Does the Earth have an end?

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.

6.slice.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.

  1. What do you think?
  2. Why?
  3. 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?

Book shopping

Math teacher mom (and long ago former student of mine), Megan Schmidt sent in the following report for Talking Math with Other People’s Kids month…

Her husband (who is not a math teacher) and three-year-old daughter—we’ll call her Marian—are playing “store”. Marian is trading coins and marbles for books and blankets.

Marian (3 and a half years old): I want to buy a book for mommy to read.

Dad: Pick one and I’ll tell you how much it costs.

M (grabbing a small book from her book shelf): This one is new. Mommy wants to read it to me.

Dad: That one will be 3 silver coins.

Photo Feb 07, 10 06 30 AM

M: 1, 2, 3. Now I want this one (picks a bigger book)

Dad: How much do you think this one should cost?

M: 5 coins!

Dad: How come this one is three (pointing at the small book) and this one is 5? (pointing at the larger book)

M: This book is large, the other is medium.

Megan writes that Marian is quoting Dad here and that Marian’s fondness for the number five may have more to do with her response here than a certainty that five is more than three.

So what do we learn?

Trading stuff is a fun game to play.

You don’t need all the fancy store equipment. A few coins and a few valued objects (here books) and you’re good to go.

There is so much opportunity to mention, discuss and ask about numbers. Fun, fun, fun.

While the idea that 5 is more than 3 is not at all beyond the grasp of a three-year old, I do love Megan’s tentative attitude here. It certainly is possible that Marian considers five more valuable than any number—that the large book should cost five coins because five is the best number, even if the medium book costs 23 coins.

Starting the conversation

A beautiful part of this conversation is when Dad asks Marian, How much do you think this one should cost? 

This question invites Marian to think about and to discuss numbers. It’s lovely, easy to do and is very low risk for both child and parent. It is low risk because there is no wrong answer. Marian is free to set her own price, but thinking about what that price ought to be engages her mind in a deeper way than does simply counting out the coins.

Don’t get me wrong: counting out the coins is a lovely activity too. But How much do you think this one should cost? is a brilliant conversational move that got even more thinking from a three-year old.

February is “Talking Math with Other People’s Kids” month

You won’t be hearing much from Griffin and Tabitha this month. Instead, you’ll hear from other children and their parents who have talked math and have shared their conversations with me.

It will be a ton of fun to get a peek into these other households, and to see how frequently ideas and questions about number and shape come up in life with young children.

I would love to hear your own reports, and to gather a collection of stories representing diverse families, cultures, languages and experiences. Shoot me a note describing conversations you have participated in or witnessed. I’ll feature as many of them here as I can.

Let’s kick things off with an example of a father and his five-year old daughter, and how Twitter helped them talk a bit more math than they otherwise might have…

Andy is a dad in Minneapolis. Let’s call his daughter Martine. Andy tweeted me on Friday (January 31).

Here is how this sort of thing would go in our house.

Martine (5 years old): If tomorrow is February first, does that mean today is February 0th?

calendar

Dad: Yeah, I guess we could call it that. If we do, what would yesterday have been?

M: February negative one.

Dad: Oooo. Nice! And what about the day before that?

Et cetera. At some point, the conversation would go somewhere else. Or if she’s still interested, I might give it a twist with a question like this.

Dad: So if today is both January 31 and February 0, and if tomorrow is February 1, shouldn’t it also have a January name?

I would be probing Martine’s double-naming idea for each day. And then…

Dad: Hey! I know! If today is both a January and a February day, then tomorrow should be both a February and a March day, right? What is tomorrow’s date in March?

As I mentioned, the conversation may very well have broken down by this point. But these what if questions are the things that turn a cool observation into a conversation. That conversation is where we turn kids’ minds on.

Dad Chris Hunter suggested that first follow up question: What about yesterday?

Andy asked Martine about that on Saturday.

Martine said that the day before February 0 would be February negative 1. Andy reports—and this is important—never having explicitly discussed negative numbers with Martine. No number lines, no backwards counting past 0.

But surely they have talked about the weather. Below-zero temperatures have been as common as snowflakes in Minnesota this year. Talking about the weather may have planted the idea. Then the calendar was an opportunity to make a connection.

All of this leads to two important ideas about talking math with kids:

  1. It’s not a conversation until you, as a parent, participate. Martine noticed something (Jan. 31 could be Feb. 0). Andy turned it into a conversation when he asked about the previous day.
  2. These conversations are facilitated by availability of objects. Turning the calendar became a learning opportunity for Andy and Martine. No calendar, no conversation.

You can read our full Twitter conversation here.

And you can read about other conversations facilitated by objects in these previous posts: