“That, my friend, is a great idea.” And with that, it was on.

Round 1

We played our first round; I was thoroughly destroyed. (I’m not sure how. I should at least be able to put up a good fight. He’s only five. And I’m not that uncoordinated.) Then—while channeling my inner Christopher Danielson and Andrew Stadel—I asked Caleb how many fish he thought we had each caught.

He made a guess about mine (7), and then we counted. I decided to line them up:

“Off by one. Not bad.”

Then we looked at Caleb’s catch. His guess? 16.

He then counted his fish. Not surprisingly, he lined his up (just as I had). But he made an interesting move:

[vimeo 111898481]

Was that a coincidence? Or was that move inspired by what he’s learned and learning about our number system?

Round 2

I find these TMWYK conversations wonderfully interesting, and Caleb is happy to play along, provided that we don’t linger for too long. With that in mind, we moved on to another round. I decided to capture a video of our second battle, and the counting that would follow:

[vimeo 111898482]

Another interesting move! Arranging in fives. Coincidence? Or is he starting to wrestle with 5 (half of 10) as another friendly number at his disposal?

Postgame

I shared the video with my wife before heading off to bed last night. She was similarly intrigued by the way he arranged the fish while counting. And though my curiosity has yet to be quenched (it will take some followup conversations to figure out his level of intentionality in arranging the fish in that way), I noticed on this second viewing that Caleb arranged the fish by color. In the first case (10 + 3), he ran out of room, and decided to put the last color (red, with three fish) on the next row.

As for the second round, where Caleb arranged things into fives? There were five different colors of fish, three per color (except for that last one).

Next Time

One of the things I love about sharing these conversations is that in writing them down I almost always think of another question or two I might have asked along the way. The arrangements of fish (complete or otherwise) now look to me like fertile soil for rich mathematical conversations about addition, subtraction, multiplication, and factors. In making estimates and checking them by counting, we have a great opportunity to discuss about “more than” and “less than,” and could easily reflect on whether we tend to over- or underestimate in our guessing.

Granted, those are things I thought of only after the fact, while writing down the less-interesting version of things (reality). But for me, that’s the value. In the same way that reflecting on my teaching practice helps me grow as a teacher, reflecting on my conversations with my kids will help me grow in my ability to challenge and encourage and excite them through our father-son or father-daughter discourse.

Update

I showed the video to Caleb. (“Look, little man! You’re on the Internet!”)

Then, regarding the first round: “Why did you arrange the fish like that?”

Caleb: “Because I ran out of room.”

And for the second round: “Why did you line them up that way?”

Caleb: “Because I love rainbows, and I made them like a rainbow.”

Well, numerical motivation for (10 + 3) and (5 + 5 + 4) arrangements may be a few months off. But he does have a nice eye for design.

And if I can pull another classroom takeaway from this conversation, it would be this: The best way to know what they’re thinking? Ask! In a parent-child exchange, this happens naturally and easily in conversation. In the classroom, we’ll have our fair share of individual conversations like this, but also a great number of whole-class-all-at-once interactions. The manner in which we ask for their thinking changes (e.g., a written response instead of a spoken one), but the importance of inquiring remains.

And here again a few months ago, with a haircut (or lackthereof) that might even make Matt Vaudrey proud:

I think Caleb’s swell. Of course, being Caleb’s dad I’m more than a little bias. But I have it on good authority from many people who aren’t Caleb’s dad that my analysis is spot on.

Anyway, one of the swell things Caleb has been doing lately is counting. Everything. Cheerios, ice cubes, grapes, cookies, and all manner of things found at the kitchen table; white tiles, grey tiles, ceiling panels, and all manner of things found in the bathroom hallway at preschool; Legos, piles of Legos, boxes of Legos, and all manner of things found on the family room table while he waits for his younger brother to fall asleep. Asked a moment ago about his favorite thing to count, he responded with a list of several things, and then: “I like to count pretty much everything. Everything in the world.” Excuse me while I go get a tissue.

Lately Caleb has been getting some joy-filled counting workouts while we play a modified version of Monopoly that he and my wife invented a few weeks ago. He’s not quite ready for the paper-money, numbers-in-the-hundreds, mortgage/unmortgage, house/hotel dynamics. In fact, he’s even having trouble with the name (he calls it “Buh-noc-oly”). But he’s totally into rolling the dice, stomping around the board, and carrying out the “everything-costs-one-Chuck-E-Cheese-token” result of wherever he lands. While watching him play—and thinking back to my own childhood, which was probably filled with about 10,000 games of Monopoly—I’ve developed a few wannabe insights about what’s going on.

• This sort of practice is super valuable because it’s fun, it has nothing to do with flash cards, there’s a point to it (in Caleb’s mind) that is much bigger than the counting itself, and there’s heaps and heaps of it built into even a relatively short game.
• The board is basically a making-fives, making-tens, pattern-finding paradise. I mean, just look at it. You’re on Virginia Avenue. You roll a 6. Jackpot! Free Parking here we come! Or you’re on Marvin Gardens. You’ve got greedy eyes for Park Place. What are you hoping to roll? One step lands on “Go To Jail” and after that it’s 5 more to the railroad and 2 more to Park Place. That’s 1 and 5 and 2… 8! Better yet, you’re on Reading Railroad, you roll a 6 + 2, so that makes 8. You break 8 down into 5 + 3, jump 5 to “Just Visiting” and then 3 more to States Avenue. Granted, Caleb hasn’t tapped into anything quite as nifty as that last example, but that’s the kind of potential packed into the board, and it will be fun to see what kinds of patterns he discovers as he continues playing.

