Coach Wang Yanwei from Fu Xue Hutong Primary School in Dongcheng District, Beijing.

Comment on Zheng Junxuan of Jingshan School in Beijing

Teaching content: Possibility (P 106 ~ 107, Case 3 and 4, Grade 3, People's Education Press)

Teaching objectives:

1. Knowledge and skills goal: to enable students to further experience uncertain events and know whether the possibility of events is large or small.

2. Process Methods Objective: To experience the process of exploring the possibility of the occurrence of events, and initially feel the statistical regularity of random phenomena. Cultivate the consciousness and ability of cooperative learning in activity exchange.

3. Emotion, attitude and values: Feel that mathematics is around, and experience the connection between mathematics learning and reality. Further cultivate students' realistic attitude and scientific spirit.

Teaching emphasis: Students know the possibility of an event through experimental operation and analytical reasoning.

Teaching difficulty: using the knowledge of event possibility to solve practical problems.

Teaching process:

First, feel the possibility. (Review the certainty and uncertainty of events. )

1. Display problem:

(1) Introduction to conversation: Through the previous study, we already know that in life, some things may happen and some things may not happen. Today, we further study this possibility.

(2) Review old knowledge: Let's review what we have learned first.

B.C.

Teacher: There are three boxes on the grass. Xiaohong hopes to touch a yellow ball at a time. Which box do we suggest she touch? Why?

Teacher: Why don't you suggest Xiaohong touch from box B or box C?

Teacher: Since both Box B and Box C can touch the yellow ball, which box is most likely to touch the yellow ball? Why?

3. Import: Is it really possible? Today we will study this problem.

[blackboard writing: the size of possibility]

Second, verify the size of the possibility.

(1) Study the possibility of two results.

1. Students guess before the experiment.

(1) Teacher: There is also a box with red and yellow balls in it. Which colored ball is more likely to be touched? Guess, and then use the remote control to choose.

(2) Show: Which colored ball is easier to touch?

① Red ball ② Yellow ball

(3) Students' choice.

Lead: Do we guess science like this? You can change your choice during the experiment.

2. Students experiment.

Teacher: Please choose two students as recorders to record every time you touch the ball by writing "positive". Boys and girls each choose a classmate to touch the ball. A classmate is responsible for holding the box and shaking the ball evenly every time. Let's pay attention to the result of each touch and tell the recorder loudly.

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* * * () times

* * * () times

3. Select again according to the test results.

(1) Teacher: We have tried it 20 times. How many times has the green ball been touched? Where is the red ball? Looking at these two pictures, do you have any ideas? If you had to choose again, what would you choose?

(2) Show: Which colored ball is easier to touch?

① Red ball ② Yellow ball.

(3) Students' choice.

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4. discover the law.

Teacher: Why did all the students who chose the red ball change places?

5. verification.

The teacher opened the lid to verify.

6. Summarize the law.

Teacher: What conclusions have we drawn from this activity?

There are more yellow balls than red balls, so they are easier to touch. There are fewer red balls than yellow balls, so it is unlikely to meet them.

Writing on the blackboard: under certain conditions:

7. Deepen the conclusion.

Teacher: Imagine what will happen if we keep touching it. If you only touch it once, can you definitely touch the yellow ball?

Summary: Only the more times you touch it, the more likely you are to touch the yellow ball.

(2) Study the possibility of three results.

1. Import: Through experiments, we know the possibility of two results. If you add another color, does it still conform to the law that the number of objects determines the possibility of finding what kind of objects?

2. Display test tips: test tips:

Touch as much as possible,

Shake it back every time you touch it.

3. Students cooperate in the experiment.

Trial record form

() () ().

Guess what:

Most likely to touch ();

The possibility of encountering () is the least.

* * * () times

* * * () times

* * * () times

Teacher: Please observe the statistics. Is the conclusion the same as your group's original guess? Tell me about it. What did you find?

4. Report to the class.

Six groups touched more red balls, while two groups touched more blue balls.

Student discussion: Is it possible for the two groups to get in touch with more blue balls?

5. Draw a conclusion that the possibility is closely related to the number of objects.

6. Introduction: We made a judgment on the possibility in the process of guessing and trying. Can we judge the possibility directly according to the quantity now?

Third, the size of the application possibility.

Company after company.

Touch one ball at a time and touch each pocket 30 times. What will happen? Can you connect these wires?

There is a great possibility of touching the red ball. It must be the yellow ball. It must be the red ball.

1. Each student writes a line in a short essay.

2. Actual investment report.

(2) Design the turntable and use it flexibly.

1. Teacher: Now, if you are the planner of this activity in the shopping mall, how are you going to design this turntable?

If you are a customer, how do you want to design this turntable? Now, please ask some students in our class to do shopping mall activities planning, and some students to be customers to design this game turntable respectively. After the design, organize your own design ideas and prepare to tell your classmates.

2. Hands-on design.

3. Student report.

(1) mall planner. (2) customers.

4. Summary: We applied the knowledge we learned to solve the problem of turntable design. We know that if the paint surface is large, the possibility of turning is great, and if the paint surface is small, the possibility of turning is small.

