Sun Xiaoli, a professor in Peking University, was the earliest scholar in China who paid attention to mathematical culture. The book Mathematics and Culture, co-edited by her and Deng Donghao, collected the relevant expositions of some famous mathematicians and recorded the thinking on mathematical culture from the perspective of dialectics of nature. Mathematics and Culture, published later by Qi, mainly expounds the cultural value of mathematics from the history of non-Euclidean geometry, especially points out the cultural significance of mathematical thinking. Zheng Yuxin's monograph "Mathematical Culturology" and so on. It is characterized by emphasizing the cultural effect produced by "mathematical isomorphism" with social constructivism philosophy.
The above works and many papers try to liberate mathematics from the circle of pure logical deduction and reasoning, focusing on the analysis of the history of mathematical civilization, fully revealing the cultural connotation of mathematics and affirming the value of mathematics as a cultural existence.
After entering the 2 1 century, the study of mathematical culture has deepened. An important symbol is that mathematics culture has entered the classroom of primary and secondary schools and penetrated into the actual mathematics teaching, so as to make students really be infected by culture in the process of learning mathematics, produce a cultural upsurge, experience the cultural taste of mathematics and observe the interaction between social culture and mathematics culture.
Then, how to carry out mathematical culture education in mathematics teaching in primary and secondary schools? The author thinks that we should understand and implement it from the following aspects.
Every nation has its own culture, so there must be mathematics belonging to this culture. Mathematics in ancient Greece and traditional mathematics in China have brilliant achievements and excellent traditions. However, there are obvious differences between them. Different political civilizations in ancient Greece and ancient China gave birth to different mathematics.
Ancient Greece was a slave country. At that time, Athens, Greece practiced slave-owner democracy (the majority of slaves did not enjoy this democracy). Male slave owners always elect consuls and vote democratically on some war and financial events. This political civilization contains some reasonable factors. When slave owners talk about democracy, they often need to convince each other with reasons, which makes the academic debate very strong. In order to prove that you are sticking to the truth, you need to prove it. First set some "axioms" that everyone agrees with and specify the meanings of some nouns, and then call the proposition to be stated the logical reasoning of axioms. Euclid's Elements of Geometry came into being under this background.
During the Spring and Autumn Period and the Warring States Period, China also had an academic atmosphere in which a hundred schools of thought contended, but it did not practice democratic politics among the rulers of ancient Greece, but practiced the system of king rule. The Spring and Autumn Period and the Warring States Period were also the golden age for intellectuals to express their opinions freely. Thinkers and mathematicians at that time, the main goal was to help the king rule his subjects and manage the country. Therefore, most of the ancient mathematics in China appeared in the form of "management mathematics", aiming at the practical goals of national management, such as measuring fields, building water conservancy projects, distributing labor, calculating taxes and transporting grain. Rational discussion takes a back seat here. Therefore, from the cultural point of view, China mathematics can be said to be "management mathematics" and "carpenter mathematics", and its existence form is official documents.
The cultural fashion in ancient Greece is to pursue spiritual enjoyment and gain an understanding of nature as the highest goal. Therefore, the proposition of "equal vertex angles" is included in the Elements of Geometry as a proposition 15, which is proved by axiom 3 (equal amount MINUS equal amount, equal difference). In China's mathematical culture, it is impossible to leave a place for such an intuitive proposition.
Similarly, China Mathematics emphasizes practical management mathematics, but it has made great progress in algorithm. The application of negative numbers, the root method of solving equations, Yang Hui's triangle (Jia Xian's), Zu Chongzhi's calculation of pi, the art of heaven and other exquisite calculation topics can only be born in China, but they are despised by ancient Greek civilization.
We should pay full attention to the practicality and algorithm tradition in China's traditional mathematics, and at the same time, we should absorb all the beneficial mathematical cultural creations of human beings, including the cultural traditions of ancient Greece. When we enter the 2 1 century, as the villagers of the global village, we must integrate into the world mathematical culture and organically combine the nationality with the world.