In contact with you these days, I found that some friends are dismissive of "learning strategies" and think that it is empty talk and useless. Actually, it's not like this. As we know, the so-called strategy, that is, the strategy of "dispatching troops", is manifested in learning, that is, being able to "call" what you have learned to solve problems better. Here, knowledge is the "soldier" called by children.
As everyone knows, in the process of solving problems, children are actually calling the knowledge they have learned. In fact, they are using the knowledge they have learned as "soldiers", and then attack the city to solve the problem. Obviously, there is a "phone call" behavior in the process of solving problems, but the child does not realize it.
Since the behavior of "yelling" already exists in children's learning, how can it be possible not to learn the ability of "dispatching troops"? How can you not learn the skill of "arranging troops and deploying troops"? Because "learning strategies" can help children better "call" their own knowledge and better clear the obstacles to the "ivory tower". On the way to study, every child can become his own strategist, just want to be a problem, that's all!
Learning strategies, to put it bluntly, are "the idea of calling knowledge" and "the method of calling knowledge". If you win the essence of "learning strategy", your child will get twice the result with half the effort.
Course review
Last class, we talked about "the source of mathematical logic ability", that is, knowledge points, that is, the ability to understand knowledge points. "Mathematical logic ability" is not produced out of thin air, but has its source. As long as the learned knowledge points are thoroughly understood and digested, a powerful "mathematical logic ability" arises at the historic moment.
Some people say that logical ability mainly depends on IQ, but I totally disagree. Now, some children are not smart. Children play games with mobile phones and computers, far behind adults. Aren't all children who don't study well smart? Are they all low IQ? Obviously not, what they lack in their minds is not IQ, but knowledge for them to call, and "soldiers" for them to send! A general without a "soldier" is an "army of one man". No matter how high his IQ is, it is useless!
If you are divorced from knowledge, no matter how high your IQ is, it will not play much role. Just like Zhuge Liang, out of the battlefield, he is a weak scholar, and the reason is the same.
Now that the source of mathematical logic ability has been found, the method to improve mathematical logic ability has also been found, that is, first understand the knowledge points thoroughly, and then do the problem, which is like knowing how to use the gun first and then going to the battlefield. What to do first, then what to do, this learning order is very important. In the right order, you can get twice the result with half the effort. If the order is wrong, you can only get twice the result with half the effort.
So, how can we thoroughly understand the knowledge points? How can we see the "truth of knowledge points"? To tell the truth, it is too easy for children to understand a knowledge point now, because there are too many ways to understand it: there are countless teaching reference books used by children to match textbooks, even more comprehensive and detailed than the books used by teachers for filing. If not, they can directly search online. There is nothing you can't find, only what you don't want to search.
Some legendary "lever essence" has emerged, saying that if you do more questions, you will have everything. I didn't say not to let the children do the problem. I mean to thoroughly understand the knowledge points before doing the problem. What I said is too straightforward, and some people will misunderstand me.
There is nothing wrong with doing problems to consolidate knowledge points, but doing problems is based on understanding knowledge points. It's like learning to drive before you hit the road. Practice makes perfect. The purpose of brushing questions is actually to let children flexibly use what they have learned in actual combat, so as to achieve the goal of practice making perfect. But you have a little knowledge of the knowledge points, even in the fog, and you are in a hurry to brush the questions. Isn't that tired? Get twice the result with half the effort. Isn't that tired?
I won't go into details about "the source of mathematical logic ability" here. Interested friends pay attention to me and then go to my homepage to watch the whole course!
universal phenomenon
Some children, especially those in the lower grades of primary school, do not pay attention to the wonderful use of draft paper when doing math problems. In their view, it is a bit troublesome and redundant to draw on draft paper and write on homework paper. They think that draft paper has increased their homework burden and they are very tired. They prefer staring at math problems in a daze. In fact, these children also know the wonderful use of draft paper, but they don't know how to use it. They prefer to spend 10 minutes to solve problems that can be solved with draft paper 1 minute. Why?
Some children often become speechless and have nowhere to start when they do math "graphics problems". What are the original graphics in their eyes? For example, it was originally rectangular, but it was still rectangular in their eyes. In fact, if an auxiliary line is added to turn the rectangle into a triangle, the problem will be solved, but he won't think so. They know the function of auxiliary lines, but they just can't draw them. Why?
The same application problem, some children can solve it neatly with "one-yuan linear equation", and some children list "multiple linear equation", and the result is that they can't find the solution of the equation, and finally they are embarrassed. Why?
