(1) comparison
To let children master the comparative thinking method, we must first provide comparative environment and comparative materials. Because there is no colorful environment and materials that can cause children to think and explore problems, they can't stimulate their thinking. In daily life, parents can consciously guide their children to compare with objects or pictures. Comparison should also be from easy to difficult, from simple to complex, from concrete to abstract.
Examples of consultation:
Mom: (takes out 2 pieces of milk candy and 3 pieces of fruit candy) Xiao Ming, tell mom which of these two kinds of candy is more and which is less?
Xiao Ming: There are more fruit candy and less milk candy.
Mom: Yo, how do you know there are more fruit candy than milk candy?
Xiao Ming: I don't know yet. 3 pieces of fruit candy and 2 pieces of milk candy. Three dollars is more than two dollars!
Mom: Why is 3 yuan more than 2 yuan?
Xiao Ming: (thinking ...) I won't talk about it. Anyway, 3 yuan is more than 2 yuan.
Mom: There are more fruit candy (3 pieces) than milk pond (2 pieces), which is a comparison. To compare the two kinds of sweets, which is more and which is less, we should adopt a one-on-one method. A piece of fruit candy is more than a piece of milk candy, and a piece of fruit candy is more than a piece of milk candy. Results Milk candy was matched with fruit candy, but a piece of fruit candy was not matched with milk candy, and fruit candy was 60% more than milk candy.
Xiao Ming: I see. Compare the number of two things and use a one-on-one method.
Mom: (takes out two red circles and two green circles) Xiao Ming, which of these two circles is more? Which is less?
Xiao Ming: There are as many circles as there are circles.
Mom: How do you know there are as many laps as there are?
Xiao Ming: Look (circle by hand), red circle to green circle, red circle to green circle, red circle and green circle are all on one page, no more, no less. There are as many circles as there are circles.
Mom: Xiaoming is so clever.
After children master the comparative method, teach them to change inequality into equality and disguise inequality in the process of comparison, thus developing children's flexibility of thinking.
Examples of consultation:
Mom: Xiaoming, let's continue to study comparative law today. (Take out three circles and five triangles, arranged as shown in the picture) Tell mom, how many circles are there less than triangles? How many triangles are there than circles?
Xiaoming: There are two fewer circles than triangles, and triangles have two more than circles.
Mom: That's right. If you want the same number of circles and triangles, consider it. What can you do?
Xiaoming: Are you allowed to touch these numbers?
Mom: Yes.
Xiao Ming: If you take two out of a triangle, there are as many triangles as circles.
Mom: By the way, is there any other way?
Xiaoming: Can you add more pictures? (Mom said yes) Put two more circles in the first row, and there will be as many triangles as circles. You can also take a circle and three triangles, and there are as many circles and triangles as there are. ....
Mom: Xiaoming has thought of so many ways. Now, there are four circles in the first row and six circles in the second row, as shown in the picture. If you want the two rows to have the same number of laps, how do you put them?
Xiaoming: This is easy to handle. (I also used the method of the above question to flow it again.)
Mom: Is there any other way?
Xiao Ming: I remember. Take one from the second row to the first row. There are just as many circles.
Mom: What's this?
Xiaoming: Because the first row and the second row are round, you can move one from the second row to the first row.
Mom: Yes! This is called shifting more and making up less. Xiaoming really uses his brain. May I ask you one more question?
Xiao Ming: OK!
Mom: (There are two rows of circles with four pictures in each row) Mom has two rows of circles with four in each row, and the number of these two rows of circles is the same. How to make the second row have two more laps than the first row?
Xiaoming: It's not easy. Take two circles from the first row, and the second row will have two more than the first row. If the circles in the first row are not taken away, two circles will be added in the second row, and the second row will have two more circles than the first row. The first line takes 3, the second line takes 1, and ... there is no other way.
Mom: Everything you said is right. There is another method that Xiao Mingcan definitely came up with.
Xiao Ming: (thinking for a long time) Ah! I remember, I took 1 circle from the first row and put it in the second row. The second row also has two more circles than the first row.
Mom: Xiao Ming is very kind. I've thought of so many kinds of statements. I will work harder in the future.
The comparison of the size, length and thickness of two objects belongs to one-way thinking. With the deepening of learning, children can take three or four kinds of objects at the end of preschool, so the thinking direction is diverse. Compare which shapes are more and which ones are less. No matter how many objects are compared, it comes down to the ratio of two objects. The method is also one to one, the upper part is the same number of copies, and the non-upper part is more than the other part. When there are more than three objects, there will be a phenomenon that one object has more than one object and less than another. As shown in the figure, there are two more triangles than circles, but there are 1 fewer triangles than squares. At this time, the child will have the question that the number of triangles has not changed. Why do you say a little more and a little less? Parents' responsibility is to help children understand: ① The number of one object is obtained by comparing with another. (2) The number of objects is relative, and when compared with fewer objects, it is more; When compared with more objects, it is less. In this way, while teaching children the comparative method, they are also instilled with the dialectical thought that everything is relative and developing, with both connections and differences.
