Why is mathematics difficult to learn?
In all human disciplines, mathematics is synonymous with the peak of human rationality. At the same time, mathematics has developed from counting thousands of years ago to a huge branch of mathematics building. With the development of mathematics, many people say that they can't understand mathematics. Most primary school students can still master mathematics. Middle school may be a bit difficult, but you can learn it well with a little effort. However, even if they work hard, they may not be able to master mathematics well in college. They even strayed from the topic and missed a few classes, but they didn't understand it at all, just like listening to gobbledygook. Is math really that difficult? What is the reason for the difficulty? In order to solve everyone's doubts, let's analyze the reasons for the difficulty. 1. The abstraction of mathematics largely leads to the loss of mathematical intuition and increases the difficulty of understanding. If we refer to the development history of mathematics, we can see that mathematics has gone further and further on the abstract road. The purpose of mathematics is to study the general laws of numbers and shapes, that is, the purpose of mathematics is to establish a universal language that is not limited to the description of specific things. It is for this purpose that mathematics has been looking for a more general description framework in its development. If you want to be universal, you have to be abstract. For example, the concept of function in middle school only represents the corresponding relationship between numbers. Later, the concept of mapping was put forward. Not only numbers can correspond to numbers, but also functions can correspond to numbers, which developed the concept of functional. Finally, whether it is a number or a function, it is simply ignored. In order to describe generalized correspondence, the concept of operator is put forward. It can be seen from this that mathematical concepts have made great progress compared with the initial stage of development, and the universality has improved with abstraction. However, many concrete features are lost in the process of abstraction, which makes it difficult for us to master mathematical concepts. Abstraction is the fundamental reason why mathematics is difficult, not the calculation and skill that many people think. Not understanding the concept, not delving into the meaning of the concept, but chasing skills and calculations is completely a kind of learning that pursues the end. The final result is that learners' understanding of mathematics is in a chaotic and superficial situation, and they fall into a situation of repeated learning and forgetting. 2. How to break the obstacles brought by mathematical abstraction to our understanding of mathematics? We know that mathematical concepts do not fall from the sky, and all mathematical concepts are derived from our abstraction of the real world, which leads to mathematical concepts getting rid of the characteristics of concrete and objective things. If you build knowledge directly, you will definitely feel that the concept is puzzling, so the best way is to build a concrete model, analyze it on specific things, and then summarize it yourself to complete the process from concrete to abstract. For example, if you directly understand the concept of derivative in mathematics, you will feel vague. If we understand it in a concrete kinematic model, we will know that the original derivative is used to describe the speed of motion change. In the kinematic model, we call the change of position speed, but in more general scenes, we need a general concept to describe all kinds of changes, so we have the concept of derivative. Mathematics is accompanied by algebra and symbolization in the process of abstraction. We know that the human brain is more sensitive to visible patterns, so it is very important to establish geometric intuition for us to understand mathematical concepts. Comparing the teaching videos about mathematics at home and abroad, I found that many foreign mathematics teachers pay special attention to finding the geometric meaning of mathematics and enhance students' perception of mathematical concepts through intuitive geometric demonstrations. We find that many mathematical figures that are difficult to explain clearly with words and symbols will be immediate, because people are naturally more sensitive to figures. The difficulty of summarizing mathematics will be accompanied by the deepening and continuous improvement of mathematical abstraction, so it is very important to get rid of the difficulties brought by mathematical abstraction to our understanding. Starting with the establishment of concrete model and geometric intuition, we can realize the transformation from difficult to easy and improve personal mathematical literacy.