This is exactly the problem. Admitting that something is cultural does not mean that it will show its cultural attributes in all contexts. For example, "fish" is very nutritious, but poor cooking methods will not only destroy its inherent nutritional value, but may even make it completely lose its nutrition and become unhealthy food.
This is true for cooking fish, but isn't it also true for teaching mathematics? In fact, it is not difficult to find that we have decided that "mathematics is a kind of culture" and the object of thinking is mathematics in the "scientific category", that is to say, we are only discussing the objective mathematical science in the general sense and in the "academic form". At this time, mathematics is not only "the crystallization of human creative activities", but also "has an important influence on people's behavior, ideas, attitudes and spirits." , it has been characterized as a broad and narrow sense of culture. However, when mathematics enters the school field of vision and classroom category, it is bound to undergo a transformation from "scientific mathematics" to "school mathematics" and then to "classroom mathematics". Whether the original cultural attributes of mathematics have been dispelled in the process of transformation is precisely the topic that we should pay attention to when discussing mathematics culture in depth.
Reality is not optimistic. On the other hand, in the current mathematics classroom, due to the excessive pursuit of instrumental values such as knowledge and skills, the original rich meaning of mathematics has been increasingly replaced by monotonous and boring mathematical symbols, which has almost become the whole of mathematics, making the cultural temperament that mathematics should have been stripped off a little, so that mathematics belonging to the cultural category is gradually losing its cultural essence. It is in this sense that reaffirming "mathematical culture" and calling for "returning mathematics to its true colors" has become an urgent problem in mathematical practice.
There are many reasons for the disintegration of mathematics culture, but the deviation of teaching action caused by teachers' different cognition and understanding of mathematics is one of the important reasons. Imagine that if teachers only agree that mathematics is a technology in the classroom, then acquisition, imitation, practice and proficiency will inevitably become a strong language in the mathematics classroom. Living in such a mathematics classroom, how can students get in touch with and appreciate the open, rich, beautiful and even fascinating side of mathematics? From another point of view, in our classroom, if mathematics is no longer just a simple combination of numbers, symbols, formulas, rules and procedures, through them, we can feel the rich methods, profound thoughts, noble spirit and character of mathematics, appreciate the colorful development process of mathematics, and share the creation and transcendence in the footsteps of mathematics, as well as the human wisdom and light reflected behind it. What will' mathematics' be like at this time?
In this way, culture can be dissolved in the classroom, but also can be regained in the classroom. The difference between the two lies in the switching of perspectives. Therefore, I have always insisted that culture should be the perspective and posture that mathematics classes should choose. Only in this way, it is possible to show its cultural nature in mathematics classroom.
In the process of practice and exploration, misunderstanding of concepts or propositions is nothing new, and mathematical culture has not been spared. How to be misread and why to be misread deserve our consideration.
The first is the narrowing of the concept. The simplicity of mathematical culture is equated with the history of mathematics, and it is thought that the infiltration of mathematical history is a course reflecting mathematical culture. It should be said that the history of mathematics is an important part of mathematical culture, but mathematical culture is far from being inclusive and covered by the history of mathematics.
The second is the generalization of concepts. Confuse mathematics culture with classroom culture. The continuous dialogue, communication and interaction between people in the classroom is undoubtedly a cultural phenomenon, which is usually called classroom culture. In fact, there is no classroom behavior that is divorced from cultural phenomena. However, the "culture" here is related to the classroom activities themselves, but has nothing to do with the mathematics content carried by the classroom. In a math classroom full of cultural phenomena, what is conveyed is not necessarily the mathematical content with rich cultural implications, which is enough to illustrate the difference between the two. Many teachers bring democratic dialogue and equal communication into the field of mathematical culture, which is obviously inappropriate and a generalization of mathematical culture, which is not conducive to our understanding of mathematical culture itself and to our accurate grasp of the true cultural value of mathematics.