I have a student who is very creative with her math. She just tries stuff, learns from mistakes and constructs her own understanding. It's pretty cool to watch. Today, she was describing to the class how she came up with the standard form of a linear equation we were playing with yesterday by using the slope of the line.
M.M. pipes up, "I don't get how she did that."
What he meant was, "Yeah, I see how that equation works, but I have no idea how she thought of doing that."
She follows her intuition and sees where it takes her.
I told M.M., "I'm not so sure that you really need to know how she came up with it any more than you need to know how an artist paints or how an author writes. What you need to appreciate is the fact that she created some understanding on her own."
I launched into a quick discussion on Duplication, Application and Creation and how many "advanced" kids actually live in the duplication stage, but they just do it faster than everyone else. I can teach duplication and provide opportunity for application, but creation is all them.
Here's what went down as a result.
I.N. : Mr. Cox, your class is the only one I do my homework in.
I.N. : Because you don't make us do it. Like at home, if my mom makes me go out for a sport, I don't really try because I feel like I'm forced to do it, but I'll go play sports on my own with friends or even with random people. I want to do my homework in here.
J.T.: Actually, Mr. Cox, you don't really force anything on us.
Try not to, anyway.
The conversation went to grades and grading in general and I said I don't really care for grades and wouldn't give them if I didn't have to.
S.N. : Then you need to start your own school, Mr. Cox.
Yeah, that'd be nice but I don't have that kind of money.
L.F.: I'll go work at McDonald's and give you my paycheck.
One kid said, "you're gonna change the system, Mr. Cox" and I kinda let the comment go. But after a few minutes I came back around to it.
You guys really think I'm gonna change the system?
"Nah, we're gonna change the system."