In the eyes of many people, mathematical work means that mathematicians have their own ideas, which have been confirmed through some efforts. This is a science of individual combat. In this forum, both mathematicians and front-line teachers unanimously denied this view.
Academician Ding, a famous mathematician, expressed his views. When he was in middle school, the teacher taught him the method of square root. He was not satisfied, so he simply followed this method and found out the method of square root. ? Don't wait for the teacher to ask questions, we can ask ourselves questions in our daily study. ? He said.
Academician Zhang Jingzhong had the same experience. In 1950s, he studied in Peking University. A class is divided into several groups and there are often various discussions. During the discussion, various viewpoints collided, and inadvertently generate showed a spark of wisdom.
In the process of learning mathematics, we often encounter such a situation: we think clearly about some problems, but we can't say clearly. Academician Zhang said that if an American student wants to take any course, the professor will advise him to apply for teaching this course. ? You can explain it clearly to others, and you will understand it yourself. ?
In the 1950s, the examination in the Department of Mathematics of Peking University was an oral examination, which was quite similar to the suggestion of American professors. Academician Zhang Jingzhong recalled that the teacher would prepare many questions for students to draw lots, and each student had 45 minutes to prepare. Students explain the topic clearly on the blackboard, and the audience is the teacher and the judges.
Zhou Peigeng, a special teacher of Beijing Institute of Educational Sciences, agreed with the two academicians' teaching methods. ? There are two levels in learning mathematics: the first level is to understand what others say, and the second level is to understand what others say. ?
Enlightenment can make a math lover go up a storey still higher and learn the fun of independent thinking.
Teacher Zhou Peigeng once taught such a female student, and her grade in the second grade was average. That summer vacation, she carefully read a math book. As a result, soon after school started, she won the prize in the city competition. Thanks to such efforts, she won a gold medal in an international competition.
The female classmate summed up her experience and said, I'm not smart. Sometimes others can understand the teacher's class, but I can't. But I have to find out for myself and try not to ask anyone. I don't read many books, but as long as I do, I must understand them. ?
Jong Li, a professor of Peking University and chairman of the Beijing Mathematical Society, agrees with this female student's practice: learn to think independently, don't ask others how to do the problem easily, and try to enjoy the pleasure of getting the answer. ?
Professor Jong Li once asked a foreign mathematician what was the secret of his success. The mathematician replied? Patience.