Why do some children have special feelings when doing thinking?

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Parents often say that they are also doing children's thinking problems. Some children just have feelings about problems. Even when they encounter a problem for the first time, they can quickly understand the meaning of the problem and always solve it. After entering primary school, these children also performed well on more difficult math problems.

Are these children born smarter? Not necessarily. Did they spend a lot of time brushing the questions? Not necessarily.

Then why are some children prone to problems? We take the most common and flexible "perception of graphics and space" (this paper is called spatial logic for short) in the thinking and math problems of primary school children as an example.

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Space, Stereo and Logic

These problems account for a large proportion.

Parents who have studied the enlightenment of children's mathematical thinking know that "space concept, three-dimensional graphics and mathematical logic" is a very important part, which is crucial from kindergarten to the lower grades of primary school, and it is also a compulsory question for many famous schools.

The perception, positioning, projection, combination, local and whole, superposition, spatial reasoning, symmetry, rotation, spatial change and graphic decomposition of graphics are also one of the most difficult contents to teach in kindergarten, and they are also the most varied questions.

Let's find a common book about children's thinking at random. Let's take a look at the catalogue of the low edition first. Of 16 thinking knowledge points, 6 are directly related to "spatial orientation", more than one third.

Let's take a look at the catalogue of thinking books in the first grade of primary school. 16 knowledge points, the number directly related to "spatial orientation" has increased to 9, more than half!

No matter what set of thinking books you make for your children, He Qiuguang or flowers, talents or ladders, no matter which organization you report to your children, you will find that these spatial concepts, three-dimensional graphics and mathematical logic are the highlights!

Why do these classic children's thinking books and junior high school Olympic math books attach so much importance to children's "spatial logic"?

Because it contains the concept of space, three-dimensional graphics and mathematical logic, it is not only a knowledge point of plane/three-dimensional geometry, but more importantly, the process of children's reasoning according to spatial orientation, which is very important for children's visual sensitivity, sense of direction and logical ability!

Then the question is coming. After doing the questions in these books, will children's spatial thinking ability really be greatly improved?

Not necessarily.

Let's take the most basic "multi-angle observation" as an example, that is, face up, face down and look sideways.

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The trap of "multi-angle"

The so-called multi-angle observation is to observe an object from different angles. For example, the top view is an image seen from top to bottom, and the side view is an image seen from left to right or from right to left. The basis of multi-angle observation is to face up to the perspective, that is, what it looks like from the front.

This is one of the important cornerstones of children's thinking.

For example, the simplest overlooking topic usually appears in children's thinking books and pamphlets of 4-5 years old-for example, what does this cup look like from top to bottom?

Parents/teachers usually use physical objects as examples, and children will practice several times against physical objects. This difficult topic is basically not a big problem.

But the problem is coming, because the difficulty of many basic children's thinking books only ends here, so many parents think that "multi-angle observation is very simple, done!" .

But once the topic changes, many children are embarrassed immediately.

For example, if it is the front view of the combination graph, we should also consider the left and right distribution. Many children will make repeated mistakes even if they do the problems repeatedly.

Sometimes the concept of three-dimensional is added. In fact, we adults look simple, but children make mistakes easily.

Sometimes the topic is like this

The above questions are actually not difficult, but children are prone to make mistakes.

When there are problems such as "graphic superposition", it is more likely to make mistakes because the foundation of multi-angle observation is not firmly laid.

Looking back, in fact, to make this kind of topic invincible, the method is very simple, just use three-dimensional blocks with any basic shape at home, the building blocks are the best, and the others are ok.

10 minutes, get it now!

Many children's thinking books are just a combination of living items and even items, but in fact, multi-angle observation means showing children the simplest and most basic shapes first, and then unfolding them a little bit.

For example, take a basic cuboid building block as an example.

Let the children observe first, and observe what figures are on all sides of this rectangular building block from all angles.

Similarly, you can let children observe the basic shapes such as cubes and cylinders and look at each side of them.

Simple, isn't it?

Then let's use our brains, find a cube and observe at what angle the following picture will be displayed.

Let's spin this cube building block. When looking up at a 45-degree angle, do you find that when the edge of the cube is in the middle, it looks like the above picture?

One-on-one view, isn't it intuitive? The child will suddenly find out, "You can still see it this way!"

With the foundation laid in the above picture, let the children observe it again. Which observation angle of the triangle does the following four views correspond to?

Can't stop playing? Then let's use arches to strengthen it. It doesn't matter if there are no arched blocks at home. Watching the video will be very intuitive.

Again, this is a semicircle, but the question is, what about the middle and right views?

When you show the building blocks to your children, you will immediately find that the bottom of a semi-circular building block and the plan of one side are two rectangles with different shapes!

Look, the power of multi-angle observation is slowly emerging!

When we help children lay a good foundation and see any figure, children's thinking will be conditioned and viewed from all angles. A little flexibility in the topic will solve it.

For example, let's introduce the concept of "graphic overlay".

How do the semicircle and cylinder overlap, as shown by the white line in the figure below?

Look, the plan view of the cylinder is actually rectangular, and the bottom of the semicircle is also rectangular. Hide the bottom of the semicircle behind the cylinder. It's done.

The above logical reasoning ideas are difficult for children to understand if they are simply brushed or dictated, but they will be understood at once through the demonstration of building blocks.

You see, the seemingly difficult problem in the picture below, in fact, after the above 10 minutes of teaching, the child can easily solve it, and his ability to acquire new knowledge is actually stronger than you think!

Transformation from physical objects to themes

Multi-angle observation. That's it? No!

Let me ask you first, how do you teach your children to "observe from multiple angles", such as from head-up to overlooking?

Do you squat down to look at the front view of a cup first? And stand up and look down at the top view of this cup? Sometimes you have to move to the left and right of the cup to observe the side view;

Even if you are tired, the angle of observation between you and your child is often biased; Especially when several items are combined together, and even there are some traps in the topic, the child may be confused immediately.

In fact, as long as a child has undergone several standard perspective changes, he can immediately construct the imagination of spatial thinking; However, it is often difficult to provide a "standard top view" or a "standard side view" even if the institutional teacher teaches, just drawing and showing.

Actually, it's not difficult. You can do it in the video-

Observing the superposition of graphics from multiple angles is a problem that many children will do wrong, but let the children follow the channel of the lens and observe it from head-up to standard overlooking at once. Is it exactly the same as the picture and text on the topic?

Children can finally connect the topics in the book with real life!

Also, for example, if you look from right to left, which picture do you see on the topic? Gently turn in front of the child with a special turntable to immediately present a standard side view.

The above videos are from "Big Hands Holding Small Hands" and "Building Block Thinking Classroom" jointly produced by primary school mathematics teachers, Olympic mathematics teachers and children's thinking teachers from top schools in Shanghai. They not only grasp all the knowledge points of spatial thinking from kindergarten to primary school, but also use a variety of lens special effects that are difficult to achieve at home and in institutions, so that some particularly important and difficult children become intuitive and easy to understand at once.

We often say that some children have special feelings when doing problems.

This feeling is not imaginary, but let the children operate and perceive themselves through very intuitive sensory understanding from the beginning.

When the child sees the corresponding relationship between the actual object and the meaning of the question with his own eyes, he immediately establishes the corresponding concrete concept in his mind. Over time, concrete concepts rise to abstract thinking, and children's application of knowledge points will become more and more complete.

No matter how flexible and difficult the topic is, the child will have an answer.

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