Junior students are lively and active, and their classroom attention is short-lived, but they are very curious and easily stimulated by external conditions. As the saying goes, a good beginning is half the battle. This requires us to attract students' attention at the beginning of class and bring it into classroom teaching.

The introduction of mathematics class can make students enter the kingdom of mathematics with the least words and time, and can connect the preceding with the following, review the old and learn new things, stimulate the desire of learning and prepare for the climax of learning. For example, when I was teaching the course "Corner of Understanding", I used a story to introduce it: the king of the mathematical kingdom wanted to build a library, but the invited designer said: Everything is ready, and a corner is needed. So the king ordered the whole country to find a corner, and after layers of screening, only four contestants were left. This day is the final, they are all standing in the palace waiting for the call of the king, and the designer comes out to check it out in person.

Smart boy, who do you think is the most suitable? Through the study of this course, I believe you can use what you have learned to help designers choose the right players. This will undoubtedly set off a wave of heated debates and stimulate students' desire to explore new knowledge. Teachers will strike while the iron is hot, organize and guide, and gradually introduce new courses.

Second, grasp the main points of teaching and start an effective discussion

On the basis of students' life experience and existing cognition, a solid class should focus on the learning objectives, grasp the important and difficult points of this class, conduct effective discussions at the teaching points, and deepen the understanding and mastery of the knowledge of this class.

For example, in the lesson of "take one and take one (1)", the learning goal of this lesson is to understand the remainder in combination with the operation process of building a square, to experience the process of exploring the relationship between the remainder and the divisor, and to understand the meaning of division by the remainder. One of the key points in teaching is to explore the relationship between remainder and divisor, which is abstract for senior two students. The textbook arranges a big inquiry activity, that is, a square is built with a group of sticks with continuous roots of 14, 15, …, 20, and students are asked to explore and discuss in groups of four by filling out a form. In the classroom, the following interactive process appeared between teachers and students:

Teacher: What did you find in the process of building and filling out the form?

Health 1: The number of bonus sticks keeps growing 1. .

Health 2: The divisors are all 4.

Teacher: Why is the divisor always 4?

Health 3: A square is made up of four sticks.

Teacher: What else did you find?

Health 4: The remainder is constantly changing, sometimes big and sometimes small.

Health 5: The remainder is 0 or/kloc-0 or 2 or 3.

Teacher: Just look at divisor and remainder. What did you find?

Health 6: The divisor is 4, and the remainder does not exceed 4.

Teacher: Is the remainder equal to 4? Why?

Health 7: No, because if it is 4, four sticks can make a square.

Teacher: So the remainder can't be equal to the divisor. So can it be 5 or 6?

Health 8: No, if it is 5, you can also build a square, leaving 1 stick; If it is 6, you can also build a square, leaving 2.

Teacher: Through the communication and discussion just now, can you sum up the relationship between remainder and divisor?

Student: The remainder must be less than the divisor.

Teacher: You summed it up very well! The teacher is testing you. If the divisor of the division formula is 7, what is the remainder?

Health: less than 7, namely: 0, 1, 2, 3, 4, 5, 6.

Teacher: Why? Can you give me an example?

Health: For example, there is a pile of apples, which are put on seven plates on average. If seven apples are given to each plate, you can divide/kloc-0 apples into each plate. If the remaining 8 can also be divided into 1 per episode. But the remaining six or five are more than seven hours, so they can't be divided equally. One for each plate is not enough.

Teacher: It seems that everyone really understands the relationship between the remainder and divisor in the division formula with remainder, that is, the remainder must be less than the divisor.

Third, self-made teaching AIDS, accumulate activity experience in operation, and promote mathematical understanding.

Psychologists point out that if children's hands-on operation ability can be exercised in mathematics teaching, students can directly acquire perceptual knowledge and master knowledge. Therefore, when designing mathematics activities, we should take students' activities as the main line, stimulate students' active participation, practice, thinking and exploration, and solve mathematics problems flexibly and effectively through various hands-on activities, so as to learn and understand mathematics in activities and help students accumulate experience in mathematics activities.

Primary school students' mathematics learning is mainly based on thinking in images, so with the help of learning tools, students can operate by hand, which can enrich their experience and promote mathematics understanding. In normal teaching, I instruct students to make such learning tools and guide them to understand knowledge through hands-on practice. In the teaching of Children's Paradise, students will list the multiplication formula "4×2" to understand "How many people fly?" Question, but I don't know what "4×2" means. So, I use a small disc to assist teaching, guide students to read the mathematical information in the situation, put it on a small disc and say: There are 2 people on each plane, how many people are sitting on four planes? "Six fours" means how many people are there in a small train? On the basis of full operation, students understand the principle of calculating the sum of several identical addends by multiplication. Then arouse students' thinking. There are two people, three people and four people in the three rooms. Can I use multiplication here? Why? After discussion, the students finally understand that multiplication can't be used when the addend are different. Students accumulate learning experience of multiplication in the process of posing and speaking.

The cultivation of problem-solving ability runs through teaching. In the teaching process of Chartering, combined with the problem situation: 2 1 person has to cross the river by boat, and each boat is limited to 4 people. How many boats should I rent at least? I asked the students to explore with the help of sticks and disks (sticks represent ships and disks represent people). Students soon found that five boats were not enough, so they had to add 1 boat. This is the phenomenon of "entering one" in division with remainder.

Fourth, let students know why and why.

