1. What are the new requirements for "number operation" in the curriculum standard? The new curriculum standard clearly points out that in mathematics curriculum, we should pay attention to developing students' computing ability. Computing ability mainly refers to the ability to perform operations correctly according to laws and algorithms. Cultivating computing ability is helpful for students to understand computing theory and seek reasonable and concise computing methods to solve problems. At the same time, in the interpretation of curriculum standards, it also emphasizes "downplaying the requirements for computing proficiency." It is more important to choose the correct calculation method and get the accurate operation result than the proficiency of operation. It is important to pay attention to whether students understand the reasons for the operation and whether they can get the operation results accurately, rather than simply looking at the operation speed. " This goal requires teachers to pay attention not only to the mastery of students' operation skills, but also to the learning process of students' understanding of examples and mastering algorithms. In other words, in teaching, we should pay attention to the organic combination of arithmetic and algorithm, so as to develop students' computing ability. The process of learning digital operation is the process of developing logical thinking ability. The concepts, properties, rules and formulas of number operations are intrinsically related and have strict logic. The introduction and establishment of every concept, property, rule and formula must go through the thinking process of abstraction, generalization, judgment and reasoning. When students learn, understand and master the content of "number operation", they have to go through the process from concrete to abstract and from perceptual to rational. When students apply these to practice, they have to go through the deductive process from general to special. Therefore, the study of digital operation is conducive to the development of students' thinking ability. This requires teachers not only to pay attention to the results and methods, but also to the thinking process of getting the results and methods. This thinking process is the process that students understand arithmetic and master algorithms. The thinking of primary school students is still based on intuitive images, while arithmetic and algorithms are very abstract. Therefore, how to deal with the relationship between arithmetic and algorithm in combination with students' thinking characteristics in operation teaching is often a difficult point in teaching. We can handle the relationship between arithmetic and algorithm in operation teaching with the help of vivid and interesting fairy tale situations, intuitive models and students' existing cognitive basis and life experience.

(1) Deal with the relationship between arithmetic and algorithm in operation teaching with vivid and interesting fairy tale situations. Pupils, especially those in lower grades, mainly think in images, so creating vivid and interesting fairy tale situations can not only stimulate their enthusiasm for learning, but also help them understand examples and master algorithms with the help of fairy tale situations. It is to create a fairy tale scene (PPT) for students' favorite animals. First of all, Mr. Wei asked the students to help nine animals get on the bus at the first stop and review the oral calculation of ten plus several. The students' enthusiasm was aroused at once, and they were glad that they could help the animals with what they had learned. Then, at the second stop, he helped five animals get on the bus to review the addition, and asked, "Is there any good way for us to calculate accurately and quickly?" Let students feel that it is simple and quick to add up "ten" before calculating "ten plus several", so as to prepare for understanding the arithmetic of "carry plus". After getting on the bus, five small animals were combined with nine small animals that got on the bus at the first stop. How many small animals are there in the bus? This leads to 9+5=? This is carry addition. 9+5= how to calculate? Students quickly think of dividing 5 by 1 and 4, 1 and 9 to form 10, and 10 plus 4 equals 14. In this way, students can smoothly understand and master the arithmetic and algorithm of carry addition in a relaxed and happy fairy tale situation. Through this lesson, we can see that Mr. Wei can combine students' age, psychological needs and their thinking characteristics to create fairy tale situations that students are interested in and love, so that boring mathematics becomes lively and interesting, abstract arithmetic becomes intuitive, and students can master algorithms smoothly and naturally in understanding. (2) With the help of intuitive model, the relationship between arithmetic and algorithm in operation teaching is handled. The teacher of Huangchenggen Primary School's "Two Times Two Numbers" Teacher Shi combined the thinking characteristics of junior three students and handled the relationship between arithmetic and algorithm with the help of intuitive models. In this class, Mr. Shi didn't take "vertical" writing ability as the ultimate teaching goal, but guided students to explore the reason behind the method on the basis of students' initial mastery of vertical calculation method, and provided students with intuitive bitmap as research materials. The students showed a variety of achievements. Although the students' division methods are not exactly the same, the idea of "divide first and then combine" is the same, which is exactly the basic idea of vertical multiplication. After that, Mr. Shi once again matched the demarcation point diagram with the four formulas in vertical calculation, guiding students to understand the truth behind every detail in vertical calculation step by step. The "demarcation point map" not only creates valuable opportunities for students to accumulate experience in activities. At