new field, which is a great invention from the perspective of application. " This is the third invention. "There are a hundred flowers here, and the prospects for the development of mathematics and other sciences to comprehensive science are infinitely bright."
As Mr. Hua said in May 1959, mathematics has developed by leaps and bounds in the past 100 years. It is no exaggeration to summarize the wide application of mathematics with "the vastness of the universe, the smallness of particles, the speed of rockets, the cleverness of chemical industry, the change of the earth, the mystery of biology, the complexity of daily life, etc." The greater the scope of applied mathematics, all scientific research can solve related problems with mathematics in principle. It can be asserted that there are only departments that can't apply mathematics now, and they will never find areas where mathematics can't be applied in principle.