Counting Within Twelve

This is Caleb, back in September 2009:


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

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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.

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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.

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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.

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