First, understand the history of mathematics.
Since the birth of human civilization, mathematics has been closely linked with people's production and life. When teaching the understanding of large numbers in the fourth grade, I will start with the origin of numbers, not only to let students learn to understand larger numbers, but also to let students realize how concise and vivid the current method of expressing numbers is, which is formed through the accumulation of human civilization. So, I started with the way people counted in the early days of human society. At that time, people used stones instead of prey records, or used ropes that were painted and knotted on rocks to count. These seemingly simple and clumsy ways now reveal that the development of mathematics began here. Then, by enumerating various mainstream counting methods, such as China's counting, Mayan numerals, ancient Egyptian numerals and so on. Students should not only remember them but also understand them. When I saw the enthusiasm and excitement of generate in the eyes of students, I felt that mathematics could be richer and more humane. In that class, the students studied very hard, and because of this, they learned something. When faced with the current counting method and numerical sequence table, some students could not help but say, "Our current counting method is too powerful to express such a large number!"
When I was teaching measurement units, I told students about ancient measurement methods. Students realized that without a standard life, some simple things would become troublesome. I introduced the angry foot of King John of the British Empire to the students, and a foot was born. I introduced the interesting story of "Zheng people buy shoes" to my classmates. Although it is only a few words, it makes the students enjoy it.
There are many stories behind every mathematical knowledge. We should make good use of teaching materials to make the classroom more historical and make students stop thinking that mathematics is boring, boring and boring. The synchronous development of mathematics and social civilization will help students understand the history of mathematics and make them realize that knowledge will be more scientific and charming only if human beings make continuous progress.
Second, the formation of mathematical thinking
Some people think that mathematics is an abstract subject, and all kinds of digital symbols are dazzling, but they are not. Mathematics, which objectively reflects real life, has its own characteristics. Mathematics is precise, concise, direct and efficient, which is not available in other disciplines. When describing the size of an object, we will use some data of length, width and height to illustrate it. When seeing a doctor, use data to describe the body temperature and various indicators of the patient. When teaching the basic knowledge of multiplication formula in the first volume of the second grade, I started with the theme map and asked the students to talk about what they saw. The first student stood up and said, "There is a roller coaster, there is a small train ..." He only saw things, but he didn't observe them deeply. So, I called another student. When the student replied, "There is a roller coaster, a small train, and a small airplane turntable ... The small train has four sections, each with six people ..." I praised him at the right time: "Look at this classmate, he can describe what he saw with concrete figures, which is accurate, concise and really good." I didn't ask students to search for mathematical information, nor did I ask them to count it specifically, but after listening to this evaluation, students realized how concise and accurate it was to explain it with numbers. The students who answered the questions also learned this description.
I remember that when teaching the direction and position, my situation was created with military exercises. Because this part of knowledge is boring, I asked the students, "Are there any students who want to be soldiers when they grow up?" Many students raised their hands. I said, "Then you should study the following contents well, which will be of great help to realize your ideal." So I showed a video called by the military to the students. The call is basically short, with numbers as code names, data describing direction, data commanding rotation angle and hitting position, etc. I asked the students, "Why do they talk like this? What do you think will happen if they don't use the data? " The students are very active, realizing the simplicity and accuracy of mathematics, and at the same time arousing their interest in the following contents.
Our math class should not aim at solving problems for students. As teachers, we should take a long-term view. When students consciously apply mathematics knowledge to their lives through mathematics learning, and even integrate this concise and accurate way of thinking into their actions, then our mathematics teaching will be successful.
Third, have mathematical quality.
Mathematics is a rigorous subject, and we must have a serious and meticulous attitude to learn mathematics well. It requires us to observe it as a whole and be meticulous. Many teachers are troubled by the word "sloppy". It seems that there are students in any class who can do problems and calculate, but they make a few mistakes on one page, or fall behind, or even write, or forget to write answers when solving problems. In fact, this is just a phenomenon. Many teachers classify it as incorrect attitude and insufficient attention, but repeated education has little effect. Actually, it's not exactly like this. There is no correct method except that students lack patience and experience in knowledge. Many teachers just tell students not to be careless, but rarely communicate with students how to be careless. When I met such a student, I first made him realize that this is a very serious problem, and I also cited many examples of "carelessness". Then, look for reasons and methods with him, and start from a small matter, so that students have such confidence to fight against "carelessness." Cheng Xiao in my class is such a student. After some oral examination, I found him and found out the reason with him. First, I scribbled in my calculation, and I can't tell "0" from "6". Second, I forgot to advance and retreat. So I asked him to relax in time, but one thing, he should write clearly, especially when writing "0" and "6", and he should change his position next time. After nearly a month, he got rid of these two problems, not only in calculation, but also in other things. He was much calmer. I still remember his excitement when he got full marks for the first time.
When rigorous and serious thinking becomes a habit, students will not fill in "2kg" when judging the load of a car. When calculating, they will find out how much error 3 1 times 22 equals 6820. When they grow up, they will think about how appropriate the hitting angle is. This is the stable mathematical quality.
Students form rigorous and serious habits in mathematics, which will be sublimated into a quality over time, and this quality will not only bring about progress in mathematics, but also bring about rigorous and serious habits in doing other things, which is the most important "cornerstone" of students' life progress ladder.
Fourth, study mathematical aesthetics.
In fact, mathematics is a subject with temperature. It is not a dull symbol with monotonous colors, but a fresh and pleasant "other scenery".
I have heard Professor Zhang Qihua's lesson "Understanding the Circle", which is also the starting point of his teaching trilogy sublimation. His classroom language is fluent, rich and accurate. In particular, his unique understanding of mathematics makes us feel like opening another window in mathematics. What impressed me the most was the beautiful round scenery he taught for the first time, and then the dubbing. After class, a little girl said to him, "Teacher, what a beautiful circle!" " When Mr. Zhang told his teacher about it, his teacher said, "You should ask this student again, is it the beautiful scenery in those paintings or the abstract round beauty?" "This sentence caused the teacher zhang's thinking. After that, he took this course again, and his style went to the other side, with no color, no sound and no scenery. Although it is extreme, it is another interpretation of the beauty of mathematics. At that time, I was fortunate enough to listen to the class after teacher Zhang changed his style. It is still beautiful. The perfect curve makes us realize why the circle is called "the most perfect figure". The students are really intoxicated with all kinds of wonderful things in the ocean of mathematics. Continue to arrange from triangle, quadrilateral, pentagon ... Figure, who is the end point? The students all replied, "Round. "This kind of thinking that extends from a limited classroom to an infinite space makes us listeners can't help cheering for it. This is the extreme thought I learned in high school, but it is presented in these graphic images under the guidance of Teacher Zhang.
In many ways, symmetry is a beauty of balance, golden section is a beauty of life, and order arrangement is an abstract beauty. Aristotle once said: "It is wrong to insist that there is no beauty in mathematical science. The main forms of beauty are order, symmetry and clarity. " Poincare also said: "Feel the beauty of mathematics, the harmony between number and shape, and the elegance of geometry. This is the true feeling of beauty that all real mathematicians know."
Mathematics is profound and profound, accompanied by human civilization; Mathematics is concise, it records thinking with symbols; Mathematics is wonderful, it opens a window to the future for us. Mathematics is beautiful, and its beauty is better than everything we see with the naked eye ... Of course, there are many humanistic factors in mathematics, which need us to explore constantly in the mathematics class and show them to students more truly and comprehensively, so that they can fall in love with mathematics.