How to reduce the burden of mathematics?
Academician Zhang Jingzhong: A good teacher should show students the beauty of mathematical thinking, I advocate "learning more and taking less tests"
Wenhui Education 2018-05-16
Morning Mist / Repost
Author Zhang Jingzhong
▲Academician Zhang Jingzhong
Do interesting things, do things you are willing to do, and you will be happy to do them; do boring things, things that you have to do and don't want to do. It's painful to do. But it's fun or boring and varies from person to person, drinking, playing chess, playing football, and learning math.
The joy of learning mathematics is similar to playing chess, the joy of thinking, the joy of challenge. In fact, mathematics can give us more.
For example, the sense of shock. With the deepening of mathematical understanding. You will find that there are still such wonderful laws in the world. Albert Einstein once recalled that when he learned in middle school geometry that "the three high lines of the triangle must intersect at one point", he was greatly shocked, and he felt that there must be more such "mysteries" in the world that had not yet been discovered, which had a decisive impact on his life. Laid the foundation for his determination to engage in scientific research.
For example, a sense of power. There used to be a lot of hard-to-do problems, and after mastering a way of thinking, every step forward, there will be thousands of problems solved. At this time, people will suddenly become aware of their own power, and this growth of power is often obtained in a few hours or a day. People who have been overwhelmed by four application problems will feel the power of mathematics once they learn the application of column equations to solve the problems. When Leibniz talked about the calculus method, he said that many problems that were puzzled by the learned in the past could be easily solved by an ordinary person who mastered this method, and this is the power of mathematics.
For example, a sense of liberation. At the beginning of learning mathematics, you will feel bound by a lot of "pure rules", but as you learn more, they are broken one by one. At first, you can only subtract 3 from 5, and then 3 can also subtract 5; at first only numbers can be added, and later letters can be added, symbols can also be added... The deeper the study, the more I feel this sense of freedom and liberation.
There is also the beauty of science, including the beauty of graphics, the beauty of law, and the beauty of harmony.
▲ The Beauty of Mathematics: Mathematical Fractal Geometry
"How was the fire discovered?" Some people say that it is the need for heating, some people say that it is to open up the land, and some people say that it is because primitive people are attracted by the beating of flames and decide to continue the fire. Of course, this is just a beautiful story, but people who study mathematics will indeed dream of mathematics. A philosopher once said that mathematics is all about searching for beautiful laws behind seemingly simple things. A right triangle seems to be very clear at a glance, but after exploration, it is found that there is a Pythagorean theorem hidden inside. Mathematicians can not only discover these interesting and useful mysteries, but also be able to argue, and can make you believe without doubt. And these treasures, which have been painstakingly excavated by our predecessors over thousands of years, can often be learned and easily appreciated in the time of one lesson. Exhilaration?
Good teaching materials, good reading materials, and good teachers should show students the beauty of mathematical thinking and guide students to experience the sense of shock, power, liberation and the beauty of science.
When Euclid was teaching geometry, a student asked, what benefits would it be to study geometry? Euclid immediately ordered the servant to take a few small sums of money and send him away. For Euclid believed that the purpose of learning geometry was to improve the mind and bring people closer to the truth, not to gain real profit. If the purpose of students' learning is only to advance to higher education, then the fun of learning will naturally be greatly reduced, and there will be a feeling of compulsion in learning, which will be painful.
Now everyone says that we should reduce the burden on students and advocate that the content of the textbook is simple. Advocate less reasoning in geometry and the abolition of the Olympiad training course. In fact, this is all a way to cure headaches and foot pain. Students are not afraid to learn more, but they are afraid of taking more exams. If you just make the textbooks simple, but the exams are still difficult, then students will not really "reduce the burden".
I advocate "learning more and taking less tests": the textbook may wish to be a little deeper, because if the depth of learning is not enough, it is difficult for students to appreciate the fun of mathematics; and the test is simpler. Children can find the joy of math in ease.
Why can't exams be simple now? Why do parents force their children to go to Olympiad classes? The root cause is the fierce competition for entrance examinations. Why is there so much competition for entrance exams? Because the distribution of educational resources is not balanced. Everyone wants to go to a good school. Our exams always want to divide a small number of high-scoring students, so that some good schools can catch the high-scoring students. This raises the question: is a good school with a high level of student enrollment or a high quality of teaching? If the test questions are easier, they are basically exercises in the textbook, and the burden on students is naturally lighter. At this time, there will be a large number of candidates with full scores, which is conducive to the balance of student distribution, which is good for improving the level of backward schools and exercising the ability of teachers in famous schools. Besides, the concentration of high-scoring top students together may not be conducive to becoming talents, a handful of beans spread in the field will grow into a bean seedling, put in a bowl, even if there is water and fertilizer, it is only a bowl of bean sprouts. Without thinking about it from a deep level, the textbook is simple, the teacher will give remedial work, the school's Olympiad class will be canceled, there will be someone in the society to tutor, and there will be a supplier if there is a demand.
In addition, the study of geometry should be strengthened in the curriculum of primary and junior high schools, rather than light geometry and heavy mathematical operations as it is now. The United States is the country that spends the most effort on math education, but even Americans themselves admit that their math education has achieved little success.
I think one of the big reasons is that they started in the 1960s. The geometry is cut out too much in the textbook. Graphics are not boring, they are easy to understand. When learning mathematics at the beginning, children may not yet understand many of the wonderful features of mathematics, so they should be attracted by the movement of the figures. As the learning progresses, gradually guide the child to solve geometric problems by algebra, operation, and even calculus.
Similarly, teachers can play a vital role in developing children's interest in mathematics. I think the worst kind of teaching is for students to do dozens of similar problems after learning a formula. The reform of mathematics teaching should not only focus on what to say, what not to say, what to talk about first, what to talk about later, teachers should make efforts to study whether there is a different and better way of expression outside the textbook. Not only teach students to count, but also teach students to think. Olympiad always let the players do three problems in four and a half hours, which is to promote deep thinking, so some players later became excellent mathematicians.
This article is reproduced from "Modern and Classic" (ID: xdyjd2015)
Source: 2018-05-16 Wenhui Education WeChat public account
ID：wenhuieducation