On the basis of comparing objects or pictures, teach children how to compare numbers. To compare two numbers, we can use the method of decomposing a larger number at first, such as comparing 3 with 1 to see who is bigger and who is smaller. 3 can be divided into 2 and 1, where 1 is as much as 1, leaving 2, so 3 is 2 more than 1. Conversely, 1 is 2 and less than 3. After a period of practice, when the child's mind has accumulated a lot, the large number is decomposed into two parts according to the number of smaller numbers, and then the appearance of comparing the two numbers appears, the two numbers can be directly compared. For example, 5 is greater than 4 (), 3 is less than 6 (), 9 is greater than 8 (), and 2 is less than 5 (? ),(? ) 2 is more than 3, (? ) less than 5, 1 ... In the process of comparing two numbers, don't just be satisfied with filling in brackets, but also ask why you should fill in a certain number after filling in the numbers, so that children can say their own thoughts. On the one hand, it develops children's thinking ability, on the other hand, it also develops their language expression ability.
Examples of consultation:
Mom: Xiaoming! Mom gives you some questions to test. If you get it right, mom will take you to the "Math Palace" on Sunday. It's fun there.
Xiao Ming: Mom, you are quick to give a question!
Mom: The first question, would you please answer 5 to 4?
Xiao Ming: Haha! It's too simple, 5 is more than 4 1.
Mom: How do you know that 5 is more than 4 1?
Xiao Ming: Compared with 4, 5 can be divided into 1 as much as 4, 4 and 4, and 5 is 1 more, so 5 is more than 4, 1. In addition, when counting, count 4 first and then 5, and 4 is followed by 5. 4 plus 1 equals 5, so 5 is more than 4 1.
Mom: The answer to the first question is correct and the reason is clear. Mom's second question is: How much is 8? How much is 4 smaller than?
Xiaoming: 8 is greater than 5, 8 is greater than 7 and 8 is greater than 0. Oh, I see, 8 is more than 7, 6, 5, 4, 3, 2, 1 and 0.
Mom: You can say eight in one sentence, which is more than this big string. Think about it.
Xiao Ming, (thinking)! Eight is much smaller than it.
Mom: By the way, how much is 4?
Xiao Ming: 4 is smaller than its larger number.
Mom: Xiaoming is great! Question 3: What is greater than 2 and less than 1?
Xiao Ming: There are more than two. (think) 5 is greater than 3, 2; 2 is greater than 0; 3 is greater than1; 2.4 is greater than 2; Ah! A lot. Several is less than several 1. 1 less than 2, 1.2 less than 3, 1 much better! Mom, these two questions are too many for me to finish in a day.
Mom: Xiaoming is right. Now Xiaoming has just learned the number of 65,438+00, and will learn more in the future. Comparing two numbers, one number is greater than two, and the other number is less than 1. When you visit the Mathematics Palace on Sunday, you will find the mystery of many numbers.
(2) Hypothesis
When it is difficult to solve a problem directly, the hypothetical method is often used to make the problem simple. There is such a math problem in the next semester of grade one in primary school: Xiaoqing made 1 1 red flags, Xiaolan made three fewer than Xiaoqing, and how many did Xiaolan make? Formula 1 1- 3 =8 (curved surface); A: Xiaolan made eight faces.
In order to make students understand the reason of subtraction calculation, they must rely on the idea of hypothesis. It is known that Xiaoqing made 1 1 red flag, and Xiaolan made three fewer than Xiaoqing. It can be considered that if the number of red flags made by Xiaolan is not less than that of Xiaoqing (assuming that two people make as many red flags), Xiaolan should make the red flag of 1 1, but actually Xiaolan made three less than1. If we don't use hypothetical methods,
From this perspective, it is very beneficial to teach some hypothetical ideas with toys or pictures from early childhood.
Examples of consultation:
Mom: (showing pictures) Xiao Ming, how many faces are there in this picture?
Xiaoming: This painting has 14 circles.
Mom: 14 circles. How many circles are left after 9 circles are removed? Xiaoming: (looking at the picture) There are five circles left.
Mom: How do you know there are five circles left?
Xiao Ming: I calculated it like this. I will first remove the circle on the right 10 (assuming that 10 is removed), leaving four circles on the right. Because 1 circle was removed, I added 1 circle, so there are five left.