Don't worry, we will find the answers to these questions in the following content. In fact, this is the wonderful use of "the idea of mathematical transformation of mathematical strategies" to be talked about today.
In fact, in my opinion, these problems are the legendary "knowing only one, but not the other", and "one" and "two" are not linked together, which has caused the above embarrassing situation. No suspense, get to the point:
Mathematical transformation thought
The word "mathematical transformation of ideas" is quite mysterious at first glance, but it is actually very simple. Just from the meaning of the word "transformation", it can be understood as a close relationship, which is nothing more than the transformation of "this" into "that" or "that" into "this".
In order to better understand the idea of "mathematical transformation", let's give a vivid example:
Everyone has seen the "doll machine", and it is often seen at the entrance of the supermarket. You can usually catch it by tossing a coin. If you catch it, it's up to you If you can't catch the coin, it will belong to someone else. Looking at a big bargain in front of you, it's hard to catch it. Children like to play and have fun. Whether you are caught or not, it is worthwhile to spend a few dollars to buy a happy one.
However, if this doll machine can only play with coins, paper money can't. That is to say, although they are all money, in front of this doll machine, banknotes don't play with attributes, but coins play with them. And you only have paper money and no coins. If you don't change the paper money into coins, the child may cry all the time and the problem will not be solved. In other words, only by "converting" paper money into coins and then playing with the "game attributes" of coins will children stop crying and the problem will be solved. Converting paper money into coins is a life application of "changing ideas" in itself.
In this example, it is obvious that if the paper money is not "converted" into coins, then the problem will not be solved, that is, if the "transformation of ideas" is not used, the problem will remain unsolved. It's like a "graphics problem". Without drawing auxiliary lines and "transforming" the rectangle into a triangle, the problem will not be solved. The reason is the same.
So, what exactly is changing ideas? What transformation ideas are often used in mathematics?
Whether in life or in mathematics, the application of transformation thought is actually everywhere.
The process of buying and selling things is actually the process of using "transforming ideas". Buying is turning money into things and trying to solve your own problems with the characteristics of things. Sales is to turn things into money and try to solve your own problems with the characteristics of money.
The process of cooking is actually a process of "changing ideas", transforming inedible rice into edible rice and using the characteristics of rice to solve the problem of "hunger" ... There are too many examples in real life.
Children often encounter the problem of "unified unit" when doing problems. In fact, this "unified unit" is the application of "transforming ideas". Children use draft paper to draw pictures and use the intuitive characteristics of graphics to help solve problems. In fact, this is also the application of "transformation thought", that is, the mutual transformation of "number" and "shape" To put it bluntly, "the idea of combining numbers and shapes in mathematics" is one of the "transformation ideas".
There are countless examples of "changing ideas", which can be seen everywhere. In fact, children have been using it in the process of doing problems, but they are not aware of this idea. So, what is "changing ideas"?
The so-called "transformation of thinking" is to transform "this" into "that" and use the characteristics of "that" to solve problems that cannot be solved by the characteristics of "this". The reason why "this thing" is transformed into "that thing" is because before the transformation, the characteristics of "this thing" alone are not enough to solve the current problem. Only by transforming it into "that thing" and using the characteristics of "that thing" can we better solve the current problem. To put it bluntly, there is no "this" and there is "that", and the exchange of needed goods will solve the problem!
At this point, some friends still don't understand what "transformation" is, so let's put it more bluntly, that is, transforming "one thing" into "another thing" with the purpose of solving problems, that is, helping "this thing" solve the problems it faces but this thing can't solve.
Don't you understand? Well, let's cut to the chase, turn "you" into "him" and let "him" help you solve the problems you face. Whether you understand it or not, as long as you understand that "the purpose of change is to finally solve the problem" is enough!
After reading the friends in these six classes, I believe everyone knows that I am talking about the strategies, ideas and methods of transferring knowledge. If the child doesn't even understand the knowledge thoroughly, then all this is empty talk. This is just like Han Xin, no matter how fierce he is. If there is no soldier's order, he is just one person.
Having said these six lessons, I just want to help children learn happily from a strategic perspective. I just want to express a point that "learning methods are too important" for children. Efforts without methods will get twice the result with half the effort, and efforts with methods will get twice the result with half the effort. In real life, it depends on who learns, not who spends more time. Some children have been working hard, but they just can't get into a good school. Why? That is, the method is wrong. If nothing else, never underestimate the IQ of a child.
