Many students in the Xi junior high school mathematics, especially when learning geometry proof problems, will encounter such a situation, listen to the teacher in class to understand, feel that they have learned, in fact, when it is their turn to do the problem, even if the practice Xi given is the same type as the teacher said, look at it or will not do, but the teacher said the answer, and it feels very simple, I should not think of it, this is what everyone often says:As soon as you hear it, you will do it.
If you ask this question to a math teacher, most of them will answer: do less, do more. Then parents began to assign a lot of math practice Xi to their children, and started the tactics of sea of questions. At this time, two situations will occur:
One is that after a long time and a large number of brushing questions, children will slowly start to do when they encounter problems, so parents come to a conclusion that mathematics still depends on brushing questions, but thinking that there are so many courses, I feel that there is not enough time.
The other is to brush a lot of questions, still standing still, not to mention encountering new problems, that is, I have done it, I still encounter it again, after being disappointed again and again, I have to face a "reality", the child has no understanding of mathematics, can only go to this extent, the ability is limited, and begin to accept the status quo, in the case of ensuring that the mathematics score does not fall, focus on other subjects, and try to balance the total score by other subjects.
But is that really the reason for this problem?If it is true as mentioned above, then the main factor that determines whether a child learns geometry well in junior high school is intelligence. I don't agree with this point of view, because I have always emphasized that junior high school mathematics has not yet reached the time to fight IQ, and most of the comparisons are learning XiXi habits, attitudes and methods.
So, let's analyze why this happens, I think there are two reasons:
1. Does the teacher really know how to teach?
I also often watch some teachers' lectures on the Internet, thinking that it is to improve my teaching level, but sometimes I really complain while watching. For example, I once saw an older teacher teaching a geometric proof problem, and the first thing he said was: make an auxiliary line, extend AM to point D, so that AM=DM, connect cm. And then there's: obviously, ABM CDM. Later, blabla logically proved the whole problem. Many parents still think that this teacher is very good, but they haven't noticed that the two biggest slots here are:
1.Why do you do this?You are a teacher, you have the answer, of course you know how to do this, I am a student, just starting to learn, how did I think of it?
2."Obviously"?I'm sorry, I don't think this is obvious at all, you think it's obvious that you've been teaching for decades, of course you think it's obvious, I'm a student, just starting to learn, why do I think it's obvious?
In fact, whether a teacher can teach or not really has little to do with whether he has been teaching for many years. Some people have been teaching all their lives, but they have never reflected, and in fact, they have not made much progress. (This is very similar to those students who have done a lot of questions, but never summarized and summarized) and then because of the long time of teaching, of course, every year can meet a very small number of students who learn well, and they feel that they must have no problem teaching, and you can't learn well either because you are stupid, or because you do less questions. He doesn't care whether the student has learned in advance or is talented, anyway, if he learns well, it's not his problem. The key is that you can't bar, if you ask the parents, the words he puts on his lips are: Then why can other students learn to pinch?If you ask a young teacher, he will say, "Young man, you have a lot to learn." If you're welcome, it's straightforward: I've been teaching all my life, and I need you to teach meYoung man, be humble, you are still good enough to learn. Directly rely on the old and sell the old, and kill you.
But I just want to ask, what's the difference between you talking like this and students looking at the answers directly?If I had to talk about the difference, it would be that it was faster for students to look at the answers directly!So what do you want your teacher to do?You read the answer along and copy it on the blackboard, are you sent by the monkey to delay time?
This kind of class is the most terrible, because as a parent, I feel that the teacher is experienced and there are indeed students who learn very well, so the rest is: there are fewer questions, or the IQ is not enough?Students who were quite interested in learning Xi began to doubt their IQ like this, and I don't know why. But if you calm down and think about it objectively, why does it create the illusion that you think you understand?Don't worry, I'll tell you the answer right away.
2. Do students really know how to listen to the class?
If you are lucky enough not to meet the kind of teacher mentioned above, but meet the same as me, when you talk about the topic, show you the complete idea, from how to think, how to do auxiliary lines, how to try, guess, and then verify, step by step to tell you, but still can't learn well, you have to think about whether you will listen to the class. As I said in the previous article, don't rush to take notes when listening to math lessons. The focus is to follow the teacher's train of thought, and many students pay attention to copying the steps of the problem. Then the two types of teachers described above may seem to you to be no different. And most likely, you prefer the first type of teacher. Because he won't tell you halfway through your notes that this idea is wrong, and we'll do it all over again.