Divide strawberries is the fourth lesson of Division, the second volume of the second grade of primary school mathematics published by New Beijing Normal University. The content of this section is to try quotient on the basis of students learning division by remainder and vertical method. Let the students divide the smaller number by the larger number, and then lead to the method of exploring the trial quotient. It is difficult for sophomores to understand that the remainder is less than the divisor and adjust the quotient according to the remainder. I'm glad I taught two math classes. When teaching this class, the two classes used different teaching methods, and the effect was completely different.

First teaching

Show the situation map of strawberries first, and let the students read the questions to find information. The calculation formula is 55÷8=

Teacher: Is there a number whose product of eight is 55?

Health: No.

Teacher: How much should that be? what do you think?

Health: quotient 6.

Teacher: Why not consult 7?

Health: Seven, eight, five, sixteen, 56 is bigger than 55.

Teacher: The blackboard is vertical, 8× () is closest to 55, and the quotient is 7, so it should be changed to 6. After the business test, how to calculate?

Student: Then multiply the quotient and the divisor. Subtract 55-48=7.

Teacher: Considering the situation of dividing strawberries, can the remaining seven put 1 on each plate?

Health: No.

Teacher: The remaining seven can't be divided equally into each plate, so in division, the remainder is less than the divisor.

This kind of teaching pays more attention to the results of students' learning. After class, I asked four students: How to try business in 55÷8? Why is the remainder smaller than the divisor? Only one student can tell the reason by combining the situation diagram of "dividing strawberries". Other students know it but don't know why. This shows that I just "filled in" how students try to do business. Students have not personally experienced the operation process that the remainder must be less than the divisor, and have not deeply understood that the remainder must be less than the divisor, so they cannot well understand the significance of numbered division.

After this after-class test, it is found that students have not really experienced the process of trying business and have not actually operated it. On the basis of getting to know the students after class, I changed the teaching method of another class.

Second teaching

Show pictures of strawberries. Ask students to read the questions and find information. Calculate the formula 55÷8.

Teacher: (holding up the stick) I used 55 sticks instead of 55 strawberries and gave them to 8 students instead of 8 plates. Putting a few sticks in each plate means that each student gets a few sticks and how many strawberries are left. How to divide it? Talk to each other at the same table.

Teacher: (while demonstrating) The teacher also thought of a division. First, give each student a small stick.

Health: This is too much trouble.

Teacher: (pointing to the vertical form of 55÷8) I have a diagram of 1, which is recorded from the quotient 1, so it is a bit troublesome to try. Therefore, when we divide a larger number, we can directly consider it from a larger number. How many businessmen are there here?

Health: quotient 5.

Teacher: (blackboard writing: vertical form of business 5) We saw (during the demonstration) that everyone was given five sticks, and how many were * * *? How many are left in the teacher's hand? Counting with the students, there are 15 sticks left. Write the remainder 15 in vertical form. )

Student: No, the remainder is greater than the divisor. You can continue to divide.

Teacher: Pointing to the remainder, ask the students: This vertical form is wrong, you can continue to divide it. What do you mean?

Health: You can also give it to each person 1 stick.

Teacher: (Show everyone 1) How much is each person giving now?

Health: 6.

Teacher: (rewriting the vertical style) We found that the remaining 15 sticks can be subdivided, indicating that the quotient is small, and we can increase 1 to 6. Now 48 sticks have been divided, and there are 7 left, which are distributed to 8 people on average. Is that enough?

Health: Not enough.

Teacher: Because the remainder is less than the divisor, if the remainder and divisor are equal, everyone can get 1, which is exactly the remainder and there is no remainder. Just now, some students thought of quotient 7. What do they think? (Rewrite the vertical form according to the students' narration)

Health: When I saw 55 and 8, I immediately thought of the formula "7856", but after multiplication, it was more than 55, which was not enough for each person to divide seven sticks, so I changed it to 6.

Teacher: 8 people, each with 6 sticks, * * * divided 48 sticks, which makes 55 sticks together with the remaining 7 sticks.

After two times of teaching, I found that I should pay attention to the following two points when teaching this lesson:

1, emphasizing the process and building a bridge between "arithmetic" and "algorithm". More attention should be paid to students' life experience and understanding of arithmetic, so that students can experience the process of divisor stick and understand that the remainder is less than divisor. When the rest can be divided, everyone will be divided into 1 time, which means to increase the quotient; When the score is not enough, the quotient should be lowered so that students can learn to prepare for the adjustment of quotient. In the experience, students' cognitive thinking gradually completes the development process from "knowing why" to "using why".

2, heavy law. Popularize the "algorithm". Discuss the trial operation process according to the specific situation. Students questioned "starting from each person 1 root" and found that they could start directly from the estimate and then adjust the quotient. In this process, students gradually understand that the maximum remainder must be 1 less than the divisor; If the remainder is equal to the divisor, the division has just ended and there is no remainder; If the remainder is greater than the divisor or "not less than", the quotient must be adjusted. In this way, students not only form an algorithm, but also deepen their understanding that the remainder is less than the divisor, and then understand the significance of division with remainder.

In short, in order to understand students in class and better implement teaching, teachers must be able to ask questions to stimulate and promote students' mathematical thinking, better listen to students' thinking process in teacher-student interaction, show students their opportunities, and understand and understand students' ideas. Only in this way can teachers work out teaching strategies suitable for students' understanding of mathematics.