Mathematics is a science that studies the spatial form and quantitative relationship of the real world. It has a high degree of abstraction and strict logic. Children's thinking level is mainly figurative thinking, and the low level of logical thinking makes it difficult for children to construct abstract mathematical knowledge. Children live in a colorful and complicated objective material world from birth, with different numbers, shapes, sizes and spatial positions. How to guide children to effectively construct abstract digital concepts according to their age characteristics? Can be carried out from the following aspects.

First, look for educational opportunities in life and gradually construct the concept of number.

In the past, it was often necessary to learn spatial orientation and feel one-to-one correspondence, or to learn through a concentrated activity and a game. However, we ignore the problem situations that naturally exist in life, and ignore the mathematical education materials contained in life. Teachers should be caring people in life and work, and discover and guide children to pay attention to and perceive real mathematical resources in life in time.

Case flow: Perceived quantity is less than 5.

In small classes, children begin to show interest in quantity and are qualified to learn quantity. Under such objective conditions, the amount within 5 is suitable for children to contact.

The first stage: oral counting

In daily life games, children often quarrel over a certain game or toy material, so children are encouraged to practice oral arithmetic in turn. For example, when you are swinging, ask the children in line to help you count, and then change when you count to five.

The second stage: counting by object

1.

Parent-child activities: "Count the stairs", walk one floor and count one floor.

2.

Students on duty: Before meals, students on duty should arrange seats according to the number of seats.

Number of tableware. The third stage: count and tell the total.

1.

Parent-child activities: How many people are there in the family? Count the number of electrical appliances in the home?

2.

Supermarket games: candy packaging and so on. In the process of constructing children's understanding of quantity, we can see that (1) making full use of family resources is beneficial to children's mathematics enlightenment and of great significance to children's learning and education.

Promoting effect. One-on-one individual tutoring not only enhances the affection between children and parents, but also helps children's math study greatly. Therefore, we should make full use of such a good family education environment to lay a good foundation for children's mathematics learning.

(B) to create a living environment for mathematics education and support children's integration into life.

For example, the "supermarket" game reproduces the real life situation in the form of simulation and guides children to learn in the situation. The content of mathematics in life enables children to learn "mathematics" naturally and unconsciously and gain relevant mathematical experience.

Second, provide different levels of materials in each stage of the concept construction of numbers to help children learn mathematics step by step.

In the process of small-class children's cognition of "Fa", let them interact with the environment and materials to jointly create the surrounding environment, and guide them to perceive and operate step by step in the process of creating the environment, and constantly experience the characteristics of "Fa" in the process of hands-on. In the construction of legal concepts, we provide corresponding operational materials for the mathematical objectives of each stage:

The first stage: the repetition and infinite extension of perceptual laws, that is, the transmission of laws. The second stage: imitation finishing. The third stage: then arrange it according to the arranged rules. The fourth stage: create simple laws independently.

In operational learning, operational materials constitute the medium of interaction between teachers and children. To fully realize the connection value of this intermediary, it is necessary to ensure the suitability of operating materials at each stage.

Thirdly, using appropriate teaching methods at all stages can help children to easily construct mathematical concepts.

As far as operation method and heuristic inquiry method are concerned, the same teaching content requires different teaching methods at different stages.

The research on the activity process of "Perceiving the relationship between two adjacent numbers within 10, greater than 1 and less than 1" shows that different methods are needed in the construction of the same teaching content.

Case analysis: "Perceive the relationship between two adjacent numbers in 10: greater than 1 less than 1"

Activity 1: What kind of seeds are planted by many people?

We guide the children to compare which seeds are planted, and find that the children in the inquiry group can use the existing life experience and quantitative knowledge in the activities, and actively use the methods of counting in line, occupying seats and holding hands with teachers. Compare the number of people, as many as them, and have a strong interest; The children in the operation group, under the traction of the teacher, stood side by side, holding hands and passively comparing, and their interest was not high.

Analysis: In contact with new knowledge, teachers should not interfere with children too much, but try to let children perceive and discover according to their own wishes. In the process of inquiry, children's thinking is unrestricted, and they can imagine and think boldly without restriction. Therefore, when children are exposed to new knowledge for the first time, we can use heuristic inquiry method to let children rely on existing mathematical knowledge and experience to explore and find new learning methods.

Activity 2: Compare.

This is an activity of sorting out concepts. When children find that counting in line, occupying seats and holding hands with teachers can compare the number of people, teachers should grasp the characteristics of children's interest points and digital concepts in time, and summarize the essential characteristics of comparison through counting comparison method, overlapping comparison method and parallel comparison method respectively.

Analysis: The methods explored by children themselves are messy. Therefore, at this time, induction can be used to help children sort out, refine and summarize some simple essential characteristics or laws on the basis of existing knowledge, so as to obtain a new concept of numbers.

Activity 3: How to compare more, less and the same?

Through a series of operation activities: "Which color has more flowers?" "See who picked more flowers?" "Which little pig is more diligent" and so on. Teachers provide children with gradually improved game materials, so that children can repeatedly apply the summarized concept of numbers to different situations, different problems and different game processes, so that children can repeatedly operate and consolidate the concept in the activities of continuous improvement again and again.

Analysis: In the process of constructing digital concepts, operation and heuristic inquiry are two common mathematical methods. With the help of other methods, a new mathematical concept can really enter children's thinking. The application of these methods can be repeated. When you have some experience, you can take the mathematical experience as the pre-experience of the next number concept construction and continue to guide children to explore.

Looking for educational opportunities in life, facing the whole people, giving full consideration to individual learning requirements, providing different levels of materials at all stages of mathematical concept construction, and adopting appropriate teaching methods to help children construct mathematical concepts step by step, so as to make the construction of mathematical concepts more effective.