Let the children play

Talking Math with Your Kids has been on something of a summer hiatus as I’ve geared up for Math On-A-Stick at the Minnesota State Fair. It has been a wild ride.

I have spent the last four days playing and talking math with kids of all ages for eleven hours a day.

My number one message coming out of this work is Let the children play.

Have a peek at our flickr photo albums to see what’s been going on. Here’s a sample (Thanks to Kaytee Reid for sharing these beautiful images).

I have been paying close attention to how children behave in this space we’ve built. I’ll just write about the plastic eggs today, but they stand in as an example for all of our activities.

When children come to the egg table at Math On-A-Stick, they know right away what to do. There are plastic eggs, and there are large empty egg cartons. The eggs go in the cartons. No one needs to give them instructions. (This is by design, by the way.)

A typical three- or four-year old will fill the cartons haphazardly. She won’t be concerned with the order she fills it, nor with the colors she uses, nor anything else. She’ll just put eggs into the carton one at a time in a seemingly random order.

But when that kid plays a second or third time, emptying and filling her egg carton—without being told to do so—she usually begins to see new possibilities. After five or ten minutes of playing eggs, this child is filling the carton in rows or columns. Or she’s making patterns such as pink-yellow, pink-yellow… Or she’s counting the eggs as she puts them in the carton. Or she’s orienting all of the eggs so they are pointy-side up.

The longer the child plays, the richer the mathematical activity she engages in. This is because the materials themselves have math built into them. The rows and columns of the egg crate; the colors and shape of the eggs; the fact that the eggs can separate into halves—all of these are mathematical features that kids notice and begin to play with as they spend time at the table.

We have seen four-year-olds spend an hour playing with the eggs.

I have observed that the children who receive the least instruction from parents, volunteers, or me are the most likely to persist. These are the children who will spend 20 minutes or more exploring the possibilities in the eggs.

The children who receive instructions from adults are least likely to persist. When a parent or volunteer says, “Make a pattern,” kids are likely to do one of two things:

  1. Make a pattern, quit, and move to something else
  2. Stop playing without making a pattern

We adults have a responsibility to let the children play. We can be there to listen to their ideas as they do. We can play in parallel by getting our own egg cartons out and filling these cartons with our own ideas.

But when we tell kids to “make a pattern” or “use the colors”, we are asking the children to fill that carton with our ideas, rather than allowing them to explore their own.

Here are some ideas children have explored in the last few days. I look forward to the next week’s worth of wonder. (Photos all shared by visitor and volunteers through Twitter and Intagram—handles are in the image titles. Many thanks to all for your generous sharing.)

A happy report from the field

Every once in a while, someone shares with me a lovely story of a conversation that they had with their kid that was inspired by the work on this blog. These stories are tremendously satisfying to me because they remind me that isn’t just me and my kids, and that it doesn’t just come naturally. Talking math with your kids is something you can learn.

Today’s report is from Zoe Ryder White, whom I have not met, but who heard about this site from a friend of the project, and who gave me permission to share it.

[I] used some tidbits already this morning – [My daughter] A. was making a giraffe and wanted each leg to be two wooden spools long. At first she wasn’t sure how many total she’d need, but when I asked how many a giraffe has, she quickly figured out the total was 8.

Before reading the talk math with our kids stuff I would’ve probably just said yep, you got it- but we ended up having a great conversation about all the different ways you could figure that problem out. SO FUN.

I am determined to raise a math-confident and math-curious kid. All the work you’re doing in your research is already making a concrete change! Thanks : )

That is the power of asking a follow up question. It is the power of asking, “How do you know that?”

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.

Post-Halloween Math Talk

File this under Talking about talking math with with your kids.

Waiting for the school bus this morning, the two adults and three children discussed last night’s Halloween events.

The neighbor girl, W (9 years old), announced that her brother, E (six years old), had gotten 90 pieces of candy for his trick-or-treating efforts. Griffin (9 years old) announced his haul of 51 pieces.

