How a First Grader Naturally Developed an Understanding of Multiplication
How a First Grader Naturally Developed an Understanding of Multiplication
On the free Minten × Kogaku “Parent School” members’ website, we introduce ways to help children develop a natural understanding of numbers.
Recently, we received a wonderful message from a mother who has been putting these ideas into practice.
She is Ms. N, a mother in her 30s and a member of Minten’s HGM program.
Her son is six years old and currently in first grade.
One night, as she was putting him to bed, he suddenly said:
“9 + 9 + 9 is 27… right?”
And then he fell asleep.
The next day, his mother asked him, “What did you mean by that last night?”
He replied:
“9 + 9 + 9 is the same as putting 5 + 5 + 5 and 4 + 4 + 4 together, so it makes 27, right?”
This Is Actually Quite Remarkable
At first glance, what he said may seem simple.
But when we break down what he was actually doing in his head, we can see that he had naturally developed several important mathematical concepts:
- Thinking of numbers in groups
- Skip counting
- Understanding regrouping and carrying
- The concept of multiplication
- Breaking numbers apart and recombining them
He has developed these skills naturally and is using them to think through problems on his own.
What is even more impressive is that he can explain his thinking in words.
This kind of numerical intuition can also become very useful later, when children begin learning algebra in junior high school.
For example, many students struggle when they first encounter expressions such as:
3(5X + 3)
A child who already understands how numbers can be grouped, broken apart, and recombined has a much stronger foundation for understanding expressions like this.
I don’t think he will have much trouble with mathematics when he reaches junior high school.
But What Is Especially Impressive Is His Mother’s Daily Effort
Of course, her son’s progress is wonderful.
But we also think Ms. N herself deserves a great deal of credit.
We gave her suggestions such as:
- “Count numbers together with your son every day.”
- “Next, try counting by threes and by fives.”
- “Save some coins and count together every day to see how much money has accumulated.”
- “When doing calculations, encourage him to work them out mentally rather than using written calculations.”
Ms. N faithfully put our suggestions into practice.
We are also very happy that she sends us updates on LINE showing us how things are going!
Day after day, she counted together with her son:
“1, 2, 3, 4, 5, 6…”
“3, 6, 9, 12…”
I’m sure there were days when this wasn’t easy.
There were probably times when her son didn’t feel like doing it.
But because she patiently continued incorporating these activities into everyday life, her first-grade son has naturally developed an understanding of number groups, skip counting, regrouping, multiplication, and number decomposition.
And the important point is that these abilities develop when parents help children experience numbers naturally in everyday life. They cannot be developed in the same way simply by completing worksheets.
When children are encouraged to calculate mentally, they begin discovering their own ways of solving problems.
From there, their thinking can expand in all kinds of directions.
If children only work through worksheets given to them at school or cram school, they may learn standard methods, but that alone does not necessarily bring out each child’s unique way of thinking and individual potential.
Small Daily Efforts Can Lead to Remarkable Growth
As Ms. N’s experience shows, small things repeated every day can eventually lead to tremendous growth in a child.
We will continue sharing practical things parents can do today to help their children develop the abilities they will need to thrive in the future.
All of the advice we gave Ms. N is available on the Minten × Kogaku “Parent School” free members’ website.
If you have young children, we hope you’ll give these ideas a try.
“Counting numbers”
“Skip counting”
The ideas themselves sound very simple.
But their potential is enormous.
Families who actually put these methods into practice have seen significant progress within just a few months.
%sei%, we hope you’ll try them with your child too!
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https://allgeniuses.com/ndcg
The English-language version of the website is currently under development.
