1. The significance of mathematical culture
Cultural objects in Ci Hai refer to the sum of material wealth and spiritual wealth created by human beings in social and historical practice. Culture embodies a certain value orientation of society and invisibly regulates people's behavior. Regarding the definition of culture, no matter what the academic opinions are, in the final analysis, the cultural form created by human beings is truly mature only if it is completely dissolved in people's lives. Mathematics is a science that studies the relationship between spatial form and quantity. Its content, ideas, methods and language have become an important part of culture. Mathematical concepts such as reasoning consciousness, classification consciousness, holistic consciousness, abstract consciousness and mathematical aesthetic consciousness also play a role in the spiritual field, which contains profound humanistic spirit and special cultural connotation.
2. Mathematics and cultural quality
Mathematics makes people implicit, and the scientific thinking quality formed by mathematics will play an important role in future study and work. Newton and Einstein, two great scientists, can make great contributions, which is inseparable from their superb mathematical knowledge and superb mathematical quality. Plato once posted a list at the gate of his philosophy school, stating that people who don't know geometry are not allowed to enter his philosophy school. The courses he studied at school have little to do with geometry knowledge. Plato asked his disciples to be familiar with geometry only because mathematical spirit and mathematical thought are important cultural qualities. The scientific quality of mathematical thinking and mathematical formation reflects the rich connotation of mathematical culture.
3. Mathematics and humanistic spirit
Mathematics plays a more prominent role in improving people's psychological quality than other disciplines. The strict standardization of mathematics plays a subtle role in forming a good style of being serious, practical, meticulous, United and cooperative, and obeying the law. Use the beauty of mathematics, graphics, symbols and strangeness to educate students' spiritual beauty, behavioral beauty, linguistic beauty and scientific beauty. Make students learn to study and solve problems calmly and rigorously, and form the consciousness of independent innovation. Understanding dialectical materialism and historical materialism from the perspective of mathematical development history. Let students learn from scientists' scientific dedication in the process of accepting their outstanding contributions in the field of science, which is conducive to strengthening their ideals and beliefs of learning and loving science and cultivating perseverance. Speaking of scientific dedication, we might as well mention sophie germain, a French female mathematician in the18th century. In order to learn math, she disguised herself as a man. Because of her hard work, she won the favor of Lagrange, a math teacher at that time, and was allowed to study mathematics from then on. It is because he loves mathematics and studies hard that she achieved excellent results in proving Fermat's last theorem for the first time.
4. History and culture of mathematics
The development history of mathematics is a cultural history, full of touching stories and interesting legends. The current full-time ordinary high school textbook (compulsory for trial revision), mathematics, has absorbed the history of mathematics. For example, the first book introduces the touching legends about chess in ancient India, which not only enhances students' interest in learning, but also gives them a preliminary impression on the summation of series. Speaking of equations, we might as well introduce the epitaph of Diophantine (3rd century A.D.): What is the annual geometry of Diophantine? How amazing it is that Diophantine is buried in the grave. Truly recorded the road he experienced. God gave one sixth of childhood, one twelfth of childhood and one seventh of childhood to light the wedding candle. Five years later, the poor late-born Ning Xiner, half the age of her father, walked into the cold grave. Sadness can only be made up by arithmetic research. After another four years, he completed the journey of life. This topic with both mathematical legends and poems will certainly enhance students' interest in learning mathematics and stimulate their enthusiasm for learning mathematics.
5. Mathematical Poetry and Culture
No matter in history or now, at home or abroad, there are poems and songs everywhere to publicize mathematics. They praised mathematics in this form and also conveyed a mathematical culture. /kloc-in the 0/7th century, the Englishman Apope talked about A.pe moivre. Who designed the parallel lines of spiders and determined that there were no rules and lines like DemoIVE? A few words not only praised the mathematician Modi Buddha, but also promoted the spirit of mathematics. Qian Baoyu's comments on China's ancient number tones have a long history of legislation and arithmetic. People in the field have made great achievements throughout the ages, and they all work hard to save time. Fractions are the same as those of mother and son, and the power product is shifted and supplemented, so you should study it carefully after paying attention. Make the past serve the present, why not cherish thousands of pieces of paper! Pi, slim and reasonable. If there is a heavy difference, it is not difficult to measure the island. Who is Liu Hui's private school? It is said that the father and son of ancestral home have the most brilliant achievements. People who carry forward the past and forge ahead into the future are immortal! It can be seen that the glory of ancient mathematics is expressed by poetry, which is not only a compliment to China's ancient mathematicians and their research achievements, but also shows that timeless mathematics is an important part of China's splendid culture. The famous mathematician Hua elaborated on the combination of numbers and shapes in detail. "Number and shape are interdependent, how can they be split in two? There is little intuition when numbers are missing, and it is difficult to be nuanced when shapes are few. The combination of shapes and numbers is good in all aspects. Don't forget that everything is separated, geometric algebra is unified, always connected and never separated. " This appropriate description also fully embodies the cultural awareness, that is, vivid and profound, concise, so that mathematics and culture are integrated, giving full play to the role of mathematical culture. It can be seen that this kind of mathematical poetry has pushed the cultural level of mathematics to a higher level.