Me: Did E count each Nerd as one?

Image from Wikipedia

W: Oooo…maybe he did!

P (who is W and E’s father): We were at a house last night that had a bowl with a Take one sign. E went up, then came back and announced that he had taken three.

We told him he had to put two back.

He smiled and said, It’s a package of three!

I love this boy!

I thought for a moment about how various Halloween candies are packaged.

Me:Whoppers?

P: Yeah.

whoppers

Image courtesy of Free Photo of the Day

I am not proud that I know this sort of thing. But on the rare occasion that my extensive candy knowledge is useful, I am not going to hide it either.

So what do we learn?

We learn that there is always a follow-up question, and that the follow-up question can bring out fun stories and ideas.

The conversation could have died after E’s 90 and Griffin’s 51 pieces were announced. But I got fun stuff by asking exactly what was being counted.

We have had fun with the question of what counts as one before, when Tabitha and I talked about Eggo mini-wafflesfor example.

Starting the conversation

North American residents probably don’t need my help here. Your children probably know yesterday’s candy count cold. Ask whether the Nerds (or Whoppers or Smarties or…) count as one piece.

If Halloween isn’t a thing where you are, keep an eye and an ear open for when your children are counting things that are packaged in groups.

More fun with board games [Reports from the field]

A reader sends in a report of playing Chutes and Ladders with a 5-year old.

Of particular interest is his observation of the difference between how we structure hundreds grids in classrooms and how the Chutes and Ladders board is structured (each, notice with a ten-by-ten grid). I had not thought about that before and now have something new to play with.

hundreds.chart.1

Standard hundreds grid. Left-to-right, top-to-bottom.

Chutes and ladders board. Snaking back-and-forth from bottom to top.

Chutes and ladders board. Snaking back-and-forth from bottom to top.

Oh. Here is an important thing about Talking Math with Your Kids: When you notice differences like these, see them as opportunities to talk, ask questions, wonder and even to argue good-naturedly. It is not a problem that these grids are set up differently; it is an opportunity.

Here is rjbrow‘s report. Enjoy.

I try to play games whenever I can with my kids (ages 7, 5, and 2). Great practice with turn taking, understanding rules, making decisions etc. But like you mentioned here, games involving numbers provide a great opportunity to talk math with your kids.

I’m glad you mentioned Chutes and Ladders here too. I had written this game off because in playing it with my two older boys, frustration would ensue by the abundance of chutes that would prolong the game and sabotage their progress. After reading through your Uncle Wiggly post, I played a game of Chutes and Ladders with my 5 year old yesterday and found a couple of really nice opportunities to talk numbers.

First, each time he traveled a chute or a ladder, we had the conversation of which way to go on the new row. For example, he’d land on space 51 and travel the ladder up to space 67. So we’d talk about whether his guy should be traveling to the left or to the right. Jake figured out that if he was on space 67 he should be pointing his guy toward the 68 since it was bigger than 66. We’d also practice reading the numbers out loud. Like you mentioned, Jake can count to 100 but recognizing the written numbers is not necessarily the case. This was good practice.

You also mention that learning to count can be messy. We have a write-on number grid at home that counts 1 to 100. It’s really nice at looking at number patterns when you count by 2′s, 5′s, 10′s, etc. The numbers on this grid wrap to the next row so that all the like digits in the ones place line up vertically. Very nice. We’ve done some counting and pattern recognition using this grid. The difference with Chutes and Ladders is that the numbers wind back and forth on the way up the board. This was a shift to the counting we had done on the other grid. While this provided some nice conversation about how to work our way through this board, it did point out some messiness in how we present elementary number concepts to kids.

I hope my description makes sense. I have some pictures of our activity here:
http://brownmathwbl.blogspot.com/2013/08/chutes-and-ladders.html

Now who has a Chutes and Ladders board I can borrow to play with Tabitha and Griffin?