5. Class summary.

(3) Set questions, stimulate interest and stimulate thinking.

1. Introduction: There are many possibilities to solve problems in life. For example, everyone likes watching children's programs. You must have seen the following program, which is the "Team to Team" program in the seven-color light column. What we will see is the confrontation between the green team and the blue team in the "mine clearance" link.

2. Students watch.

3. feedback.

Ask two questions and let the students go back and think:

Why don't you listen to your classmates? Can you explain why with what you learned today?

② If you want to make throwing 6 possible, how should you mark numbers on the box?

[Expert evaluation]:

The teaching design of "the size of possibility" is almost always a combination of the certainty and uncertainty of events and the discussion of the possibility of uncertain events in the first class. To meet the needs of the new textbook (People's Education Edition) experiment, the Mathematics Teaching and Research Section of Dongcheng District Primary School in Beijing decided to further study this part, and Wang Yanwei, a teacher from Fu Xue Primary School, will undertake the teaching task. Teacher Wang arranged the first two examples in the textbook in the first class, so that students can fully feel the certainty and uncertainty according to their own life experience and existing knowledge inside and outside the class. Moreover, in the real world, the phenomenon of strict certainty is very limited, but there are a lot of uncertainties, which makes necessary cognitive preparations for guiding students to focus on finding the law of possibility from uncertainty in the second class. As we all know, there are a lot of uncertain phenomena in natural environment, social life and production, also known as random phenomena. On the surface, random phenomena seem to have no regularity, but practice has proved that if a large number of similar random phenomena appear repeatedly, they will show certain regularity on the whole. The size of the possibility is actually to study the laws of random phenomena. But this is undoubtedly a brand-new concept for primary school students, and it is necessary to help students accumulate some experience about the possibility of random phenomena through teaching activities. We infiltrate this random idea into the mathematics curriculum, so that students can feel that mathematics is around and realize that mathematics learning is closely related to the real world. Let students not only learn the mathematical thinking method of inferring the possibility with data, but also educate students to understand the society and the world from a random point of view, and give play to the special role of our mathematics discipline in cultivating students' scientific world outlook and methodology of respecting facts in a subtle way.

I think Professor Wang Yanwei's lesson "The size of possibility" has the following characteristics:

First, the goal is clear, the level is clear and the links are compact.

Teacher Wang has formulated clear, concrete and operable teaching objectives from three aspects: knowledge and skills, process and method, emotional attitude and values, and the teaching process has always been carried out around the teaching objectives at different levels. In a short period of forty minutes, under the guidance and organization of the teacher, the students experienced five links of "lead-in-experience-discovery-application-extension", which made them understand the probability law of random events.

Let's review it again:

The first link: let the students observe first, then think about it. Answer: In the three transparent boxes A, B and C, there are the same number of balls, but the red and yellow colors are different. "Xiaohong hopes to touch 1 yellow ball at a time. Which box do we suggest she touch? " "Which of the other two boxes is most likely to touch the yellow ball?" Through students' discussion of these two issues, the knowledge about "certainty and uncertainty of events" in the first class is briefly reviewed, and the study of "possibility size" of uncertain events is successfully introduced.

The second link is to ask students to predict "which colored ball is likely to be found?" I wonder how many balls are in the box. This is obviously blind and inevitably contains the element of "taking chances". However, teachers allow students to correct their initial choices during the observation of the touch ball experiment, so that students can experience that it is scientific to judge only according to the data obtained in the experiment, and cultivate their realistic attitude and scientific spirit; Through this experiment, the law of "possibility size" was preliminarily experienced and discovered.

The third link is to further study through group cooperation: if another color is added, does it still conform to the law that the number of objects determines the possibility of finding out which object? In personal practice, students have strengthened their recognition of the conclusion that the possibility is related to the number of objects.

The fourth link: let students apply the mathematical knowledge of "possibility" to solve some problems in life, and deepen their understanding of the statistical law of random phenomena in application.

The last link: after-class extension, to guide and cultivate students' awareness of paying attention to mathematical problems in life.

Second, cleverly set the situation, arouse doubts and solve doubts, and find the law.

The teacher found the breakthrough point of new knowledge and skillfully and purposefully created a situation close to students' lives and containing mathematical problems. Set questions in the nearest development area of students' cognition, build a platform for contradictions and conflicts in students' thinking, mobilize students to use their original knowledge and life experience to experience the process of the generation, development and formation of mathematical knowledge, realize the construction of knowledge, and be influenced by mathematical thinking methods. Because teachers use students' favorite materials when creating situations, students will feel very kind and interesting when thinking, which is easy to understand and master, and get positive emotional experience from it.

In order to achieve the predetermined teaching goal, Mr. Wang created a lively and interesting practical activity situation, which has different requirements for each link of students' participation. Let students gradually enrich the experience of the possibility of uncertain phenomena through observation, experiment, communication and reflection. Let students realize that the possibility of a random phenomenon does not depend on individual wishes, but on the number of objects.