Now to answer the question just asked, why do many students think they understand?In fact, the most difficult part of the geometry problem is the beginning, and I can't imagine how those few auxiliary lines came about. I often meet students who come up to me and say, "Teacher, tell me the auxiliary line, and I will do it." As a result, the teacher did not explain why he did this, but directly talked about the practice of auxiliary lines, and then logically explained the proof process. As a student, do you really understand?You obviously followed the teacher's train of thought and verified that the answer was correct. This logically rigorous, unassailable proof, you listen to every step of the way, of course, you think it's right, and you think you understand. This is the same as thinking that buying a book is equivalent to reading it, and you will lose weight if you get a fitness card. It's just that this kind of "willingness" is more subtle and less noticeable than what I said later.
So what to do when this happens?
First of all, of course, learn to listen. During class,Focus on listening to the teacher's ideas rather than memorizing the steps. Here's a simple example, for example, when you go to see a movie and walk out of the movie theater, if I ask you to tell me the movie, can you tell it in its entirety?Some people only remember a few classic lines, some people remember some great shots, or some clips. These are not enough, every movie has its logical main line, if it is not an understanding memory along this main line, the plot of the movie of more than two hours, how many people can rely on forced memory and remember?It's the same with geometry proofs, a complex proof, maybe thirty or forty steps or more. If you just remember that the answer to this question is done this way, and you can't understand why it is done, and the logical connection between it and the back, then no matter how many questions you do, it will be in vain, because the exam will hardly test the original question, and if you change it slightly, you won't do it.
Second, ask a few more whys. This is after understanding the idea of the question, you can ask yourself why you do this and not thatAt this point, you may find that you can do it with a different way of thinking, but it's a little more complicated, or even simpler. Of course, it may not be possible to do it with a different way of thinking, so why can't it be done?Why can you do this in the previous question, but you have to change the method when the next question looks almost the same?But don't ask the teacher everything, think more by yourself, summarize more, classify the questions according to the test center, establish your own knowledge system, and learn to study by yourself, which is the king. When you accumulate to a certain extent, you do have difficulties, and then you go to the teacher to talk to you, and you will have the feeling of enlightenment, otherwise, even if you ask questions every day, you seem to be working very hard and thinking, but in fact you are just a formality, pretending, and moving yourself.
When you encounter a new problem that you have never seen before, there may be several different ideas and directions for solving the problem according to the conditions given by the question. Theoretically, try them all and there's always one way to go. However, if you try every question like this during the exam, the exam time will definitely not be enough. How to quickly and accurately find the right one in several routes, this is what everyone often calls "experience". The accumulation of this kind of experience is based on Xi on the usual practice, thinking repeatedly about each question, and asking more about why it is trained. Many students only pay attention to the problems they don't know, and they just leave aside the questions they have already knew, and they don't want to listen to the teacher's lectures, and they are too late to lose time. This is actually a very bad Xi habit, the question that I will do, reflect on why I made it quickly, the question that I can't, and reflect on why I didn't think of it at the time after understanding it, this is the right way to learn Xi. If you learn without thinking, you will be reckless, and if you don't learn, you will die, that's what you say!
Finally, how do you check if you really get it?Here's a very simple way to tell the topic and tell it to your classmates, teachers, or parents. When you can understand someone who doesn't know it, then you can basically say that you really know the question. It is worth noting here that the topic is also skillful, so don't fall into the way I said before about giving an answer. When I was in the next class, I asked the students to record a question for me every day, but many students read the answers I talked about in class, which was either coping with errands or not really understanding.
As I mentioned before, although the differences in intelligence between people are sometimes very large. However, the Xi of junior high school is far from the time to fight IQ, and the correct way to learn Xi can help you get twice the result with half the effort, correct the attitude of learning Xi, and improve the efficiency of learning Xi, these factors have a greater impact on Xi performance than IQ.