Middle School Entrance Exam 5th Grade: The reason why they can read the problem and understand how to solve it, yet still get it wrong

"I can read the problem text."

"I'm underlining the necessary parts."

"I can explain how to solve it."

And yet, they get it wrong when it comes to the test.

The intermediate steps aren't significantly wrong, yet the answer doesn't match.

I used to think, "Maybe it's just a careless mistake."

But I realized something when we entered the math unit on saline solutions.

The cause was at a much more fundamental level.

They aren't visualizing it.

For example,

"20g of salt was added to 300g of 10% saline solution."

They know how to solve this problem, and they know what they need to find.

But in their head,

it seems there are only the numbers "10," "300," and "20."

On the other hand, my eldest son was different.

He has a cup in his head.

"There is 300g of saline solution in it."
"20g of salt was added to it."
"So, only the salt increases."
"The total amount increased and it became more concentrated."

He can see this scene.
That's why he naturally knows which numbers to use and how to use them.

Actually, this wasn't just limited to math.
It was the same for Japanese.
They can read the text.
But the appearance of the characters and the scene aren't coming to mind.
Science is the same.
They aren't visualizing the experiment.

In other words,

the "ability to visualize" was the foundation for all subjects.

Come to think of it, even when we talk normally, things are often disjointed, the point gets missed, or things don't get across well.

They aren't listening while visualizing what I want to say!

I told them, "I don't think you are visualizing things; let's practice visualization!"

So, I first narrowed down the countermeasures to one thing.

Thoroughly turn the problem text into a diagram.

For saline solutions, first draw a cup.
For percentages, draw price tags or tape diagrams.
For speed, draw a path.
For Japanese, simply draw the characters or the scene.

"Diagram before writing the formula."

I decided to make this thorough.

It doesn't need to be a good drawing.

What's important is to create the scene in your head.

The reason why scores aren't improving might not be the method of solving.

Being able to visualize.
I also think this might be proportional to mental age.
I also think that children who can visualize naturally are the so-called top tier of middle school entrance exam takers.

Our experiment has begun to see how much this ability to visualize can be acquired and used as a habit.

If there are other children like this, before changing how you teach them,

"Is this child able to visualize the problem?"
please observe them.

Today, in our home, we are drawing diagrams before writing formulas.
A large number of beakers.