Of course, what I'm talking about is just a scratch, which is just my personal understanding. Not necessarily for everyone. If you think it's useful, take it. If you feel useless, it's equivalent to listening to me for a while. But there is nothing wrong with my direction, that is, I hope children can find a suitable learning method to make themselves learn more easily, happily and efficiently. A good learning method is a child's wings!
Let's get off topic and get to the point!
explain
"Reform thought" includes "unequal reform" and "equivalent reform". I won't say "unequal transformation" here, and interested friends will find out for themselves. Let's focus on the "equivalent transformation" that children often use in learning mathematics.
So, what is "equivalent transformation"?
The so-called "equivalent transformation" means "the essence has not changed, but the form has changed." It sounds a bit abstract, so let's give an example and you will understand. 10 Jin of water forms 10 Jin of ice, and the weight does not change, but the liquid becomes solid. Although it is in different forms, although it is called differently, it is actually the same substance.
"Equivalent transformation" is mathematically expressed as "the numerical value of the size has not changed, but the form has changed". In fact, this is easy to understand, and an "=" that often appears in children's eyes illustrates the problem. Equal to both sides of the symbol, no matter how it changes, the values on the last two sides are equal. To put it bluntly, all formulas that can be connected by "=" are "equivalent transformations". It's as simple as that, there's no need to delve into it.
Obviously, all equations, that is, "equivalent transformation", can be transformed into the right of the symbol, and the right of the symbol can be transformed into the left of the symbol. No matter "turn left and turn right" or "turn right and turn left", its purpose is to solve the problem better, and it is convenient to do whatever you want.
Let's take a junior high school question about "one-dimensional linear equation" to illustrate the application of the idea of "equivalent transformation":
The school bought 100 apples and distributed them to Class A, Class B and Class C in Grade One. If there are five more apples in class A, 10 in class B and 13 in class C, then the number of apples in the three classes is the same. How many apples did the three classes receive respectively? (Required, solved by one-dimensional linear equation)
If you haven't studied the idea of "mathematical transformation" and don't know the magical function of "transformation", then this problem will be difficult to solve, and some students may solve it like this:
Class a got a, class b got b and class c got c, so according to the meaning of the question:
a+5 = b+ 10 = c- 13； a+b+c= 100，
Here, the children have no way to start.
Then if a, b and c are all converted into one of the letters, for example, a and b are all converted into relationships with c, and then an equation containing only c is formed, the problem will be solved. As follows:
A+5 = C- 13, and a = c-13-5 = c-18 after transformation;
B+ 10 = C- 13, and b = c-13-10 = c-23 after transformation;
After the transformation is completed, list one-dimensional linear equations:
(c-18)+(c-23)+c =100. If we get C = 47, A and B will be solved.
Of course, if both B and C are transformed into relationships with A, an equation containing only A can be formed, or if both A and C are transformed into relationships with B, an equation containing only B can be solved.
In fact, the idea is very simple, that is, three different things are converted into the same value, so that an equation only contains the same thing, and it is of course simple to solve. If this "transformation idea" is clear, in fact, this problem can be solved like this:
Let three classes have as many apples as X, and then "convert" the number of apples in all three classes into the relationship with X:
X = a=x-5, then a = x = a+5;
X = b+ 10, then b = x-10;
X = C- 13, then c = x+13;
Finally, (x-5)+(x-10)+(x+13) =100, and the solution is x = 34. Then, A, B and C are solved.
No matter what kind of scheme, it is all around the "transformation idea" of "changing differences into the same"
If some children have never learned equations, in fact, this problem can be solved without equations, then I will leave it to the children to think for themselves. I won't go into details here. Interested children can write their own answers in the comment area, and I will reply when I see them.
Course summary
It's really a collapse to be generous enough to confiscate horses. As long as we can get the essence of "transforming ideas with mathematics", we can think that I have not worked hard in vain.
Cut the crap and summarize directly:
The idea of mathematical transformation mainly uses equivalent transformation, that is, transforming this thing into that thing and solving the problem of this thing with the properties of that thing. In a word, "invariability" should be "change", what remains unchanged is "size value" and what changes is "expression form".
When solving the "quantity problem", the left side of "=" is generally transformed into the right side of "=", or the right side of "=" is transformed into the left side of "=", and any transformation can solve the problem. What is often used is to use the relationship between different things to "equivalently transform" them into the same thing and then solve it.
When solving "graphics problem", it is generally to convert one graphic into another, and then use the "properties" of another graphic to solve the graphics problem before conversion.
Ok, let's call it a day. I don't know if I made it, but I'm exhausted myself. Let's talk about "the punching method of learning strategies" in the next class, so be there or be square!