Still, there are times when you just have to place that bet...
Yesterday I was in Jan's third and fourth grade class, where students are working on logic and attributes. The focus for the lesson was on Venn diagrams. You know, overlapping circle thingies, like this:
(My college roommate, Bernie, was a double major in science and philosophy. After taking a class on Tibetan Buddhism he once accidentally referred to these things as "Zen diagrams." I'm still tempted to call 'em that sometimes.)
In addition to the Zen, I mean Venn, diagram, we also had a bunch of blocks of various sizes, shapes, and colors, and labels with categories that described the blocks: "triangles," "small," "red," "yellow" and so on. I had chosen two labels at random ("What does that mean, 'at random?'" I'd asked earlier in the day, and the response was "Randomly," which was accurate if not perhaps revealing) and placed one in each circle of the Zen, I mean Venn, diagram. I got to look at the labels. The kids didn't.
The object is for the students to identify the two labels. They name blocks one by one, and I place each piece where it belongs: in the overlapping section of the diagram if it fits both labels; in one of the circles but not the other if it matches just one label; or outside both circles if it matches neither one. For instance, a small green triangle goes inside a circle marked "small," "green," or "triangle." Students use logic and the position of blocks in the diagram to determine what the labels CAN and CANNOT be.
Yesterday, after just three blocks, we had the following situation:
In the left circle, but NOT in the overlap, was a small blue rhombus. (A rhombus, for those not in the know, is not a method of transporting rhoms; it is a four-sided figure in which all sides are equal.)
In the overlap between the circles was a large blue rhombus. And outside both circles looking in was a small blue triangle.
"Talk to each other," I said. "Tell your partner what the labels COULD be and what they COULDN'T be. Then share your ideas with the rest of us."
{WARNING: SPOILERS AHEAD. You may wish to see if you can solve the problem on your own based only on this information. Remember, labels name only colors, shapes, and sizes, and we only choose two labels. Read down when you're ready...}
After the partner conversation, one of the third graders raised her hand. "I think I know what it is," she said. "This circle"--and she pointed to the one on the left--"is the circle for rhombuses. And this circle"--and she pointed to the one on the right--"has to be for big blocks."
"Why couldn't they be for blue blocks?" I asked.
"Because we tried blue with the blue triangle," she said, "and the blue triangle didn't go in either of the circles. So it can't be blue."
I asked a couple more questions like that, inquired if anyone had other ideas, and then turned back to the girl who had spoken first. "How sure are you?" I asked.
"I'm pretty sure," she told me. "Maybe 80% sure. No, 90%." (I like having kids this age express "sureness" in percentages. They seem to like it too.)
I drew a quarter out of my pocket and examined it closely. "90% sure is pretty sure," I said, "but it isn't certain. We only have three blocks so far. It's kind of early to be naming both labels, don't you think? I'm thinking it COULD be something else. I'm thinking it probably IS something else." Pause. "What do you think?"
"Umm." The girl frowned and looked back at the diagram. A classmate next to her whispered something. The girl nodded. "I still think I'm right," she informed me.
I tossed the quarter into the air and caught it nonchalantly. "I have a quarter here that says you're wrong," I said. If the labels were "rhombus" and "large," I explained, the quarter would be hers. (That got everybody's attention.) On the other hand, I added oh-so-casually, if she was wrong she would owe ME a quarter.
"Don't do it!" somebody hissed at my, ah, victim, just as someone else leaned in close to her and said "Go for it!"
"All right," she said, rolling her eyes, "you can have my allowance..."
As it turned out, of course, it wasn't necessary. We went through her reasoning, failed to find any holes (bummer, man), and revealed the labels in the Venn, I mean Zen, diagram. The girl's reasoning had been one hundred percent correct, and she had stuck to her guns despite my best attempt to rattle her. I handed over the quarter as the class cheered and surrounded her to offer their congratulations to the kid who had, if not broken the bank at Monte Carlo, at the very least outwitted the Math Guy.
I'd lost (again). But though my pocket was lighter, I was convinced that the reasoning and confidence the child had demonstrated during the lesson had been worth the very real financial hit to me...
And at any rate, now you know why I am not (generally) a gamblin' man!
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