Mathematics is the foundation of all sciences. It can be said that every major progress of mankind is backed by mathematics. In the first industrial revolution, man invented the steam engine. Without mathematics, there would be no advanced automobile automation production line. In the current information revolution, if there is no mathematics, how can information exchange be so fast? Mathematics is a tool discipline, which is the basis of learning other disciplines. Often breakthroughs in mathematics will lead to major breakthroughs in many other disciplines.
Mi Shan Kunsan, a Japanese mathematician and math educator, once said: After students enter the society, they rarely have the opportunity to apply what they learned in junior high school or senior high school, so mathematics as knowledge is usually forgotten within one or two years after leaving school. However, no matter what industry they are engaged in, the mathematical spirit and mathematical thinking method engraved in their minds have already played an important role in their lives and work.
Finally, what influence does mathematics have on students' thinking and development? Learning mathematics is not the content of learning mathematics, but cultivating students' thinking ability. It pays attention to ways and means, which can make students' thinking more acute. In the teaching process, we will also do the following: 1) solve problems in life and apply what we have learned; 2) Create life scenes to stimulate interest in learning; 3) Restore the essence of life and cultivate students' thinking; 4) To meet the needs of life and promote the development of disciplines. In a word, in mathematics teaching, students should experience the close connection between mathematics and daily life, and cultivate their ability to find mathematical problems from surrounding situations and solve practical problems with what they have learned, so as to cultivate their mathematical consciousness and constantly strive to improve their ability to solve practical problems comprehensively with knowledge.
Recently, I attended two extraordinary lectures at the Joint Mathematics Conference held in Atlanta, USA in June+10, 5438. The first one is Alice Silverberg, who talked about Diffie-Hellman key encryption technology. After clearly expounding the basic knowledge, she showed the new achievements she and her collaborators have made, and she provided mathematical insights on why the Diffie-Hellman method is effective and why it is sometimes not so effective. In the lecture, she took Alice in Wonderland as the theme, and took the lovely, gentle and humorous pictures of the original classic John Tenniel as an example.
Mathematics is beautiful, presentations are easy to get, entertaining and beautiful. What more can you ask for? Alice silverberg wants more, for herself, for her audience and for her community. In the last twenty minutes of the lecture, she understood what she had learned by working with cryptographers, whose needs and methods were very different from those of mathematicians. The lesson she learned from this experience is simple and profound. Listen to others and give them your full attention. Listen to your thoughts and don't think about what you will say. Don't think you can read other people's minds. Instead, ask him or her what he or she thinks. If someone makes you angry, don't respond angrily. "Curious, don't be angry," she said. "To borrow a sentence from a book published by Martin Hailmann and his wife Dorothy Hailmann) 20 16, Duffy Hailmann refers to this Hailmann."
It's easy to get conceited in this kind of lecture, but Alice silverberg's sense of humor humbled her. She didn't take these lessons as her own. On the contrary, she encourages her fellow mathematicians to welcome profound mathematical interaction, which is essentially the experience of truth, goodness and beauty meeting to influence other parts of their lives, especially their attitude towards others.
After the lecture, I thought, "Of course, this is a woman who dares to talk about how mathematics leads us to a more humane life. Female mathematicians are changing things. Let us hear the warm cheers from all walks of life! " This is my rather chauvinistic reaction-here, I don't mean male chauvinism, but female brands-and another lecture I attended, "Blown out of Water", was given by Su Zhenchang, the retired principal.
Extensive and profound, Francis Su's lecture is difficult to summarize, but let me try: mathematics can transform people's hearts and turn to compassion. Let this change be repeated in the interaction with students. A famous saying by Wei Yi formed a theme in the dialogue: "Everyone silently shed tears and read in different ways." Francis Su appealed to the audience to interpret their students' efforts in different ways-to interpret them with sympathy and encouragement.
He began his speech with a sharp letter from Christopher, a prisoner who has been studying mathematics. It tells the story of his wife's early misguided life because of drugs and crime, but it was through Alice silverberg that she was saved. Alice silverberg encouraged mathematicians to have in-depth mathematical communication. "When you think of math, who do you think of, and Christopher?" Francis Sue asked. "Everyone is crying silently and reading in different ways."
Mathematics has the ability to redeem by bringing the mind into contact with truth, goodness and beauty. However, this connection often leads to the fact that mathematics itself is not a mathematical effort, but a social and institutional structure embedded in mathematics. Mathematics students often lack a sense of belonging, which is commendable. Francis Sue described Wei Yi's own efforts in mathematics, which were reflected in the shadow of her great genius brother André Weil.
Francis Su also told the story of some students whose math homework was blocked by prejudice. In this case, a female student with a neutral name was among the best in his math class, and it was not until the third year of high school that she discovered that this impressive student was not a boy. After that, her homework performance declined, and on the basis of the fuzzy evaluation of "give more details", her performance declined again. In another case, a student who did well in a summer math course was told by her teacher at her home that she should change from a math major to an "easier" major, and finally she turned to an engineering major.
Francis Su also told the story of his growing up in a small town in southern Texas, where he was the only Asian family and he desperately wanted to be white. My share: As a white child who grew up in a black middle school, I want to be black enough to ask my parents to buy me an African wig. ) In the graduate school of Harvard University, he felt it was inappropriate because he lacked an Ivy League background. A professor even told him that he didn't belong to graduate school. When another professor contacted him and became his advisor, Francis Su was on the verge of dropping out of school. Francis Su also witnessed the cost hierarchy of Harvard undergraduates, such as two grades of honorary calculus sitting in the general calculus class. Although they have become top students in the world's top universities, calculus students with "low" honors feel unequal.
Many of us have such stories to tell. I have always been an excellent student in high school, so as a freshman, I believe I will do well in calculus class. Of course, there are hundreds of students, but I am still quite fearless. Francis Sue told the story that students' math homework was hindered by prejudice.
I often raise my hand to ask questions in this huge lecture hall. One day after class, the professor said to me, "Keep asking questions. I am very happy to receive a letter from a student who has obtained a B grade. " This prevented me from asking questions. As expected, I got a B in Cal 1A, which is my only non-A score as a math major. In many such stories, not everything about me is black and white. This professor is actually an outstanding and good teacher who cares about his students. If I have the courage to tell him the effect of the comment, he will listen.
"Everyone will cry silently and read in different ways." When Francis Su repeated this sentence many times in his speech, his insight itself seemed to be breathed by people. He painted a group portrait of the students and recorded their efforts. Francis Su called on his colleagues to discover the efforts made by each student and make it a long-term proposition. Say to your students, "I know you, and I think you have a bright future in mathematics." Be a person who looks for opportunities for them and pulls them to virtue. When they skipped class, the person who woke them up asked, "Is everything all right? What are you going through? "
This is no ordinary math lecture. The audience was absorbed from beginning to end, and stood up and applauded at the end of the lecture. Many people have tears in their eyes, and so does Francis Sue.
The lectures given by Alice Silverberg and Francis Su were held before the inauguration ceremony of the president, which was held against the background of one of the most serious racial divisions in American history, international suspicion and fear of the future. None of these speeches solved political problems or deep social disharmony. By showing how mathematics can open the mind and embrace more sympathy, understanding and humanity, Alice silverberg and Francis Su put forward a challenge: Can mathematics light up a better world?