The operation of numbers is the most widely used mathematical knowledge in people's daily life, and it has always been the basic content of primary school mathematics teaching. Curriculum standard (20 1 1) points out: "Computing ability mainly refers to the ability to perform operations correctly according to laws and algorithms. Cultivating operational ability helps students understand operational logic and seek reasonable and concise problem-solving methods. "

As one of the three abilities of mathematics (computing ability, spatial imagination ability and logical thinking ability), the value of computing ability is reflected in: first, its wide application in daily life; Secondly, the process of learning arithmetic and arithmetic laws plays an important role in cultivating students' thinking ability; Thirdly, having computing ability is the premise for students to study astronomy, geography, physics and chemistry in the future. Therefore, computing ability is one of the basic qualities that every citizen must possess, and our teachers must not relax the cultivation of students' computing ability. So how can we cultivate students' computing ability?

1. Clarify the reform ideas of operation teaching, and clarify the meaning and scope expansion of operation ability.

Regarding the operation, the general requirements of the first phase are: "pay attention to verbal calculation, strengthen estimation, and advocate diversification of algorithms; Simple skill training should be reduced to avoid complicated calculation and stylized narration "; The general requirements of the second stage are: "pay attention to oral calculation, strengthen estimation and encourage algorithm diversification;" "Let students experience the process of abstracting quantitative relations from practical problems and solving problems by using what they have learned; It is necessary to avoid complicated operations, avoid the separation of operations and applications, and avoid mechanical stylization training for application problems. " It can be seen that the operation has expanded from focusing only on written calculation to paying equal attention to written calculation, oral calculation and estimation, from focusing only on skills in the past to focusing on mathematical thinking in the operation process, from a single operation category in the past to "seeking reasonable and concise operation methods to solve problems" now.

2. Pay attention to help students deeply understand the connotation of various numbers.

In primary school, students will learn the meaning and operation of integers, decimals, fractions and percentages. In practice, we find that when the algorithms are diversified, students' methods are single and conformist, and students are confused when solving fractional application problems. The deeper reason is that students don't deeply understand the meaning of these numbers. Insufficient understanding of meaning directly affects the understanding of arithmetic and the choice of algorithm in the operation process, and affects the modeling of operation law and the determination of problem-solving methods. Therefore, students should pay attention to the understanding of integer position values and the synthesis and division of logarithm in teaching; When learning decimals, the understanding of the relationship between decimals and integers and the understanding of counting units; Understanding and significance of numerator and denominator when learning fractions and percentages. The meaning of numbers is well understood, and there are also methods of operation and paths to solve problems.

3. Pay attention to help students deeply understand the meaning of the four operations.

With the development of society, only the calculation of results will eventually tilt towards the calculator. In addition to obtaining results, the significance of operation lies in solving problems with the results of operation, and a deep understanding of the significance of four operations is obviously the premise of choosing an algorithm. For example, the understanding of the meaning of multiplication is deeper and the consciousness is stronger. When learning the multiplication table, we will not only grasp the external form of the multiplication table, but will understand that a C plus b C equals (A+B) C. With addition, subtraction can be solved by reasoning. Such as 37× 19+37, can be solved.

A Case of "Small Problem" or "Big Homework" —— A teaching clip of multiplying two digits by one digit for oral calculation

Teacher: Is 24×5 equal to 100? It seems that students have different opinions. Let's discuss: (1) What is 24× 5? (2) How to treat students with the number of 100 and how to calculate them? (3) How to overcome the recurrence of this error? (Students discuss and report the results)

Health 1: Our calculation result is 120, so 24×5= 100 is wrong.

Teacher: So, what do you think of the students who passed 100?

Health 2: I think he may have calculated 4×5=20, 20×5= 100, and forgot to add 20 to carry it.

Teacher: So, is there any way not to leave out the rounded figures?

Health 3: You can write a small 2 in ten places to remind yourself.

Teacher: This method is just like when we calculated addition. After dozens, we will push forward one by one. That's a good method. Do you have any other opinions?

Health 4: I didn't forget my back, mainly because I read the wrong question. I thought 24×5 was 25×4, because the teacher said 25×4= 100, and I wrote 100 as soon as I saw it.

Teacher: There are quite a few formulas that are easily mistaken like this. Can you still find such a formula? (Students found out 16×5 and 15×6, 26×3 and 23×6, 14×5 and 15×4, etc. )

case analysis

In teaching, we will find that many students will make mistakes such as 6×9=45, 14×5=60, and it is difficult to correct them even for a long time. The reason is that when I made a mistake at first, I just changed the answer right, but I didn't find out the reason from the root, so there was a strange circle of making a mistake again.

The teacher is a very caring person and found the students' sexual mistakes. He does not simply ask students to correct, but magnifies the mistakes and guides students to find the sexual problems reflected in them. Specifically, the teacher's teaching behavior in the following aspects is worthy of recognition.

First, from the perspective of teaching objectives, pay attention to the essence of the problem. Guide students to find and correct mistakes in calculation through "what is 24×5"; Guide students to expose their subconscious calculation habits and problems through "how do you guess the students with the number 100 think and calculate"; There are quite a few easy-to-read formulas like this. Can you still find such formulas? Guide students to rise from individual phenomena to sexual problems; Through "how to overcome the recurrence of such mistakes", guide students to prevent the recurrence of such mistakes from the source of thinking. Originally, a simple correction of wrong questions has been promoted from point to face, from small to large, from external form to thinking essence in the teacher's artistic guidance and constant questioning.

Secondly, from the perspective of teaching methods, teachers are good at waiting, paying attention to retreating behind the scenes and giving instructions in time. Students' basic quality and learning ability are different, which leads to different learning situations. If the teacher's logical thinking is used to judge the students' situation, the real learning situation will often be hidden behind the assumptions. In this class, the teacher didn't make subjective assumptions about the students' mistakes, and at the same time, he didn't give them emergency help. Instead, he asked students to fully express their ideas, determine their ideas and deepen the discussion. The sentence "Can you guess what the students think and how to calculate the number 100" moves the teacher from the front desk to the back position, allowing students to communicate independently, so that teachers and students can feel the various reasons for the emergence of 24×5= 100. Teachers have captured a lot of information through students' reflection and introspection, and it is the teacher's waiting that makes it wonderful: 24×5 and 25×4 exchange numbers in units of two numbers, but the results of the two formulas are different, which is different from the multiplication exchange law, so we should not be misled by the special formula 25×4 when calculating 24×5.

It can be seen that when students make mistakes, appropriately magnifying them is conducive to developing students' thinking and promoting diversified thinking. It turns out that "fuss" can also be "fuss"!