Before asking questions, he volunteered, read the questions and analyzed the known situation, but he still had no clue.
Obviously, he has figured out my routine.
Before talking about the topic, I have a request, that is, I will not be a hand-holding party.
When he was in the first grade, I told him, as well as other children in the remedial class, that it was normal to meet questions that he couldn't know, but don't expect me to tell the answer directly.
You need to read the questions yourself first. If you don't understand it once, read it two or three times. After reading the questions, I know every known information like the back of my hand, and make appropriate reasoning and analysis of these known information, and then ask questions with the analysis results. I only do inspiration and guidance in key places.
Why are you doing this?
It aims to cultivate their independent thinking ability, independent analysis ability and associative reasoning ability. Only with these abilities can we learn independently.
Some children, too lazy to think, take a look at the topic and blurt out "no" without thinking. Always rely on others in study and always be lazy in thought. If you are lazy, the learning effect will naturally not be much better.
As the saying goes, if the mother is lazy, the children will be diligent, if the mother is diligent, the children will be lazy, and life and study will be the same.
So when he comes to ask questions, he should read and analyze the questions and make sure that he really can't, instead of being too lazy to think.
I took over the topic, and the topic was this: "Make a big square with an area of 100 square centimeter with four identical rectangles. What is the circumference of each rectangle? "
To tell the truth, this question is not difficult. He didn't solve it and he didn't know where the card was.
I said, tell me about the process of your analysis and the results you got.
He said that to calculate the perimeter of this problem, you have to know what the length and width are.
I said, yes, that's right And your thinking is very good. This idea has a nice name, called "result-oriented", which is a way of thinking. This method, also called reverse thinking, is simply retrogression.
Usually our idea is to know this condition, know that information, and calculate the required result according to the known information. This is called positive thinking.
When the topic becomes difficult, the known information is often obscure. If you follow the positive thinking, you may not be able to walk or go astray, and you will get unnecessary results, but the really needed results are not obtained. At this time, it is necessary to think backwards and deduce the required information and conditions according to the results.
As you said just now, if you want to calculate the circumference, you must know the length and width. So what information did you get from the topic?
He said, I calculated that the side length of a big square is 10cm, but I can't calculate the length and width of a rectangle. I counted it several times and it's stuck here.
I said, well, it doesn't matter. Let's follow your train of thought and walk backwards step by step. Solve your card point, the card point will be solved, and the result of the problem will be achieved.
To solve the problem, we must use the known information in the topic and carefully analyze and deduce it. This is a graphic problem, and the known information includes graphic information in addition to the written information clearly told you in the title. Did you get all the information on the chart?
He said, I haven't read the information on the picture carefully. Let me take another look.
I said, okay.
After a while, he said, I saw nothing.
I said, all the information you calculated is marked on the map. Then find the connection between this information and the chart.
He said that the side length of this square consists of two sections, one is the length of a small rectangle and the other is the width of a small rectangle. I don't know what the other connection is.
I said that the link you found is the key information and your card point, but you didn't make full use of this key information. If you can figure it out here, the problem will be solved.
There is another way to solve the problem. There may be many ideas. If one fails, look at the others. I can only remind you to come here.
When he heard me say this, he frowned and reluctantly thought again.
I want to frown, because I can't tell you the answer directly. I can accept being angry, let alone frowning.
After a few minutes, he suddenly let out a cry and said excitedly, I have worked it out.
I said, how did you do it? Share it with me.
He said, tell me first, is the answer 20cm?
I said, yes.
He said, I began to think about calculating the circumference, and I had to figure out what the length and width were. You asked me to start with the key information, and I listed a formula, length+width = side length.
I thought about it for a long time, only to find that I don't need to calculate the difference between length and width, I just need to know their sum.
I smiled and said, you are really amazing. You sum up the experience gained from this problem and extend it to other topics.
Learning mathematics, starting from known information, associating relevant knowledge points, completing simple reasoning and getting results, is a common method, also called positive thinking.
When the topic becomes more and more complex and the difficulty gradually increases, positive thinking often doesn't work or goes astray. If we can cultivate children's reverse thinking, be result-oriented, push backwards, and solve key nodes in the process of pushing backwards, we will often usher in a "bright future."