Orange: 4 years old, 10 months.
Mom: Orange, how about playing math games with mom?
Orange: OK, Mom.
Mom: Do you remember the Bible story your mother used to tell you? There was a man named Zeus, who was very powerful, so someone built a "Temple of Zeus" to commemorate him, but during the Roman War, an officer destroyed the temple, leaving only a few pillars destroyed. The Athenians thought Zeus was very powerful, so they decided to repair these pillars again. Can you compare the number of repaired columns with the original ones?
Orange: (I counted it quickly, and I counted it twice to make sure it was correct. In the process of counting, there is no sense of order for the first time, and the second time she counts sideways, which is not easy to miss than the first time. Mom, there are five on the left and six on the right. There are many more after the repair.
Mom: It seems that this game topic has not stumped you. Do you want to continue the challenge?
Orange: Yes.
Mom: Then guess what the story of the following game is?
Orange: The police catch thieves.
Mom: The more things you steal, the heavier or lighter the punishment for this thief?
Orange: The heavier it is.
Mom: Then can you help me compare which of the two thieves was punished more severely?
Oranges: (Oranges chose the counting method this time, and it was quick) Mom, the thief above stole eight things and the thief below stole nine things, so the thief below will be punished more severely.
Mom: You are great! It seems that my game topic today is relatively simple, so I can't beat you. I want to increase the difficulty of the game topic, so you should be prepared.
Orange: OK, Mom.
Mom: Look at this game topic. Tintin and Xing Xing are tidying up the same room. Figure 1 was compiled by Ding Ding, and Figure 2 was compiled by Xing Xing. Can you help mom compare who has packed more things?
Orange: (Her first reaction is to count things on both sides, but there are many things. She tried to count several times, but she always repeated or missed it. ) Mom, this game is a bit difficult. I can't count them.
Mom: Yes, it's a little hard to count. What do you find when you look at the things in these two pictures?
Orange: There is the same thing. There are trousers on the left and the same trousers on the right.
Mom: Is there any good way for you to compare who cleans up more?
Orange: I can't think of it.
Mom: Do you remember when mom used to play black and white with you? Two piles of chess pieces, one is white and the other is black. How to compare their figures?
Orange: Oh, I remember, let them be good friends, one is white and the other is black; A white man and a black man; Finally, there will be more people left.
Mom: Then can you apply this method to this game topic?
Orange: Mom, I know. I can make things on the left and things on the right become good friends.
Mom: So how are you going to help them become good friends?
Orange: I want to use the same thing to make them good friends.
Mom: That chess piece can be taken out. These things are all in the book. You can't take it off. How do you solve this problem?
Orange: Mom, I want to draw a circle.
Mom: Then let's try it together.
Orange: (Soon, she circled the items in Figure 1 and Figure 2 one by one. Finally, when the figure 1 left leather shoes and trousers, the figure 2 left leather shoes, trousers and pistols; Look, mom, there are many things on the right.
Mom: What's the result before you turn around? I'm curious.
Orange: Look, Mom, the shoes and pants on the left can correspond to the shoes and pants on the right. Finally, the pistol on the right is on the left, so there are many things on the right.
Mom: You are amazing! Explain clearly that you have created a very important word: "correspondence". How did you come up with this word?
Orange: Because I think every time I take one from the left, I have to take one from the right, so it corresponds.
Mom: Yes, you are right. In the chess game and this game just now, we did use the mathematical idea of "one-to-one correspondence". You came up with it with a mathematician. You are really something.
Orange: Mom, I know "one-to-one correspondence", said the kindergarten teacher, but I don't know what it means. Now I know.
Mom: Do you think there is such a "one-to-one correspondence" between the stories we told before?
Orange: Mom, the story you told about the blind giant herding sheep is like this. Every time a sheep comes out of the hole, the giant will put a stone.
Mom: You are amazing! You are absolutely right. Then I guess I can't beat you in the next game. Let's see:
Mom: There are two zoos. They have many small animals. Can you compare which zoo has more animals?
Orange: Yes, just use the same method.
Mom: Why not choose the counting method?
Orange: It's too much trouble and easy to miss.
Mom: Then let's get started.
Orange: (This time she is quick) Mom, there are many animals on the right, because penguins, snakes and dinosaurs have no good friends.
Mom: It seems that mom must invite her best brother Gao Xiao, which is problematic, otherwise it won't always be difficult for you. Look at this topic. Tintin bought two colorful chocolates, but the shapes were different. Ding Ding wants to eat big chocolate first. Can you help him find it?
Orange: Mom, the chocolate on the right is big. Eat this first.
Mom: Why?
Orange: Look (she indicates with her hand that the chocolate on the right is longer and wider than the first one), so this one is bigger.
Mom: I still have some doubts. Let's make sure again. Look, how many colors do these two kinds of chocolates have?
Orange: There are seven kinds.
Mom: Do you know the numbers in seven colors?
Orange: There are squares, triangles, and this, I don't know (she points to a parallelogram).
Mom: The name of this figure is parallelogram. Now my mother has blocked the rest of the two chocolates, leaving only one square. Who do you think is older and younger?
