Imagine flipping a coin a hundred times. Then doing it again. And again—in fact, flipping it a thousand times. Well, when I was a kid I did. More than once.

You might think that this was the product of one of those dreary summer days when the rain is falling in buckets and none of your friends can come over to play. Nope. This was a staple of my play repertoire—right up there with matchbox cars, Star Wars figures, and wiffle ball.

What was I thinking? Basically, I just loved watching events unfold. I was drawn to the experience of anticipating a result and seeing what would happen. And since we lived out in the middle of nowhere with only four t.v. channels and no video games, I pretty much had to create my own arenas for the unfolding of events.I could always find a coin to flip, and I could instantly be absorbed in the drama of the game. Who would win—heads or tails? Would heads start off with a big lead and then lose it to tails in the last few flips? Would the results be the same at 10 flips, at 20, at 50, 100, 1000? It was like my own easily-staged Olympic games, and it was awesome.

So, OK, I was a really nerdy kid if that’s the kind of thing I did for fun. But it wasn’t just fun; it was education. Looking back, I’ve realized how much I learned:

- That sometimes what you expect to happen, happens—and sometimes it doesn’t: “Heads will come up for sure this time …”
- That sometimes what you expect to happen becomes what you want to happen: “Come on, heads!”
- That sometimes what you want to happen changes: one minute you want the underdog to upset the balance (“Come on tails, you can do it!”) and the next you want the status quo to reign supreme (“Heads! Heads! Heads!”).
- That improbable events are probable: 4 heads in a row?, 5 tails in a row?, 6?, 7?, 8?—flipping a coin a thousand times makes these events seem normal.
- That there is power in large numbers: you might get 9 tails out of 10 flips, but you’re never going to get 900 out of 1000.
- That events are different from trends: events happen now and you react to them (“Heads with its sixth flip in a row—cool!”), but trends happen before, now, and next, and you think about them (“Tails took the lead, then heads came back, then tails jumped ahead, and I bet heads will take over one more time before I reach 1000 flips …”).
- That scale and chance can change what you see: looking at flips 711 through 720 (9 heads, 1 tail) or 701-800 (62 heads, 38 tails) might make you think the coin is unfair or that the person flipping the coin is cheating, but looking at flips 731-740 (5 heads, 5 tails), flips 201-300 (50 heads, 50 tails), or flips 1-1000 (504 heads, 496 tails) would make you think otherwise.
- That numbers can represent many things: I can use the number 1 to mean “heads was flipped” (and 0 to mean “tails was flipped”), but 1 can also simply mean that something happened once (“1-1” would mean “heads was flipped once,” while “1-0” would mean “tails was flipped once”), or it can mean “most often” (“1: 1-1/1-0” would mean the number one result that happens when flipping a coin twice is 1 head and 1 tail”), etc.
- That data inherently select from and reduce reality: if I say that “Out of a thousand flips, heads came up 504 times and tails came up 496 times,” that obscures all of the up and downs (10 lead changes), amazing runs (10 heads in a row), and interesting patterns (heads-tails-tails-heads-heads-tails, etc.).
- That data can be easily manipulated because they select and reduce: “If I just focus on this set, then it would look like …”
- That a person who creates data or even one who observes it can change it if they’re not careful: “That flip didn’t count because it dropped off the table.”
- That the minute you want something to happen you are biased: “Come on tails! Heads—oh, well, that didn’t count because it was partly on the notebook.”
- And that everyone—for reasons they may or may not be able to explain—is biased sometimes: “Mom, why do you always pick heads when I ask you to call it?”

Clearly I couldn’t articulate all of these concepts at the time, but I am certain that I grasped them intuitively, and I believe that activities like these prepared me to understand the deeper ideas I was exposed to later in high school and college. I know that flipping coins for hours is unlikely to be the unstructured play activity of choice for most kids, but I’m sure that others would come up with even more instructive and enriching things to do with the everyday objects in their own family rooms. Sometimes we forget that learning is not merely about receiving information and experiences designed by others, but is fundamentally about us taking an active role in our environment. All kids should have that chance.

For those of you with an interest, here’s an example (referred to above) of a thousand coin flips, with 1’s designating heads and 0’s designating tails. See if you can find the streak of 10 straight heads.

00100001111010000110001100001000101011011111010010

10111000110110001100101110001010010100010100011111

01111000010110110001110110010010110010011010001101

01001000100110011000010100000011110110101011011111

1001010011101101100101110001001010101000010001001

01100000100111011011010111010101101101110110110010

001111011010001111111001101011001010100001101011111

01000000011010110000010011101110100101000110001100

00100001111010000110001100001000101011011111010010

10111000110110001100101110001010010100010100011111

111100110110010100011010110000011001100101011101100

01100010010000000110010011110100111111100010010101

011110010110000110110011111110100010010111000000011

01110011111000010100001101011010100000011101011000

100001111111111011101111000101011101001110001010110

110110011111010110101101111101001101000111100111011

11011111000000101111000001000010110001001101010011

001110010001000101011011101111001111010111001110010

10011001011010000100000010010101111000010001100111

000100111010111111010101010100101010111111100