Only when highly abstract mathematics is combined with other subjects can it be vivid, concrete and vivid, and students will enjoy and love learning. Mathematical culture can be applied by combining mathematics with English, literature, natural science, society, fine arts, physical education and other disciplines. For example, famous teachers such as academic leaders and teaching rookies can be invited to give lectures on mathematical culture, so as to cultivate students' culture and let students know "mathematical culture" unconsciously. For example, a famous teacher infiltrated mathematical culture in the teaching of Tang poetry;
When appreciating Tang poetry, we often find many sentences containing numbers. These simple figures, as far as they are concerned, are neither vivid nor lyrical, but they can create various wonderful artistic realms and express endless fun through the subtle brushwork of the poet. Clever use includes the combination of numbers, the comparison of numbers, the finishing touch with numbers and the collocation of numbers. For example, the collocation of numbers-"two orioles sing green willows, and a row of egrets go up to the sky." Outside the window is the autumn snow in Xiling, and the Wu Dong Wan Li boat is parked at the door. "This is Du Fu's impromptu poem Jueju." Two "birds" sing in pairs on the new green willow branches, presenting a pleasant scene. "A Line" describes the natural and beautiful flying posture of the egret against the background of "blue sky". "Qian Qiu" said the snow scene for a long time. " Wan Li said that the space of the ship scene is wide, which gives readers endless associations. This poem has a beautiful and harmonious artistic conception. There are countless examples of using numbers in Tang poetry. This alone can explain how amazing the aesthetic taste of numbers written by poets is. ...
2. Implement mathematical aesthetics education.
Aesthetic education in mathematics teaching has the following four levels: beauty, beauty, wonder and completeness. Aesthetics means that mathematical objects are symmetrical, harmonious and concise in form, which brings beauty and beautiful feelings to people's senses, for example, (a+b) × n = a× n+b× n. However, the aesthetic representation is not necessarily true and correct. Many things in mathematics, only by recognizing its correctness can we feel its "beauty". For example, the beauty of "logarithm" is that it can change the complicated operation of "multiplication and division" into "addition and subtraction" and understand its function, so as to obtain the satisfaction of "beauty". Wonderful feelings often come from "unexpected" but "reasonable" things. For example, students draw their own pictures and find that the three high lines, three middle lines and three bisectors of a triangle intersect at one point, which is really "wonderful". Mathematics is always perfect and perfect, which is also the highest "quality" and the highest spiritual "realm" of mathematics-perfection. For example, to solve an equation, we should not only answer whether there is a solution, but also find a solution, but also prove that it does exist, know how many solutions there are, and finally find out one by one, and none of them can be less. Aesthetic education for students can cultivate sentiment, cultivate mathematical culture and make students develop in an all-round way.
3. Conduct math experiments and games.
Traditional mathematics teaching is often demonstrated by strict logical reasoning, so experiments are excluded. However, many mathematical discoveries actually come from experiments, and experiments can also be used to test conjectures. Therefore, it is very beneficial for students to taste mathematics, experience thinking process and mathematical thought by introducing experiments into mathematics teaching. In fact, experimental operation is one of the important ways to infiltrate students' mathematical culture. We should carefully design mathematics experiments and guide students to participate in the process of mathematics learning. The experimental materials are provided in the reading material "The Crown Mystery and the Law of Buoyancy" in the second volume of the compulsory education standard experimental textbook "Mathematics" of Zhejiang Education Press. I arranged for students to calculate the mass ratio of the two metals in the nickel-plated steel core of 1 yuan coin released on June 6, 2000 and the copper-plated alloy of pentagonal coin released on June 6, 2002 through the knowledge of buoyancy law and fraction, so that students could be divided into groups, design experimental schemes and collect them after class. Then exchange the experimental results in class, which not only cultivates students' research spirit, but also enhances students' practical ability and interpersonal coordination ability. Students also use RMB to learn cultural knowledge about mathematics, which is very beneficial.
Mathematical game is a popular intellectual activity, which embodies a mathematical culture. Some game materials are introduced into the new mathematics textbook of Zhejiang Education Publishing House, which provides a broad innovation space for front-line teachers' teaching. However, the theme of the game is still a bit monotonous, and some educational games, such as Sudoku, can be appropriately added to the teaching.
Sudoku is a mathematical puzzle game that originated in Switzerland, developed in the United States and developed in Japan at the end of 18, and was fully introduced to China in 2005. A puzzle is a square with nine squares (that is, three squares wide by three squares high), and each square is subdivided into nine squares. Fill in the numbers of 1 to 9 in each small nine-square grid, so that the numbers in each column and row of the whole big nine-square grid are not repeated. The game seems to be similar to the traditional crossword puzzle, but it is widely accepted by players because of its advantages of simple input, convenient calculation, beneficial to mental exercise, and no limitation of time, place and language. Some experts believe that the unique gameplay of the game transcends the boundaries between words and culture. It is reported that Sudoku has millions of players around the world.
This subtle game teaching of "sneaking into the night with the wind and moistening things silently" can make students gradually realize the rare charm of mathematical culture, gradually develop the habit of being diligent in thinking and good at analysis, and learn to analyze and solve problems from the perspective of mathematical culture.
4. Students write weekly math diary.
As the innovation of students' math homework, I ask students to write a math weekly diary. Mathematics weekly diary is a kind of written record for students. I assign students to write an article every week, including students' understanding and problem solving of concepts, students' problems, students' emotions, students' personal exercises, especially the biography of mathematicians and the history of mathematics.
There is an interesting Kjellbing carpet (as shown below) in the first volume of the compulsory education standard experimental textbook of Zhejiang Education Press: first, make a regular triangle, dig out a "central triangle" (that is, the triangle with the midpoint of each side of the original triangle as the vertex), and then dig out another "central triangle" in the remaining small triangle. We use a black triangle to represent the excavated area. If the above method continues indefinitely, the area of Scherbinsky triangle approaches zero and the perimeter approaches infinity. I asked the students to talk about their opinions in the weekly math diary after solving the problem, and asked them to write an article "Enlightenment from it". After nearly two years of similar practice, I found that math weekly diary is an effective communication tool, which can help students think carefully and develop their creativity and freedom. It can enhance students' understanding and application ability of mathematical culture and develop their expression ability; It can also help teachers to effectively understand students' mathematics learning situation.