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How to Cultivate Pupils' Sense of Numbers in Mathematics Teaching in Primary Schools

Sense of number is a kind of consciousness to solve and use numbers actively and consciously. In the general goal, the mathematics curriculum standard puts forward that students should "experience the process of describing the real world with mathematical symbols and graphics, establish the consciousness of numbers and symbols, and develop abstract thinking". The mathematics curriculum standard (discussion draft) clearly puts forward the sense of number as the goal of primary school students' mathematics learning for the first time. For every primary school math teacher, how to understand the sense of number and how to help students build it in the teaching process is a problem worth studying and thinking about.

First, the purpose of cultivating students' sense of numbers is to improve students' mathematical literacy.

1, building a sense of numbers is a sign of improving students' literacy.

Building a sense of numbers can be understood as learning mathematical thinking, that is, the ability to form a mathematical and abstract point of view, to use mathematics to make predictions, and to use mathematical tools to solve practical problems. However, the previous mathematics education overemphasized the single knowledge and skill training, neglected the connection between mathematics and reality, and ignored the practical application of mathematics. Among students, jokes like this often appear. For example, the length of a bed is 2 cm, the weight of an egg is 2 tons, and the area of the school playground is 1 square meter. The Standard takes cultivating students' sense of numbers as one of its important goals, aiming at overcoming the tendency that mathematics education is divorced from life and reality, giving students more opportunities to contact and experience real problems, thinking and solving problems in different ways, and cultivating students' innovative and practical abilities.

2. Cultivating students' sense of numbers can help students understand and recognize problems mathematically.

To cultivate students' sense of numbers is to let students know more about real questions and consciously establish the relationship between real questions and quantity. For example, if a student collects eight bags of peanuts at home and sells them, how much RMB can he get? It is necessary to estimate how many kilograms there are in each bag and how much RMB per kilogram. For another example, when students go to a stationery store to buy exercise books, pencils, ink and other school supplies, they must consider the quantity, unit price and how much money to bring. The process of thinking about these problems is a "mathematical" process, in which students can gradually learn to understand and solve practical problems with mathematical thinking.

3. Cultivating students' sense of numbers is helpful to improve students' ability to analyze and solve problems.

Students may need more than one strategy to analyze and solve a problem in real situations, and they must consciously and actively contact with certain mathematical knowledge and skills in order to build a mathematical model related to specific things. A certain sense of number is an important condition for completing this kind of task. For example, how to code the mobilization of all participants in the school sports meeting is a practical problem. There is no fixed solution, but it can be compiled in different ways, and different arrangement schemes may be different in practicality and simplicity. For example, you can distinguish classes from boys and girls by the number of people, or quickly know what kind of projects a team member is participating in.

Second, the teaching strategies to cultivate children's sense of number

Mathematics education in compulsory education stage should be oriented to all students, and the purpose of mathematics education is to improve students' mathematics literacy. Mathematics literacy is not only measured by the level of calculation ability and the ability to solve book problems. Students learn mathematical thinking, understand and explain practical problems with mathematical methods, and can see mathematical problems from real situations, which is an important symbol of mathematical literacy. An important way to improve students' mathematical literacy is to establish a sense of numbers. However, the establishment of students' sense of number is not achieved overnight, but is gradually experienced and established in the process of learning. In the teaching process, it is necessary to combine relevant contents to strengthen the cultivation of students' sense of numbers.

1. Cultivate students' sense of number in the teaching of the concept of number.

"Mathematics Curriculum Standard" emphasizes: "We should guide students to contact with concrete and interesting things around them, feel the meaning of numbers through rich activities such as observation, operation and problem solving, and understand the role of numbers in expression and communication, so as to initially establish digital consciousness." The practical experience and understanding of the concept of logarithm is closely related to the sense of number. In teaching, it is necessary to combine students' age characteristics and the logical order of the textbook itself, so that students can have more contact and experience with relevant situations and examples in the process of understanding numbers, and feel and experience them in the realistic background, which will enable students to grasp the concept of numbers more concretely and deeply and establish a sense of numbers. Specifically from the following aspects:

(1) Take in the living materials and let the students perceive the numbers.

The life experience of primary school students is full of activities related to numbers. To cultivate students' sense of numbers is to let students perceive the world around them with quantitative meaning. Therefore, in the process of understanding numbers, I consciously guide students into life, look for numbers, observe numbers and perceive numbers according to the contents of numbers they have learned, so that they feel that numbers are close at hand and inseparable from numbers every day.

