If you follow me on Twitter, you know I am a devoted acolyte of Christopher Danielson and his Talking Math With Your Kids ethos. I truly love teaching middle schoolers, but nothing compares to the joy I get from talking with young children about how they perceive numbers, shapes, and patterns.

A couple of years ago, Christopher wrote a great post about the board game Uncle Wiggily, which I promptly ordered online. It sat on the shelf until my son Joel, who is 3 1/2, asked to play it.

And so we played Uncle Wiggily. And then we played it again the next night, and the next. And we have continued to play it five or six nights a week for the past three months. My wife and I may not always read to Joel for 20 minutes a night, but we definitely play Uncle Wiggily for 20 minutes a night.

As you might guess, I got bored with playing Uncle Wiggily much faster than Joel did. It is a game that is entirely based on luck, which means there are no decisions to make during the game. So to stave off boredom, I have found questions and minigames to play with Joel. I realized that they provide a good roadmap for how I talk math with my own kids.

Uncle Wiggily has been a wonderful way to help Joel develop one-to-one correspondence (the idea that each number corresponds to one item in a group). In the game, you hop your bunny along the path according to the number listed on the card.

He was pretty good at counting objects in groups of ten or less, but he was less comfortable counting spaces. He would often speed up his counting so that he would count to ten but only hop seven or eight spaces.

So I tried to mess with him by taking a cue from Christopher and deliberately messing up, seeing if he would catch me. But I was much less subtle than Christopher. I would draw a three and then jump seven spaces at a time. Or I would draw twelve and only hop a couple of spaces while I raced through the numbers as fast as possible like "onetwothreefourfivesix…"

Joel loved acting as the Uncle Wiggily police and showing me how to play the game correctly. He found it very funny, which showed me that he was beginning to understand the importance of one-to-one correspondence. This sort of violation of the rules is only funny if he knows which rules are being violated.

Having gotten bored with counting and miscounting, I started asking Joel to compare cards, as in the videos below:

This was a fun extension because the game gave Joel a reason to care about the relative size of the numbers. By playing the game over and over, he got a sense of which cards allowed him to move farther along the path to Uncle Wiggily’s house. If I had shown him the numbers 7 and 4, I don’t know whether he could have told me which number was greater. But in the context of the game, he has a reason to care which is greater. The math is embedded in the game.

Notice in this video how he doesn’t have a complete understanding of the difference between 8 and 9. But he knows how they relate to 7, 5, and 1. It’s really interesting to me to see those ideas as they begin to cohere. Also note that I have followed Christopher’s advice and chosen not to correct every little mistake he makes. I am much more interested in the overall idea of comparison that Joel is working on.

But then Joel got bored with this game, and it kind of interrupted the flow of Uncle Wiggily, so I needed a new activity.

Space 58 on the Uncle Wiggily game board is a very important space. It’s the Rabbit Hole, which automatically sends the lucky rabbit all the way to space 83. Consequently, Joel spends most of the game talking about how he hopes he lands on the rabbit hole. So once he got to space 45 or 50, I started asking him “What card will get you to the rabbit hole?"

This is a bit of a reversal of the normal game because Joel has to count first and then decide which card will get him to the rabbit hole. If he counts five spaces, he knows he needs a five (this is known as cardinality, the idea that the last number you count to represents the total group).

Joel liked this idea so much that he now checks every round when he is close to the rabbit hole to see which card will transport him to space 83. Nothing has made me happier than to see him count out five spaces, say “I hope I get a five!” as he draws the card, draw a six, and then glumly move his bunny directly to space 59. This is the only time I've ever seen him move his bunny directly to the correct spot, by the way.

One night, I picked my card but didn’t show it to Joel. Instead, I told him to guess. Joel loved this game, and insisted we play often. It really slowed down the game, but it was worth it.

Let’s say I draw a three. Joel guesses “Ten!” and I say “Lower!” Then he says “eight!” and I say “Lower!”

We continue on like this until he gets the right number. Joel liked this game so much he asked if he could be the picker and I could be the guesser. I have a video of our first or second round:

(Joel’s rash is from a penicillin allergy. He stayed home from school for a day and we played Uncle Wiggily. A lot.)

Notice that Joel is much more confident earlier on in the game than in the last couple of rounds. This game requires a much stronger sense of ordinality (the relative value of numbers) than simply picking whether seven is greater than four.

(Watching this video again, I realized that I always move in the direction that Joel indicates. I wonder what Joel would do if I said "four," he said "higher..." and I said "three!" Now I have a new question to try out next time we play.)

One big idea I've gotten from Natural Math's wonderful books is that any child can engage with any math idea at some developmentally meaningful level. So naturally I wanted to see whether Joel could grapple with integers!

One night, I drew the dreaded “Go Back Three” card. I asked Joel to guess what it was.

As he neared one, his shouted numbers got more confident.

Three!

Lower...

Two!

Lower...

ONE!

Lower...

...

Joel paused for a moment, then looked at me and said “Go back two!"

I looked at him despondently and said “Even lower…"

Another, shorter, pause.

"Go back three!"

As Joel has gotten better at one-to-one correspondence, he has been less reliant on counting out loud. Sometimes he makes noises instead of counting, and sometimes he says nothing at all, as in the video below.

Joel called this “counting without counting.” I don’t know the name for it in early math literature, but it’s pretty cool. He can do this with numbers up to about 5 or 6. His favorite is to yell five nonsense syllables while moving five spaces. Really, he takes any opportunity to yell nonsense.

I still have a couple of ideas for how to continue exploring new math ideas with Joel using Uncle Wiggily. Aside from the idea I had above, my big new idea is to replace the game cards with a pair of dice. I feel like there is a lot of great conversation to be had about subitizing, adding, and commutativity. Also, I have thought about playing a variant on the game where we each draw 3 cards at the start of the game and choose which card to play.

I hope this blog post gives a sense of the ways that I’ve tried to guide Joel into new mathematical territory by finding interesting questions within a game that he already loves. Three year olds love routine and repetition, so I think it's useful to harness that natural desire and aim it in a mathematical direction.

And man, does Joel love repetition. I don’t always love playing Uncle Wiggily with Joel, but I do like those nights when I see him stumble on a new idea. Since we play almost every night, I don’t have to worry about pushing him to new ideas every day. Sometimes I can just sit back and let him play around with the math ideas we’ve discussed over the least week or so. And sometimes the lesson of the night is more about winning and losing with dignity than it is about math. Joel reaalllly likes to be the first person to 100 (probably because to him, everything is out of 100).