Tell Me About Zero, Jonah

Conversations with My Five-Year-Old Grandson

I have a five-year-old grandson named Jonah. He is five going on fifty—curious, thoughtful, and full of energy. Jonah loves learning, especially anything involving numbers, letters, and patterns. He can spend hours watching Numberblocks, Alphablocks, and just about anything that challenges him to think mathematically.

Since I love mathematics, I have decided to spend this summer exploring mathematical ideas with him and sharing our conversations here on the blog.

Today's conversation was about one of the most fascinating numbers in mathematics: zero.

Zero is a unique number. Sometimes we think of it as a placeholder in our place-value system. Other times, we think of it as representing "nothing." But how does a five-year-old make sense of such a powerful mathematical idea?

So, I asked Jonah.

Me: Jonah, what does zero mean?

Jonah: Zero means none!

Me: What do you mean by none?

Jonah: It means nothing.

I wanted him to explain a little more.

Me: Can you tell me more?

Jonah: Like no numbers, no blocks, and no colors. (Pointing to the television.)

I loved that response. Jonah wasn't just giving a definition—he was connecting zero to real situations where something is absent.

Then I asked another question.

Me: So, is zero a number?

Jonah: Yes!

Me: How do you know zero is a number?

Jonah: It's a number because it's none.

His answer fascinated me. Jonah recognized zero as both a number and as representing "none." While his explanation wasn't mathematically precise, it revealed that he already sees zero as something that belongs with the other numbers rather than as simply "nothing."

Next, I decided to push his thinking.

Me: What number is bigger than zero?

Jonah: I don't know.

Me: Is one bigger than zero? What does one mean?

Jonah: One wonderful world. One of a kind.

I have to admit—I wasn't expecting that answer! Five-year-olds have a wonderful way of blending mathematics with imagination.

What Does the Research Say?

After our conversation, I did what many educators do—I started searching for what researchers say about children's understanding of zero.

Here's a summary of what I found:

• Ages 1–3: Children understand the idea of "all gone" or that something is missing, but they do not yet connect that idea to the numeral 0.

• Around age 4: Children begin connecting the word zero and the symbol 0 with an empty set—for example, understanding that 0 cookies means there are no cookies left.

• Ages 5–6: Children typically include 0 when counting and can solve simple addition and subtraction problems involving zero. However, researchers at Stanford's DREME Center note that many children are still developing the idea that zero is a real number. Some even think that 1 is smaller than 0 because they associate zero with "nothing."

That last point made me wonder about Jonah's understanding.

Putting Zero on a Number Line

So I gave him another challenge.

I asked Jonah to draw a number line from 0 to 10 and place zero where he thought it belonged.

After a little negotiating (okay...a lot of begging from Gigi!), he finally drew one.

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What interested me most wasn't whether the drawing was perfect. It was his thinking.

Although Jonah initially said he didn't know which number was larger, he correctly placed 0 at the beginning of the number line. That tells me he is beginning to connect zero with the ordered sequence of numbers.

Like many five-year-olds, Jonah seems to understand that zero represents "none," but he is still developing a deeper understanding of how zero behaves as a number. That's exactly what we would expect at this stage of development. Mathematical understanding grows over time through conversations, exploration, and meaningful experiences—not simply by memorizing facts.

As a mathematics educator, I find these moments incredibly exciting. They remind me that children's answers are windows into their thinking. Even when an answer isn't completely correct, it tells us what ideas they are building and where we can help them grow.

What Should We Explore Next?

Now I'm curious.

What mathematical ideas should Jonah and I investigate before he heads back to school?

Should we explore:

• How zero works in addition and subtraction?

• Why zero comes before one on a number line?

• Whether you can have zero groups of something?

• Why zero is an even number?

• Or something else?

I'd love to hear your ideas.

Oh—and I video recorded our conversation! If you'd like to see Jonah explain his thinking about zero, let me know in the comments. I may just share the video in a future post.