One is to guide the flexibility of definitions, theorems, rules, properties and formulas. This is the difficulty and key point for children to learn mathematics. For example, the order of elementary arithmetic is to multiply and divide the formula without brackets before adding and subtracting, and the formula with brackets is solved from brackets to brackets and then to braces. Another example is the new characteristics of negative number operation encountered in junior high school, such as the formula of typical application problems, the formula of area, the formula of volume, the axiom of junior high school students, the square of two sums and the square of two differences, the square of two differences and so on. How to understand and use each of these items, we must give children more in-depth guidance on the basis of what the teacher said, and then do some exercises to further understand the spirit and meet the requirements of flexible use. If you follow the same formula, it seems that you are on the right path and save time, but in fact you are astray. Because some topics are not sure what formula to use, only on the basis of in-depth understanding of the quantitative relationship, master the method of deducing the formula, can it be regarded as a real application. The loving father gave an example: there was a cage with chickens and nine-headed birds in it. If the total number of heads is 60 and the total number of feet is 40, how many chickens and nine-headed birds are there in the cage? If this problem is not solved by the formula of chicken and rabbit in the same cage, it will be solved by the deductive rule. Because nine-headed chickens and birds have two feet, if all chickens have only 20 heads, the fact is that 60 heads have 40 more. If a bird with nine heads is replaced by a chicken, in order to reduce 40 birds, it is necessary to replace 40 (9- 1) = 5 birds with a chicken. So there are five birds with nine heads and 15 chickens (that is, 20-5) in the cage.
The second is the rapidity of the problem-solving process. This includes training the calculation speed of solving problems, finding hidden information from given known conditions and getting new information. The former training should be combined with mental arithmetic and quick calculation, while the latter training should have certain analytical ability, and often find relevant problems from real life and establish a direct connection between them. For example, this loving father said this question: How many trees should be planted in a parallelogram pond with various 15 trees on both sides? Some people can easily find the phenomenon that the four sides of trees overlap, so they avoid it when calculating. And some people can't think of this kind of information, so they get the wrong result. The speed of solving problems depends on whether these two trainings are in place.
The third is the understanding of mutual translation of coaching model. Children have a basic skill in learning mathematics: to "translate" formulas (formula questions) into written questions described in mathematical language, and to "translate" text questions in mathematical language into formulas (formula questions). There is a problem of how to understand this kind of translation, which is a difficult point for children to learn mathematics. It is difficult for some people to understand the meaning of the question correctly, which often leads to translation errors. The key to counseling is to teach how to read, usually by marking, that is, while reading, make various marks under the topic with a pencil, separate the conditions of the topic from the questions, and then mark the data and keywords. For example, this question: the sum of 45 and 39, divided by the difference between 45 and 39, what is the quotient? The formula can be listed quickly: (45+39)÷(45-39)= 14. The transition from simple copywriting to this compound copywriting is a "bridge" to practical problems, and it is very important to practice this basic skill well.
The fourth is the accuracy of the counseling results. Children should also have the habit and ability of self-examination after solving problems, so they should coach the methods of self-examination, such as estimation, reduction and emphasizing exercises. Let the children check their own mistakes and make the result of solving the problem meet the requirements of accuracy. For example: 9.8-2.9, if you get 69, it is impossible to estimate, because the minuend is 9.8, and the problem is that the decimal point is missing; This problem can also be tested by the inverse operation of addition and subtraction. If it is 6.9, add 2.9 to get 9.8, which is correct. With the deepening of learning, more and more self-checking methods will be learned, which can improve the accuracy of problem-solving results, which is the mathematical knowledge that children must learn.
Learning mathematics should pay attention to the above four aspects of counseling, in the final analysis, it is necessary to improve the learning ability of mathematics. As mentioned above, several problems are all started from this aspect. If you master this kind of counseling method, you will get the joy of harvest.