6. Mathematical Language and Culture
Basic knowledge of mathematics, mathematical thinking method and mathematical comprehensive ability are the most essential elements of mathematical quality education and the central content of classroom teaching. Teachers' cultural accomplishment, that is, the inside information of mathematics culture, directly affects the effect of mathematics classroom teaching. If the language is rich and beautiful in the teaching of mathematical concepts and propositions, it will greatly infect students and improve the quality of lectures. In the process of concept formation and theorem formula reasoning, it will be very effective to explain it in simple terms and vividly. In the process of the formation, development and problem solving of mathematical knowledge, humorous language is always accompanied, which will certainly adjust the classroom atmosphere and stimulate students' interest in learning. Teachers should be detailed and concise when giving lectures, so that students can have enough time to master mathematical knowledge and form a good mathematical cognitive structure. Happy teaching and happy and relaxed study are conducive to the healthy development of students' body and mind and improve their quality of life.
7. Mathematical Symbol Language and Culture
Besides words, mathematical symbols and figures are also a language of mathematics. As a special language, it has its representative significance and rich connotation. This language is vivid, concise and lively, and can convey the beauty of mathematics to people. As a culture that can be widely communicated, the translation and application of mathematical language is very important. If the language function is impaired, that is, there is no language foundation, it is impossible to communicate at all. Of course, when encountering specific problems, you may often be at a loss. For example, 200 1 national college entrance examination science 20 questions: I, m and n are known as positive integers, 1
8. Mathematical thoughts, methods and culture
Mathematics thoughts and methods have high cultural and educational functions. If you can only solve a few problems, then you don't know math at all. Only by mastering the ideas and methods of mathematics can we really learn mathematics well. With the concept of mathematical culture, we can better grasp the mathematical thinking. Once the mathematical thinking method is mastered, it can in turn promote the improvement of mathematical culture level, so strengthening the teaching of mathematical thinking method also reflects the cultural consciousness of mathematics. Mathematical thought is the basic viewpoint of mathematics and the most essential and advanced part of mathematical knowledge. It plays a leading role and is the guiding principle for analyzing and solving problems. Common mathematical ideas include: reduction, function and equation, symbol, combination of numbers and shapes, set and correspondence, classification and discussion, movement and change, etc. Mathematical thinking method is the embodiment of mathematical thinking and a tool to solve problems, such as matching method, undetermined coefficient method, decomposition and synthesis method, mapping inversion method such as method of substitution, symmetry method, discriminant method and expansion method. Through the training of a large number of questions, these methods can only be done very skillfully within a fixed framework. Once you encounter some practical problems, you may not get to the point, and you don't know how to use various methods. If we can sublimate from the perspective of culture, we can understand it to a higher degree, and then let all kinds of mathematical thinking methods play a greater role.
9. Teaching methods and culture
Mathematics teaching methods can also reflect a culture. Teaching is a cognitive process of human beings, and teaching is a bilateral unified activity composed of student-centered learning and teacher-led teaching. With the renewal of teaching ideas and the gradual understanding of mathematical culture, people reflect on classroom teaching methods from the perspective of multiculturalism, and more and more feel that educators are not only teaching the educated knowledge, but also cultivating a high-quality person. Therefore, various teaching methods came into being, among which discovery method, inquiry method and guided discovery method are mainly characterized by cultivating exploration and innovation ability and paying attention to the improvement of people's quality. In terms of education and teaching, it has also created a variety of educational models such as "happy education", "successful education", "harmonious education", "goal education" and "I can educate". These educations have jumped out of the category of pure subject knowledge education, that is, what they study and pursue is the education of cultivating people's quality, which has actually become a cultural phenomenon of education. For example, there is a problem of "chickens and rabbits in the same cage" in elementary school arithmetic, that is, how many chickens and rabbits are kept in a cage, and a * * * has 35 heads and 94 feet. How many chickens and rabbits do you want? Some teachers talk about the golden rooster independence method, which makes both chickens and rabbits become one foot. At this time, the number of rabbits is 47 feet MINUS the number of heads 35. It is difficult for primary school students to understand this solution. How does a good chicken become a foot? This teaching method is beyond students' cognitive scope and existing cultural level. However, some teachers can enlighten and induce students according to their age characteristics and discuss with them like telling stories. Originally, they were going to guide students to turn rabbits into two legs and inspire them to say, do students know how many legs a chicken and a rabbit have? Of course, the students will answer, students, the chicken has two legs and the rabbit has four legs. Is this reasonable? It is unreasonable for students to speak loudly. Then let's find a way to make rabbits have two legs, shall we? The teacher tried to guide the students to think about their own ideas, let the rabbit sit up or bring something to the rabbit. But some students immediately suggested that chickens have wings, and the teacher immediately had a brainwave according to the students' ideas. Very good. If a chicken has two wings, of course it's fair. A chicken and a rabbit each have four legs. How many legs does a 35-head have? Students can naturally calculate 140. If you subtract 94, the number of extra wings is 46. A chicken with two wings can easily calculate that there are 23 chickens, 12 rabbits. This kind of education is not to impose the adult concept designed by teachers on primary school students, but to respect their thinking habits, give full play to their whimsy and skillfully solve problems that many students find difficult. It can be said that this is a quality education and a kind of cultural education.
Science, technology and culture
When computers and networks enter the mathematics classroom, it will inevitably add more cultural atmosphere to the mathematics classroom and make the color of mathematics culture more intense. The mathematical knowledge displayed by multimedia courseware is dynamic, illustrated, vivid and vivid, which can give people a sense of beauty. The network makes resources available, which can greatly enrich mathematical knowledge, widely absorb knowledge and information, and is conducive to enriching the connotation of mathematical culture, thus improving mathematical cultural literacy.
It has a long history, a long history of mathematics, an ancient culture, the origin of mathematics, and the civilization and development of human beings are inseparable from mathematics. In the new century and new economic era, the importance of mathematics in science and technology and human social life is increasing day by day, with more and more application fields and richer cultural connotations.