# Now Socrates is Smiling?!?

Posted on November 11, 2011

So am I.

“She told us not to do the ones with the semicircles because she hasn’t talked about it yet…. but… maybe we could just learn it?”

(Okay, I could just end right here. No kidding, that’s what she said.)

“Okay, why can’t you just do this the same way as the whole circles?”

“Because…” (fingers tracing the rest of the circle that’s not there…)… unquotable musings… and the realization that “you have to cut it in half.” (physical demonstration with gross motor ;)) “And in math that is…?” … thinking… not sure… “Divide?.. Yes, divide by two.”

“So. Same formula, pi times r times r… then divide by two.”

And even sweeter was the next problem, the One That Throws Them All — of the half circle with a triangle whacked out of it. We Socratically deduced from the same direction (“why can’t you do what you did up here? What’s different?”) … figured out which line was the radius, even without the rest of the circle, and were duly amazed that the long one was 20 which would be a diameter… yes, that’s my point, dear reader, all that stuff is “obvious.” To me. Perhaps to you. To almost every math professor out there. Well, it wasn’t *obvious* to these students — but it was discoverable and they discovered it. Then they figured out that “some space” had to be … hmmm… subtracted. NOw, they wanted to subtract 20 (that elusive diameter), and… we were kinda at saturation point for making the connections between space and symbol, because it was all about guessing at numbers, so I just said “space … that’s what area means, and the area of a triangle is 1/2 the base times the height” with the usual gesticulations across the space of the triangle. Stumbling calculations happened (they forgot to halve the area of the semicircle)… but serious inroads were made into that elusive “how to approach a new kind of problem” skill.
Now, the trick is not to “teach the math and just move on.” WHat I *reallY* like about this scenario is that this is what “flipped classrooms” are wishing they were. They’re walking into class now, and the “lecture” is going to be going over what they have just learned.
And if I’d made my app, they’d be able to “play games” on their mobile devices to catapult angry lagomorphs through triangles and circles or something đŸ™‚