Orange: The same.
Mom: It's different. Is the one on the right bigger? (I have drawn the length and width of these two pictures by the method of orange-orange relatively complete picture. )
Orange: The same mother, look (she repositioned the book so that the square on the right looks the same as the one on the left). The diamond on the right becomes a square. I was a little surprised when she said diamonds at this time, because I had contact with her before, but I didn't mention much.
Mom: I see. It seems that I was really wrong. Similarly, can we compare the other six figures?
Orange: Yes, Mom. . . . . . Oh, I see, mom. It is the same. These two pieces of chocolate are the same size, because each piece is the same, but it looks different.
Mom: Really? Can you use your little hand like you used to play the previous game?
Orange: (Soon, she pointed out the same 7-to-1 number with her finger. )
Mom: You are great. So which of these two chocolates should Tintin eat first?
Oranges: Eat them together, because they are the same size, but they are put in different places.
Mom: Yes, they are the same size, but they are put in different positions when they are spelled, and the shape of chocolate is different at last.
Mom: Now I take three books to simulate three small chocolates. Shall we spell them together?
Orange: The one on the right is big.
Mom: Huh? Why?
Orange: Because. . . No, they should be the same size. Just like before, they are all the same size, but in different positions.
Mom: Yes, then you can pose to test your mom now, ok?
Orange: (She asked the same question after changing her position)
Mom: So we just ate chocolate. Let's have another piece of cake this time. Would you like to choose again?
Orange: Same size. Eat together.
Mom: Can you tell mom the reason again?
Orange: It's the same size, but it's not in the same place, and the shape of the cake is also different.
Mom: Mom should give two thumbs up. Like you! It seems that I have to find a topic that is super, super, and super troublesome. Dare to try this game? It seems really interesting.
Mom: There are many small triangles on the left and many squares on the right. The two small triangles on the left can spell a square on the right. What mom wants to ask you is: If I put the small triangle on the left into a square, who will have more squares on the left and right?
Orange: I can count.
Mom: How to calculate? Now there is a triangle on the left and a square on the right.
Orange: Mom, look, the two triangles on the left, a pair, form a square. I can count two triangles on the left and a square on the right. They are the same. She gestured with her hand, her left hand pointed to two triangles and her right hand pointed to a square.
Mom: Can you draw a circle just now?
Orange: Yes.
Mom: How did you draw it? Just now we drew one on the left and one on the right. Is it the same this time?
Orange: It's different. This time, we need to draw two triangles on the left. These two triangles have the same meaning as 1 square.
Mom: Then try it.
Orange: (She is not slow at all this time) Look, Mom, there are many squares on the right.
Mom: Well, I see a square with no good friends on the right.
Orange: I can also make up numbers (she marked every whole in the left and right pictures with numbers, with 6 squares on the left and 7 squares on the right). When marking the right picture, I thought that Orange should be marked with 7 in the last empty place, which means the seventh, but it didn't, and I found that she was still used to using the concept of radix.
Mom: So this time, mom has a little problem: Just now, we all had a "one-to-one correspondence". Is there a one-to-one correspondence here?
Orange: There are two pairs of 1 and two pairs of 1 square triangles.
Mom: Yes, if you look at the triangle alone, it is really 2 pairs1; Then you just made up the numbers. There are more than six triangles on the left. You only marked six. What does 6 mean here?
Orange: 6 squares.
Mom: As you said, two triangles are a square. So we can regard two triangles as a whole, corresponding to a square on the right, which is also a "one-to-one correspondence", understand? Baby.
Orange: Mom, this question is really a bit difficult. You're trapping me.
Mom: Never mind, take your time. There is one last topic, from Grandpa Gao. There are many small squares in the picture on the left, and many big squares in the picture on the right. The four small squares on the left can be combined into 1 squares on the right. Similarly, when I put the small square on the left into the big square, which one is more and which one is less?
Orange: It's a little troublesome this time, because I have to draw four at a time. You have me stumped, Mom. You draw the first stroke first.
(So I am responsible for the right picture, and the orange is responsible for the left picture. In the process of painting, Juzijun did make a mistake, but she quickly corrected it. )
Today's game is over.
Summary and analysis: From this game, I saw the child's progress. From recalling her concept of "chess game", I have established a simple one-to-one correspondence, and I can explain the reasons clearly, but I haven't played for a long time, and the child has not mobilized her existing experience. After this game, she has re-recognized the "one-to-one correspondence" and can understand the problem of "seven-color chocolate". Compared with chess games, this kind of problem is. In addition, it is not easy for children to understand the "many-to-one" or even "many-to-many" trading relationship in the "one-to-one correspondence" similar to mosaic graphics. Children also have difficulties in painting. Juzijun's daily hands-on ability and drawing ability are still excellent, but during the competition, it can still be seen that she is a little overwhelmed.
In this conversation, I obviously felt the fluency of my conversation. I can better respond to the child's reply and let the child play the game in a happy environment and context. The game lasted for an hour. Orange is not bored, which is my deepest experience, including the communication with children during this time. I found that my continuous study and communication with children had a preliminary effect. I hope I can continue to work hard and go further.