the same time, with the help of the intuitive model, students can better understand the reason behind the two-digit multiplication algorithm. In our previous teaching, many teachers either did not pay attention to guiding students to explore the calculation process, or guided students to learn vertical immediately after students explored the method, and began to pursue the calculation method without really understanding every link of vertical operation. This is likely to cause students to pursue calculation methods without really understanding the truth. Methods and techniques can only be obtained by backrest rules. This is obviously not conducive to the development of students. Teacher Shi's class provides vivid and typical cases for students to truly and solidly experience the process of understanding. In teaching, teachers should be willing to spend time to give students opportunities to experience, feel, understand and create. The new curriculum standard also clearly puts forward the goal of students' activity experience The far-reaching significance behind it also requires teachers to use their brains, dig deep and concentrate on understanding in their own practice. (3) With the help of students' existing cognitive foundation and life experience, handle the relationship between arithmetic and algorithm in operation teaching. Ping Yu, a primary school in Beijing, once took the course of "addition and subtraction of decimals", which was based on students' existing cognitive foundation and life experience. Help students understand the arithmetic of decimal addition and subtraction. The teacher asked the students to make up the questions independently, and one of them made up a 0.8+3.74=. This kind of "decimal point alignment" to be revealed is the focus of this lesson, and it is also an important opportunity to summarize the decimal addition and subtraction algorithm. In order to give students a chance to mobilize the existing cognitive experience of integer addition and subtraction and experience the process of judgment, reasoning and abstract thinking, the teacher asked each student to try it himself. Teacher: You have done a lot of addition and subtraction problems before, all to align the last two numbers, but what is this topic? Student: The last bit of an integer is a bit, and the last bit alignment means the last bit alignment. But the last digit of a decimal is not necessarily the same, so it cannot be aligned. Teacher: Although you didn't align the last point, who did you align? Student: Align the decimal points, that is, align the same numbers. Teacher: Your point of view is profound and accurate, so there must be a reason for doing so. But why do you have to align the decimal point with the same digit? Health 1: it is not right if it is not aligned. Health 2: The decimal point is not aligned, but the last digit is aligned, so the decimal 8 is aligned with the percentile 4, and the addition must be wrong. S3: Let me give you an example. For example, if you buy two things, one is 0.8 yuan, and the other is 3.74 yuan. If you add the last digit of 8 and 4, it is. That's definitely wrong. Teacher: When we study the same problem, we can study it from different angles, such as reasoning or giving examples. Just now, some students thought of using the familiar "Jiao Yuanfen" to explain it. Simple things explain profound truth. You're great. It seems that only numbers with the same counting unit can be added or subtracted. Summary: decimal point alignment seems to be different from integer addition and subtraction, but it is actually the same as the last digit alignment, and the reason behind the same digit alignment is that "numbers with the same counting unit can be directly added and subtracted". You not only found the method, but also understood the mathematical reason behind it. It's amazing. Decimal addition and subtraction are elementary schools. How to grasp its relationship with integer addition and subtraction? How to present the essence of knowledge in this class and grasp the core concepts for teaching? Ping Yu's teaching practice answered the above questions. In the process of guiding students to explore decimal addition and subtraction methods, teachers always grasp the "soul" of this lesson to implement teaching. Instead of satisfying the students' ability to correctly calculate the results, she guided them to approach the understanding of the essence of mathematics step by step and aroused students' deep understanding of the principle of decimal addition and subtraction, that is, the essential meaning of decimal addition and subtraction is the same as that of integer addition and subtraction. That is, increase and decrease the same counting unit. In this way, the organic combination of "reason" and "clear method" allows students to sum up algorithms on the basis of understanding arithmetic, which is helpful for students to understand the core concepts of mathematics more deeply. Only in this way can we better achieve the goal of "cultivating students' ability to operate correctly according to laws and operating rules". "III. Suggestions on the Teaching of Number Operation (1) Handle the relationship between intuitive operation and abstract operation. This principle is not easy for students to understand. Teachers can help students understand it through realistic situations, intuitive charts and students' existing knowledge base. (2) Deal with the relationship between algorithm diversification and algorithm optimization. Pay attention to students' personality. Maybe this student is suitable for this method and that student likes another method, but the reasons behind them are the same. Teachers should find ways to make students understand this truth in different ways, so that students can learn mathematics more effectively. (3) Handle the relationship between skill training and thinking training. It is not a simple, mechanical, problem-solving accumulation. In this process, we should pay attention to helping students accumulate experience.