Cultivating students' thinking through algorithm diversity in junior high school computing teaching is an idea advocated in mathematics teaching today. It requires teachers to break the traditional teaching mode, not to train students as simple problem-solving tools, but to give students more time and space to think in class. In actual teaching, under the guidance of teachers, students will find many ways to solve problems. So, the more calculation methods, the better? What problems will the diversity of calculation methods bring to students? I began to pay attention to and think about this problem. I once heard a teaching class of "two-digit plus one-digit carry addition" in grade one. The following is a clip from teaching: Teacher: (Show: 27+6 =) What do you think of doing this problem? Please put on your school tools. The teacher checks the students' study. Every student in the class immediately started to buy school tools, and the students showed a serious, positive and positive state. The teacher visited the students and expressed satisfaction with their status. ) Teacher: Let's have a talk. You can put a sign on the table every time you speak. Let's see who gestures the most, who talks the most and who comes first. The students raised their hands in succession to prepare to speak. ) 1: Divide 27 into 20 and 7, first add 7 and 6, which is equal to 13, and then 20+ 13 = 33. The students used the method of number alignment. ) Health 2: Divide 6 into 3 and 3, 27+3 = 30, 30+3 = 33, so 27+6 = 33. Students use the method of dividing numbers into ten digits. ) teacher: can you tell me the reason for "dividing 6 into 3 and 3" Health 2: Because 27+3 = 30, we have to split 27 into 30, so we split it like this. Teacher: That's good! Is there any other way? Health 3: I use the method of putting a small disc (demonstrating on the position board while talking). Put 27 first, and then put 6 discs in place. So it is 33. (The teacher nods and smiles. ) Health 4: (I have been anxious all my life) No, it should be put like this ... (Demonstration on the stage: take ten small disks in one position and put one small disk in the other. ) teacher: (puzzled) why can ten small disks in one place be replaced by the last ten? Health 4: Because putting 10 in one place is 10, and putting 10 in ten places is also 10. Teacher: What a clever boy! 10 1 Yes 1 10 Therefore, when one digit exceeds 10, go to the tenth digit and enter 1. The teacher demonstrates on the position board. ) that's great! Anything else? The students scrambled to raise their hands. ) health 5: I counted from 27 to 6 and it was 33. Health 6: I made it with several rays. (Student demonstration) First find 27 on the shooting line, and then jump back to six squares to 33. Health 7: I made it on the counter. (Mr. Sheng runs forward and holds up the counter to demonstrate. ) Dial 27 on the counter first, then 6 on the unit. When the unit is full of 10, change it to the tenth one. So it is 33. Health 8: I use a vertical column ... One digit goes from ten to ten, and the result is 33. Students say the teacher demonstrates and points out the problems that should be paid attention to when writing vertically. ) Health 9: Take 27 as 30, 30+6 = 36, 36-3 = 33. Teacher: That's good. 27 is closer to 30, so it adds up to 30, plus 3, so subtract 3 after adding it. ..... After putting forward a variety of problem-solving methods, the teacher summarized them. From this teaching clip, we can easily find that students' learning enthusiasm is quite high, and we have come up with eight methods to solve this problem. The performance of students in class makes teachers very happy, because students' thinking is so active that there are so many ways to solve this problem, which may not even be expected by teachers. I think the positive performance of students may be related to the evaluation methods adopted by teachers. The teacher asked the students to evaluate their answers by putting markers. This method has changed the single teacher evaluation method in the past, but let students record the number of speeches in class. In this way, students' enthusiasm for speaking can be fully mobilized, and teachers can understand students' speaking situation by observing the markers placed on the table by students, so as to give targeted opportunities to those students who don't speak or speak less. This evaluation method is an innovation, which I have used in my own class. Practice has proved that this method can effectively mobilize students' enthusiasm and really make students learn from "I want to learn". However, I don't think this method should be used often. Students who often use it lack freshness, and putting signs in class may distract them. So we can use this method, but we can't use it often. We should use it properly and pay attention to the grasp of "degree". If you look at this clip in depth, you will find some noteworthy problems.