• Subitizing and basic addition automaticity are undeniably cool, and counting pips on a pair of dice has ’em both in spades. I’ve seen Caleb go from counting all the pips individually on each die, to recognizing 5 as 5 and 3 as 3 (and the sum as 8) without counting them one at a time, in just a few games. I love when students develop their own shortcuts—whether in Algebra 1 or in Calculus—and it’s been fun to watch my son develop some of his own speedy strategies without any promptings from other kids or adults.

One day we’ll learn how to actually play the game. And one day he’ll probably tire of it (or of playing with me). But along the way, I plan to enjoy watching little a-ha moments flash across his face as he steers that big ol’ boat around the board.

P.S. The other thing that’s great about Monopoly? Swindling Negotiation. As in, four player game, tough luck at the start, three properties to your name when the wheeling and dealing begins. And somehow—Somehow!—you weasel negotiate your way to three complete monopolies and total domination. And some upset family members who refuse to play with you in the future. But sometimes that can’t be helped.

Tuesday evening this week my parents took three of the kids to their place so my wife and I could take our oldest (Caleb) out for a special Caleb-only dinner date. Let’s be clear from the start: It was, from the beginning, all about the dessert. Dinner was just a necessary formality. Fortunately, dinner included bacon, so it was a rather delicious formality… But I digress.

A TMWYK Measurement Opportunity

Shortly after we finished our burgers, pizza, and the like—and with a few minutes to spare before the real deal would arrive—I asked Caleb a few measurement questions about the width of the table. We regularly count things around the house and while we’re out running errands, but I haven’t asked a great many measurement questions. Inspired by some of the conversations I’ve heard and/or read from others in the #TMWYK corner of the #MTBoS, I figured “Why not start now?”

So I asked a few questions. And we had a blast. Here’s a partially-remembered record of what we talked about.

Ready, Set, Measure!

Michael: “Hey Caleb, I wonder how long this table is. How many of my hands do you think it would take to go from “here” to “there”? (I motion across the table.)

Caleb: “Um, I don’t know. 10?”

M: “Okay. Let’s check it out. Count with me… (Sliding my hands across the table…) One. Two.”

C: “Three. Four. Five.”

(At this point, I pause for a second to let him consider whether his guess was a good one. We’re a little past half way, so I think we’ll come in under 10. Then I resume…)

M: “Six.”

C: “Seven. Eight. Eight!”

M: “Wow, so you guessed 10, and it was eight. Very cool. What about Caleb-hands? How many Caleb-hands across?”

C: “Um, 11?”

(Here I missed a great opportunity to ask why he thought that. “You know, Caleb-hands are smaller than Daddy-hands, so we’ll need more of them,” or something like that. But he was a little distracted. We were at BJs, and there are like 42 televisions scattered across that place… So instead, I took a page out of Dan Meyer’s three act playbook and asked…)

M: “Caleb, what do you think would be a number that’s too high? Too many hands?”

C: “28.”

M: “Okay. And what about a number that would be too low?”

C: “Um, 6.”

(By the way, that would be his “too high” and “too low” guess for all of the remaining questions. He would alter the “just right” guess, but not the upper and lower bounds.)

M: “Okay, here we go. (I lead his hands, and we start counting…) One. Two.”

C: (He continues moving his hands and counting…) “Three. Four. Five. Six. Seven. Eight. Nine. Ten.”

(I pause him, and ask…)

M: “Okay, we’re at 10. What was your guess?”

C: “11.”

M: “Do you think it will only take one more hand?” (In my estimation we’re about 75% of the way there.)

C: “Uh.” (Squirm, squirm, squirm. Glance at a television. Then another. One more squirm for good measure. So I decided to abandon this tangential interrogation and get the party started again…)

M: “Okay, let’s finish. (I jumpstart his hands again…) Eleven. Twelve.”

C: “Thirteen! Yeah!”

M: “Very cool. Hey, what else could we use to measure?”

Rounds 3-7

We then played the same game with leapfrogging crayons, kids cups, napkins, half-napkins (folded over), and crayons again (the skinny way). All in all, we had a blast, and some nice conversations. And then dessert arrived. And it was fantastic.

Inspiration

Thanks for the inspiration, everyone in the #TMWYK steam (and especially Christopher, for sparking my thinking about much of this on your own blog and more recently over at talkingmathwithkids.com. If you haven’t been to that website, and you interact with little ones (your own, or someone else’s) on a regular basis, check it out. Great, great stuff.

P.S. There’s a video of one of our last exchanges, but it’s out of focus and Caleb is losing interest (“Squirrel!”), so I’m not sure it’s worth sharing.