Idea
One of the most common worries I hear from parents and see on online forums is:
“My kid didn’t fully understand this concept. Should we slow down? Should I be worried?”
The truth:
In fact, many mathematicians would say it takes three to five exposures to really understand something.
The first time: you get the shape of the idea
The second time: you notice what you missed
The third time: it starts to click
The fourth and fifth time: you can actually use it
So if your kid does not fully understand a concept the first time they see it, that’s not a problem.
It’s natural and expected.
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This is not a flaw in your child, nor is it a flaw in the material.
It’s just how learning math works.
Even if they are a “math-y” kid.
Story
There’s a wonderful (and very human) story about two famous mathematicians: Hermann Weyl and David Hilbert.
Hermann Weyl and David Hilbert are discussing this very topic.
For some context, a quick snapshot of their background.
Hermann Weyl was a German mathematician whose research was in theoretical physics and number theory, and he had been described as one of the “last great universal mathematicians of the nineteenth century.”
David Hilbert was a German mathematician described as “one of the most influential mathematicians of his time,” and in 1900 presented a collection of 23 problems known as “Hilbert’s problems” that have helped drive mathematical research ever since (note: many of them are still unsolved!).
Weyl asked Hilbert:
“How many times do you have to explain something to your students before they understand it?”
Hilbert replied:
“Five times, Hermann, five times. But for very talented students like you, three times is enough.”
Even among the greatest mathematicians, understanding wasn’t expected to happen instantly.
It took repetition.
Personal Example
A few months ago, one of my kids was learning a new concept in geometry.
They followed the lesson and could do some of the homework.
But there were some problems they couldn’t solve because they couldn’t quite grasp how the lesson topic related to the problem.
Instead of stopping everything, we kept going.
As a rule of thumb, if they’re getting about 60–80% of the material, we move forward, trusting we’ll see it again.
A week later, the same idea showed up again, only this time inside a new type of problem.
And suddenly:
“Ohhh… that’s why we did that.”
The problems that once felt impossible became solvable (and were!).
This has happened to us so many times that we now expect it to happen
Which is why we don’t aim for 100% mastery the first time.
Getting to 100% is nearly impossible the first (or even second) time, so we keep going, knowing eventually they’ll get it.
Each time they revisit the concept, their understanding deepens, not because they stayed longer, but because they saw it from a new angle.
What at first looked like confusion was actually the beginning of understanding.
Why it matters
If we expect children to “get it” the first time, two things happen:
Kids feel like they’re failing when they’re not
Parents feel like they need to intervene too early
Real understanding of math is layered and takes time.
This is why many math curricula (even traditional ones) are designed to spiral:
Concepts come back again and again
Each time with slightly more depth
Each time making more sense
With space in between, so the idea feels “new” again
There’s also another important piece:
Sometimes a child doesn’t understand something because they don’t yet see why they need it.
For example, many students struggle with high school algebra, not because algebra is too hard, but because they haven’t yet seen why it matters.
Then they encounter calculus or physics, and suddenly those same algebra rules become essential.
When I’ve spoken with (high school and college) calculus teachers, they often say:
It’s not the calculus that students struggle with; it’s the algebra.
In many cases, a student’s real understanding of algebra arrives during calculus.
There’s even a saying:
“You don’t understand a class until you’ve taken the class that depends on it.”
That is, understanding often arises when the context for why and how it’s used emerges.
Practical tip
Instead of asking:
“Do they fully understand this?”
Try asking:
“Have they seen this enough times to be familiar with it?”
And if they haven’t seen it enough times, you don’t need to:
You can simply:
One of the advantages of learning today is that “another source” is easy to find:
Different explanations unlock different insights.
Takeaway
Your child does not need to understand a concept the first time they see it.
They need to see it multiple times, in multiple ways, over time.
The key to getting good at math is to keep doing math.
So if frustration creeps in (for them or for you(!)), take a breath and keep going.
That’s how deep understanding is built.
How to practice
Try this small shift the next time your kid says:
“I don’t get this.”
Say:
“That’s okay. You might not have seen it enough times yet.”
Then:
You can even make it explicit:
“You’re going to have to see this idea a few more times before it clicks.”
Over time, your child will internalize the incredibly powerful lesson:
Really, truly believing this lesson will help them not only in math, but in anything else they choose to learn.
That’s all for today :) For more Kids Who Love Math treats, check out our archives.
Stay Mathy!
Talk soon,
Sebastian