1. From the above example, it is not difficult to find that the first few students did not use the school tools to answer the "27+6" question, but after the teacher's instruction was issued, almost all the students put the school tools. What is the reason? It is not difficult to understand what the teacher said in the connection clip, "Please put on your school tools". When students hear the teacher's "one size fits all" instruction, they execute the instruction and start the operation. Those students who can work out formulas without operating learning tools must also obey the "command" of setting learning tools. In fact, these students are more to meet their own "play" needs. In other words, classroom teaching is not based on everyone's existence. As we all know, every student is not a blank sheet of paper, and the first-year students have learned the teaching content in advance before entering school. For some students, it may be learned in advance through other channels such as preschool education or family education; For some students, it may be brand-new knowledge. This requires teachers to pay attention to "being in the first state" before students learn new knowledge. Teachers' questions and guidance should be targeted, and students' development should not be sacrificed because they have to take care of those students with learning difficulties. I try to change the problems in my teaching. After showing 27+6 =, ask the students to be flexible: "Everyone does it by himself. You can directly calculate what you can do, and if you can't, you can use learning tools to help. Everyone should think about how I did this problem. See whose method is faster and smarter. " Sure enough, some students began to operate learning tools according to their own needs; Another part of the students are already talking about the calculation process. In teaching, we should not only encourage students who have mastered knowledge to think positively, but also protect those students who use learning tools to solve problems from harm. Don't feel stupid and inferior to others just because you put learning tools. Teachers should tell students that putting learning tools is also a way to solve problems.

2. This method was put forward one after another. From the case, we can see that students have come up with many methods and their thinking is very active. However, the representation of this method is quite confusing. According to the theory, students' thinking is from concrete to abstract, generally from placing learning tools to calculating and solving problems with heart. However, in the fragment of this lesson, we can see that the answers of students of 1 ~ 9 are abstract methods such as mental arithmetic first, and then concrete methods such as learning tools. Why do students' answers move from abstract to concrete? I think one of the reasons may be that when students answer questions, teachers usually call the clapping students first, and then the ordinary students, which leads to the decline of the quality of each speech; Secondly, it may also be that when students communicate, the teacher randomly calls the roll, and the teacher doesn't know much about the students' learning. For the above two reasons, teachers are led by students in class. When students begin to seek solutions to problems, I use the students' self-study time to go down and check the students' learning situation, understand the students' learning situation, and ensure that students know their own practices and answers. In the subsequent class communication, I consciously gave the opportunity to speak first to the students who operated the learning tools and let them participate in the discussion and exchange. Then, please communicate with students who don't use learning tools, and try to present the calculation methods in the order from concrete to abstract, so as to play the role of teachers as classroom teaching organizers. After the reflection and reconstruction of the above teaching cases, I have a further understanding of the problem of encouraging students to adopt various methods in calculation teaching and other mathematics teaching. Cultivating the diversity of students' algorithmic thinking is what we have always advocated. However, the diversity of methods cannot be formed overnight. Teachers should encourage students to think about different methods, but they should not let students think about methods for more methods. As a result, they came up with many troublesome methods and abandoned the existing methods of learning and accumulation, which led to the extreme of formalism diversification. What should students do after they have more methods? I think, first of all, we should master the basic methods and learn new methods at the same time. Before there is a clear new method, we can borrow old methods to solve new problems. Take the above example, the first student is number alignment (column vertical), which is a basic and universal method in addition and subtraction. We can use this method to solve all carry, carry, abdication and non-abdication addition and subtraction, so let all students master this method. This ensures the correct rate of calculation for students with learning difficulties. The solution of 27+6 is to divide 6 by 3 and 3, 27+3 = 30, 30+3 = 33, so 27+6 = 33. The student used the method of decomposing numbers and rounding. Health 9 adopts the method of rounding up ten numbers first and then calculating: 27 is 30, 30+6 = 36, 36-3 = 33. These two methods are simple and convenient, and students need to master and use them flexibly. In a word, we hope there are many ways to solve the problem. But it is not enough to have more methods. The important task of teachers is to be good at improving students' thinking level, teaching students to choose different methods for different topics, and providing students with opportunities to "solve" different forms of "topics". For example, we can design problem group exercises, 44+7 =, 49+7 = ... so that students can use the method of dividing numbers into integer tens and the method of rounding first and then calculating. In the process of solving problems, students will certainly find it more convenient to round off the number of 44+7, while it is more convenient to calculate the number of 49+7 after rounding up. The purpose of doing this is to cultivate students' ability to observe the characteristics of the topic before choosing the calculation method, which is helpful to improve students' consciousness of choosing the method rationally through judgment.