Professor Shi Ningzhong, president of Northeast Normal University, said: "Mathematics teaching should be introduced from real life situations, and students should be trained to observe the world with mathematical eyes, think about the world with mathematical thinking and express the world with mathematical language." Here the vision of mathematics is abstract, the thinking of mathematics is reasoning, and the language of mathematics is model.
? So, how to make the first-grade children experience abstraction, reasoning and model? Are these basic ideas of mathematics too obscure for the children in the first grade of primary school? It is. Not to mention the first-grade children, even many adults, it is difficult to understand these mathematical ideas clearly. However, the lack of clarity does not prevent children from having a preliminary experience and understanding.
Such as abstraction. Pupils learn to count in kindergarten and know that 3 is greater than 2. However, if the teacher gives an example of three chickens and two big hens and asks, "Who is the big one?" Then, many children will be cheated and don't know who is older. This involves abstract mathematical ideas. It can also be seen that although children can count in kindergarten, they have not yet established an abstract feeling.
? Mathematics is a subject that studies the quantity and spatial form of the real world. In the study of quantity, mathematics only pays attention to the number of objects, and has nothing to do with everything else about objects. For example, in class, the teacher said there were six apples on the left and three apples on the right. But the teacher drew six circles and three circles; Or 6 people on the left and 3 people on the right, and the teacher still draws 6 circles and 3 circles; Furthermore, whether there are six things on the left and three things on the right, the teacher uses circles to represent them. At this time, some children said that these circles are really awesome, and everything can be expressed. You can say anything. At this time, the child has a sense of abstraction. The teacher further elicited: Do you think the circle is awesome? Or is this 6 more awesome? The children all said: it should be 6. Because this six means there are six items. This process is gradually abstracted from real life.
? I think of a theme map of digital teaching in grade one. The picture shows the yard of 1 grandma, 2 chickens and 3 pumpkins ... I think if I can guide the children to know that everything is included in 1 yard. In other words, this is a code, which can also be expressed by 1. But this "1" is bigger than the 1 aunt in the yard. Isn't this the unit "1" that is often said in grade six? The unit "1" in mathematics can be large or small and all-encompassing.
? That's the end of abstraction. Now let's talk about reasoning. Through abstraction, people abstract things related to mathematics in the real world into mathematics, forming the research object of mathematics. For example, 6 apples and 4 Sydney. Children will know it in kindergarten. 4, but why is 6 greater than 4? The child said that six would be greater than four, which makes no sense. In fact, the textbook guides children like this: connect six apples and four pears, one by one. After the connection, it was found that four of the six apples were in one-to-one correspondence with four pears. At this time, I found two more apples. That is to say, the number of apples is more than the number of pears, and then the number of more is converted into more. This transformation process is both a learning process and a mathematical reasoning process.
? With the gradual deepening of learning, through reasoning, people start from the research object of mathematics and logically get the nature of the research object and the propositions and calculation results describing the relationship between the research objects under certain assumptions, thus promoting the internal development of mathematics. When the internal knowledge of mathematics accumulates and gradually leaves the living environment, it is more pure mathematical calculation and application. At this time, mathematics gives people the impression that it is boring, boring, obscure and difficult to understand. ...
? Therefore, children in senior one should often calculate some addition and subtraction within 100, such as 2+3=? 9-7=? Wait a minute. However, many children still like to calculate these. Because I learned this in kindergarten. Even if you can't get the answer right away, you can get the correct answer by hooking your fingers. However, for some specific cases, we don't know whether to increase or decrease. This is about the language of mathematics-mathematical model.
? What is a mathematical model? The mathematical model also comes from the reality of life. For example, there are 6 apples on the left and 3 apples on the right. How many apples are there altogether? In life, children combine life experience. Yes, merger means that the left and right parts are mixed together and the number will increase. (For this, children can understand. If children don't have this kind of life experience as the basis, then teachers really don't know how to teach. So in life, such a combination is the mode of addition. We use the+sign to indicate the meaning of merger. Or pull the left and right upper parts together with straps, which is also a merger. When these four words are put together and replaced by another word, it is a * * *. In this way, the model of addition is established. Similarly, the subtraction model can be established by separation. Of course, more mathematical models will be established in the future. Through the model, people use the language, symbols and methods created by mathematics to describe the stories in the real world, and build a bridge between mathematics and the real world.
? Therefore, it seems that mathematics comes from life and acts on life at the same time. The learning of any knowledge has a process, and mathematics is no exception. Generally, the lower grades of primary schools are from life situations to abstract models, while the middle and upper grades of primary schools will have knowledge content from mathematics to mathematics one after another.
? In junior high school, functions are abstracted from the existing simple quantitative relations, and then richer mathematical models are known.
On the basis of learning a variety of models, senior high school chooses the appropriate model to deal with math problems. Universities and later (if they are lucky enough to learn mathematics) will start with practical problems and discover the new continent through big data software optimization models.
? The whole process is from life to mathematics and back to life. From the first grade of primary school, we learn mathematics from life, experience the inner learning of pure mathematics, and then apply the learned mathematical knowledge to life or somewhere in the real world to promote the development of human understanding with mathematics. Of course, many people will not go through such a complete process. Most people will go straight into pure mathematics and find that mathematics is really boring, difficult to understand and has no practical function. Perhaps the only function may be for exams. Of course, exams are particularly important, because only by passing exams can we further study advanced mathematics. It is best to have your cake and eat it. ...