Teacher Wang realized that only when students' actions have a clear purpose can the enthusiasm of students to participate in learning be really mobilized, which became the starting point for teacher Wang to set up the situation. Let's give two examples from the whole classroom teaching activities:

Situation 1: After the introduction of the new lesson, in order to concentrate the students' attention, the teacher said to the students: There are two kinds of balls in the box. Do you know which color has more balls without opening the lid? After asking the above questions clearly, let the students make corresponding guesses. "Then how do you test whether your guess is correct?" At this time, the whole class agreed that "we can test the conjecture by touching the ball". With this understanding, touching the ball has become a conscious and active demand of students and a concern of the whole class. Students care about the color change of the ball and the statistical data on the blackboard with great enthusiasm, and will keep thinking about whether their initial prediction is correct. Do you still need to adjust your choice? As the situation becomes clearer, we see that students' choices are becoming more and more consistent. The teacher asked the students to explain the reasons for changing their choices in time, and then came to a conclusion smoothly. At this time, the teacher unveiled the mystery of the lid and verified that the students' choice was correct. In this way, students have experienced guessing, observing, thinking, analyzing and choosing, experienced success and gained new knowledge in the process of actively paying attention to touching the ball.

Situation 2: In group cooperation activities, the teacher gave each of the eight groups a bag of balls. Although the number of balls in each bag is equal, the number of balls in the same color is different. The students don't know this situation. When the operation was over and each group reported, the students saw that the conclusions drawn by the six groups were completely consistent. I thought the students might be influenced by thinking set, and I want to know whether the conclusions drawn by the other two groups are different from their own, because of improper operation or other reasons. However, the actual situation in the class is that some students actually applied the knowledge they just learned about "the size of possibility" and explained the reasons. When the two groups show the number of balls of different colors to the class and verify the correctness of everyone's analysis, joy arises. We also see that when students sum up the rules, they understand that the specific expressions of the six groups and two groups of conclusions are different because of different colors, but their connotations are all * * *, which once again shows that the possibility of random phenomena is closely related to the number of objects.

In addition, when asking students to apply what they have learned today to solve practical problems, Mr. Wang designed a lottery turntable with different roles of "planner" or "customer", and the students actively participated in it, which was quite immersive. Especially when students use the knowledge of "possibility" to tell their own design ideas, there are constant laughter of appreciation and approval in the classroom. In short, in order to let students explore the law of "possibility" in random phenomena and learn to use the law to solve some simple problems in life, this lesson reflects the teacher's good intentions in creating situations in many places, so I won't go into details here.

Third, implement the concepts of internalization, reform and innovation.

Teachers' teaching should sincerely serve students' learning and learning. Teachers should push students to the stage of autonomous learning with enthusiastic encouragement, positive guidance, patient expectation and objective evaluation, so that students can acquire knowledge, develop intelligence, cultivate ability and improve personality and cognitive structure in the process of feeling, guessing, thinking, operating, communicating and reflecting. Teacher Wang plays the role of a good guide, organizer and collaborator in classroom teaching, allowing students to play the main role of learning in a series of activities such as hands-on operation, independent exploration, cooperation and exchange, so that they can truly become the masters of classroom learning activities.

In order to stimulate students' enthusiasm for learning and arouse students' enthusiasm for participating in learning, Mr. Wang adopted various teaching methods in combination with teaching needs. Some students can directly observe intuitive materials to make judgments and choices; Let the whole class look forward to using the statistical data obtained after touching the ball to decide whether to adjust their original choice; The form of group cooperation was adopted to further study the relationship between quantity and possibility; There is a written exercise to let each student judge the corresponding relationship between data and text expression independently, and then start matching and connecting; Understand the possibility and quantity of application, and understand and analyze the marketing strategy of merchants' promotion activities; Some students can use the knowledge of possibility to design lottery turntable according to the wishes of customers; Also, let the students look for knowledge related to today's study from the video clip of "Minesweeping" and extend the content of classroom learning to after class. In short, the diversification of teaching forms has greatly enriched and satisfied students' learning needs and stimulated students' strong desire to explore new knowledge.

Practice is an important part of classroom teaching activities, and feedback in practice has also attracted widespread attention. Timely, accurate and comprehensive information feedback is the key to promote the classroom teaching process. In this class, the teacher not only used our common feedback methods, such as personal oral answers and online homework, but also reported the cooperation results in groups and showed a small turntable designed by himself. It is particularly worth mentioning that the use of "selector", a modern means of information feedback, not only enables teachers to fully, timely and accurately grasp the true thoughts of every student in the class in a very short time, but also facilitates the observation, study and communication among students. Traditional teaching means and modern information technology means cooperate with each other, complement each other and complement each other, which greatly improves the efficiency of classroom teaching.

In addition, teachers have done a good job in using evaluation language to encourage students to participate in learning, in the allocation of classroom teaching time, in the design of sketching blackboard books, and in the teaching attitude and teacher-student relationship.

If there is any deficiency, it is that the use of teaching language needs to be improved in the future teaching practice in order to give full play to the unique charm of language in teaching.

As the saying goes, "there is no end to learning", I think "teaching" should also be "there is no end to learning". I hope Mr. Wang will continue to work hard on the road of mathematics teaching reform and make new achievements for education.