For example, when teaching mathematics, there was a debate contest on "making friends with mathematics every day". Some students boasted: "It depends on what time you get up according to the table in the morning; The call depends on the phone number; Entering the classroom depends on the floor and class ... We can't do it without dealing with numbers every day. "

For example, when teaching multi-digit reading and writing, let students talk about the numbers around them and the numbers used in life. Students are scrambling to say their student number, birthday, height, weight and shoe size; Street number, house number, car license plate number, telephone number of your home, and postal code of your living area; How many pages are there in a story book you like, how many words are there in 1 page, how much you buy in the vegetable market, and the prices of various dishes; Shopping in the mall depends on the marked price of the goods. These marked prices and shopping expenses are meaningful figures. By guiding students' perception and experience of specific quantities, students have a deeper understanding of the meaning of logarithm and laid the foundation for building a sense of number.

(2) Design various ways for students to express numbers.

Abstract mathematical symbols are not the only way to represent numbers. Guiding students to express numbers in different ways is helpful to understand the development process of numbers and enhance their sense of numbers. For example, through mathematical stories, students can be introduced to the way that ancient people used "knotted ropes to count" to represent numbers and used computer chips to calculate them.

(3) Open the thinking space, let students learn to find, speak and use numbers, find and think about problems from the data information expressed by peers, and learn to describe and communicate with numbers. For example, after teaching "Understanding Numbers within 10,000", I designed a practical activity of "Numbers in the Family" to let students collect "Numbers" in their own homes and communicate in class. The figures collected by students are simply varied: how much savings they have, how much electricity they use in a month, and how many tons of water they use; How many books, clothes and bowls are there at home; How many tiles have been laid on the floor, and so on. Some students questioned: Xiaoming's family uses 390 degrees of electricity a month. How many kwh of electricity is used on average every day? If it is calculated at 50 cents per kilowatt-hour, how much electricity will it cost a month? How to save electricity? ..... Students associate specific problems with mathematics, and think about problems with mathematical methods, which embodies students' awareness of using numbers and develops their sense of numbers in communication.

2. Cultivate the consciousness of numbers in the operation teaching of numbers.

"New Curriculum Standard" puts forward: "Pay attention to oral calculation, strengthen estimation and advocate diversification of algorithms; Simple skill training should be reduced to avoid complex calculations and stylized narratives. " Choosing the appropriate algorithm combined with specific problems can enhance the understanding of the practical significance of operation and cultivate students' sense of numbers.

For example, when teaching "application problem of remainder division", I designed such an open question: "There are 2 1 students visiting the park, and each boat can take up to 5 people. How many boats do you need to rent at least? What is the most reasonable way to take a boat? " By calculating 2 1 ÷ 5 = 4... 1, students realize what quotient 4 and remainder 1 mean in this practical problem, and come to the conclusion that five boats are necessary, but this is only a solution. Some students have come to the conclusion through analysis that three boats can also carry five people each, and the other two boats can keep three people each; Or five people in one boat and three people in each of the other two boats; Or five people in a boat, four people in a boat and so on. In the process of exploring practical problems, students really understand the meaning of calculation and how to use the results of calculation.

3. Cultivate students' sense of numbers in practical activities.

Mathematical knowledge is abstract, general and logical. Only by connecting with students' life experience and actual background can students be guided to participate in learning through hands-on, oral examination and brain thinking. Only in this way can students truly understand and feel mathematical knowledge and establish a sense of numbers.

For example, when teaching the "Preliminary Understanding of Kilogram", I designed the operation activities:

(1) Weighing: Students weigh apples (1kg), salt (500g, 2 bags) and washing powder (250, 4 bags).

(2) Count: Students, how many bags of salt are there per kilogram? 1 kg How many bags of washing powder are there? 1 kg How many apples are there?

(3) Weighing: Students weigh their own 1kg items by hand, then exchange items in groups and close their eyes to realize the weight of 1kg.

(4) Find out: The teacher asked the students to take out three boxes with the same shape and different weights prepared before class, and asked the students not to use scales to find out the boxes with the weight of 1 kg by hand.

Through the following series of operation activities, students "touched" the knowledge of mathematics, experienced the actual weight of "1kg", gained personal experience, felt the close connection between mathematics and real life, and realized the weight of 1kg by feeling the equal weight of apples, so as to use this direct experience to measure the weight of other items and cultivate students' interest for the future.

With the growth of students' age and rich knowledge and experience, students can be guided to find out the hidden relationships and laws in practical problems in the senior stage of primary school, and initially master some tools to effectively express, deal with and exchange quantitative relationships and changing laws, so as to further enhance students' sense of numbers. Combining the establishment of number sense with the understanding and application of quantity relationship, and combining the establishment of symbol sense with the establishment of preliminary mathematical model will play an important role in improving students' overall mathematical literacy.