Mom: Xiaoming thinks very well. There is such a question: How is 2+2+2+4 = □ calculated?
Xiao Ming: Think of this problem as six additions, and one * * * is 12. (Think about it) 2 when 3, 4 3s are also 12.
Mom: What's the matter that 2 equals 3?
Xiao Ming: I divide 4 into 4 1, each 2 plus 1, and 2 becomes 3.
(3) Reasoning
Reasoning is a common thinking method in primary school mathematics teaching. Generally speaking, children have the ability of direct reasoning within the scope of things or phenomena they understand. The key is that parents should pay attention to guidance and training. How to cultivate children's reasoning ability? First of all, we should provide reasoning materials. According to the characteristics of children's thinking in action and concrete image, we can create reasoning situations in games or play. At first, let the children find the rules and make simple reasoning. If the apples in the picture below are colored in the order of red, yellow and green, parents should paint the first six apples and let their children paint them down.
After children master simple reasoning methods, they will introduce preliminary three-stage reasoning.
Examples of consultation:
Mom: Xiaoming, bring me the puzzle. Will mom give you some math problems?
Xiao Ming: OK!
Mom: (taking out two right-angled triangles of the same size from the puzzle, saying) Two triangles can make a square. If you spell a rectangle with four such triangles, how many triangles do you need to spell a big square?
Xiaoming: It takes 8 triangles to spell a big square.
Mom: What do you think?
Xiaoming: Because four triangles can spell a rectangle and two rectangles can spell a big square: a rectangle has four triangles and two rectangles have eight triangles, so a big square has eight triangles.
Mom: Xiaoming got it right. Look at the picture below:
A big circle is equal to two middle circles,
A middle circle equals two small circles,
How many small circles are there in a big circle?
Xiao Ming: (thinking and talking) A big circle equals two middle circles, and a middle circle equals two small circles. Two circles in the middle are equal to four small circles, right! A big circle is also equal to four small circles. Put four in brackets, mom, right?
Mom: Yes, it's called reasoning. Mom has another difficult problem to test Xiaoming.
Xiao Ming: OK (eager to try).
Mom: Look at the picture, five chickens for 1 big chicken (refer to the picture), 1 goose for two big chickens, and several chickens for 1 goose?
Xiaoming: This question is so difficult. Mom, where do you think we should start?
Mom: OK! I'll give you a hint: let's start with 1 goose for two big chickens.
Xiao Ming: (thinking) Oh, I see. 1 geese can be exchanged for two big chickens, 1 big chickens can be exchanged for five chickens, and two big chickens can be exchanged for 10 chickens. Then, 1 goose can also be exchanged for 10 chicken.
Mom: Why can 1 goose be exchanged for 10 chicken?
Xiaoming: Because 1 goose can exchange two big chickens, 1 goose can exchange 10 chicken.
Mom: Xiaoming learns so fast that even such a difficult question can't beat you.
After a period of training, some reasoning problems represented by graphics are introduced. Usually, children's toys can be used to design various reasoning questions, so that children can think and deduce. This learning method of combining learning and playing not only conforms to the psychological characteristics of children playing, but also can learn knowledge and develop intelligence.
Your child is about to go to primary school. If you want to know what achievements you have made in cultivating children's mathematical ability, or want to examine children's intelligence, please use the following questions to test (***40 points).
Question: What is this picture? Compare the two pencils, which one is longer than which one? Conversely, what do you say? (2 points for correct answer)
Question: What are the pictures in these two circles? How many chickens are there in each circle? How do the chickens in this circle compare with those in that circle (referring to the right circle) Conversely, what do you say? How did you know? (3 points for correct answer)
Question: (referring to the apple in the middle) What about this apple and this apple (referring to the big apple)? How does this apple (middle) compare with this apple (small)? Similarly, how did this apple (middle) get bigger and smaller? (4 points for correct answer)
Question: Who is taller of the two children? Why is this child tall? (5 points for correct answer)
Question: There are three fish in this fish tank. I don't know how many fish there are in this fish tank (referring to the tank without fish), but this fish tank (the tank with fish) has two more fish than that one. How many fish should there be in that fish tank? what do you think? (Correct answer 6 points)
Question: (referring to the cake tray) There are four cakes in this tray, and how many are put in that tray? I don't know, but I know that this tray (cake tray) is less 1 cake than that tray. How many cakes should be put in that tray? what do you think? (Correct answer 6 points)
Question: These two glasses of water were the same before. Which is more than which now? Which cup pours more? What can I do to make two cups the same? There are four answers: ① add some points to the cup on the right; ② Pour some from the left cup; ③ Pour some from the left cup to the right cup; Pour some from the two cups, so that there is as much water left in the two cups.