**What? How could addition in a column possibly hurt a child?!**

Addition in a column is actually a convenient way to calculate for someone who has understood the way we write numbers. For a child who has not yet understood it in depth, addition in a column is a way to solve the exercise without understanding anything!

If I see it that way

This is a beautiful way to calculate the result

But if I see it that way, thoughts are running through my head

Why do we do this? How is it related to the exercise? Is the result I arrived at correct? Why?

**What is the child experiencing and understanding?**

In the latter case, the child experiences enormous frustration. The main thing the child understands subconsciously is “Math is not for me.” It is possible to solve exercises without understanding – that’s how math is.”

From experience with many children, at this stage psychological barriers develop that are not yet visible. They usually break out in learning multiplication tables or fractions.

**So how do you know if my child is hurt?**

It’s just like asking if my child understands or solves technically without understanding.

Over the years, I have discovered a good way to identify if the child understands how a number is built.

I give him to solve these exercises. Row by row in order.

And I see if he calculates the right exercise or for example in the first row if he understands that if 5 + 1 equals 6 then 50 + 10 equals 60 and therefore solves it right away.

If he calculates each exercise again, it is a sign that he has not yet internalized the decimal system for writing numbers.

Then I give him to solve exercises like this in a column

And I see if at some point he understands in this example that the units digit will always be 6

If he calculates each time again, it is a sign that he has not yet internalized the decimal system for writing numbers.

**What percentage of children are affected?**

In my rough estimate, at least 25% of children learn addition in a column before they are ready to understand the decimal system.

The thought that all children are ready to understand how a number is built at the same age is completely crazy.

For example, at a university in the United States, they checked at what age children can solve an exercise like 4 + 3 without counting on their fingers. And they found that half of the children in second grade are still not ready for that.

Another example, I asked Bard, Google’s AI, to assess the readiness of children to start learning math, and these are the results:

Age | Percent of Children Ready to Learn Mathematics

——- | —————————————-

3-4 | 20%

5-6 | 50%

7-8 | 70%

9-10 | 80%

11-12 | 90%

13-14 | 100%

**What to do if my child solves the exercises without understanding?**

All children will understand in their own time how a number is built, even if they do not learn mathematics.

If possible, wait with solving exercises in a column and in the meantime solve only horizontally.

If you must accelerate the process, there are a few options:

- You can use the lesson series Creating a numerical language – Part I & II from our blog
- You can give them exercises like in the pictures
- In our learning course, there is a dedicated application for this. Soon it will also appear in the worksheets section in our site.

I hope I was helpful,

Ami.