Learning mathematics, the introduction of abstraction is a hurdle for many students. What is abstraction? Many students who learn mathematics well in primary and secondary schools are easy to fall behind when they study in high school. One of the reasons for backwardness is that the problem-solving in senior high school is much wider, and another important reason is that the research methods of abstract problems have not been learned or adapted. In senior three, we introduced the abstract concept of function for the first time. We also studied functions, linear functions, quadratic functions and inverse proportional functions in junior high school. At this time, we studied their definitions, images, parameters and so on, all of which were very specific. They are nothing more than drawing pictures to find equations, which is very simple, that is, the problem of calculation. In high school, we made a 180 degree turn to the definition of function. In high school, we introduced the concept of mapping, such as one-to-one correspondence between things and pairs. A function can be regarded as the relationship between two groups of non-empty numbers. Then give you a function f(x), but don't give you the type, just give you its domain, find the domain of f(x- 1) and so on. Many students don't understand it here, but they accumulate more and more. The more they learn, the more they can't learn.
As a high school math teacher, I always think that abstract function learning is the first threshold of high school learning. After this hurdle, mathematics is rarely bad. On the contrary, after this hurdle, mathematics has become more and more interesting and devoted.
In fact, the reason why high school mathematics is abstract is mainly for functions. I hope the above can help you.
Ha ha! You have a lot of questions! Words are abstract! What is abstraction: things are informatized, and the only image of things is obtained based on informationization. This process and this conscious behavior of human beings are abstract.
"Pumping" means sampling from the site. This sampling can be random or conditional. According to fatalism, it is unique. . .
"Elephant", the image here, should be the "phase" in ideology, which can be grasped without specific shape consciousness, but people have formed this intuitive combination, using elephants.