Talking Math with Other People’s Kids Month continues…

A while back, Rafranz Davis reported a conversation on her blog. She writes frequently about the adventures she has with her nephew Braeden. I asked, and she gave me permission to remix a conversation she and Braeden had about the ends of shapes—especially the ends of the Earth.

—

Rafranz and Braeden (8 years old) are spending some quality weekend time together when he asks a question.

**Braeden:** Does the Earth have an end?

**Rafranz:** Braeden what do you mean by “does the earth have an end”?

**B:** I’ve been meaning to ask you this question for a long time, at least 2 months. I’ve always wanted to know if the earth stops when you get around it.

Rafranz is a master at the art of mathematical conversation. She asks Braeden a question that gets him talking and thinking.

**R:** What shape do you think that the earth is?

**B:** I think that it’s a circle.

**R**: Really, why a circle?

**B**: A circle is round.

**R:** Hmm, interesting. So what shape is that basketball? (The nearby ball may have sparked Braeden’s thoughts)

**B:** It’s a circle.

**R:** What about a pizza?

**B:** It’s a triangle.

This is great! Miscommunication. Rafranz is asking about the *whole *pizza. Braeden is thinking about a slice of a pizza.

**R:** I mean a whole pizza. What shape is a whole pizza?

**B:** It’s a circle

**R:** Why do you think that a pizza is a circle?

**B:** It’s round and has a center.

**R:** Earlier you told me that a basketball is a circle and a pizza is a circle. Are they the same?

Again—great move here. Braeden has identified the basketball and the pizza as being round, and therefore circular. Rafranz asks him to *compare* these two things and to look for differences. She is using Braeden’s curiosity to pursue some deep and important mathematical questions.

**B:** No, the pizza is flat. The basketball is round…like Earth. The pizza does start and stop when you get all the way around but the basketball can keep going around and around and around.

**R:** What do you mean around and around and around?

**B:** If you had a really long string, you can go around the pizza one time but a basketball, you can keep wrapping the string forever. I know why. The basketball is a sphere. (I had no idea that he knew this word)

**R:** What about Earth?

**B:** I think that earth is a sphere too and I don’t think that you can go to every single place on earth. I bet that you can keep going around and around and around.

## So what do we learn?

Rafranz asks three simple questions at exactly the right moments in this conversation.

- What do you think?
- Why?
- Are they the same?

It turns out that Rafranz really didn’t know enough about Braeden’s original question to answer it the first time around. Those were sincere questions she asked, and they produced a genuine conversation.

Ultimately, Braeden knew that if you walk around the outside of a circle, your path comes to an end—you end up back where you started, having visited all locations on the circle. But if you do this on a sphere, it seemed to him that your path does not necessarily end up back where you started. It’s a lovely insight about the relationship between two-dimensional objects and three-dimensional ones!

## Starting the conversation

If you are new to talking math with your kids, don’t worry about getting the timing right. Just start to make a habit of asking those questions. The first few times, you may not get much. That’s OK. It can be like introducing new foods—children need multiple exposures to new things before they accept them. The other question to add to this collection is *How do you know?*