Just finished first period and I wanted to make some notes on it before I forget what happened. It was truly a whirlwind! I'm thinking that half of the class walked out without a clue of what had gone on.
1. Started out showing my facebook powerpoint. When looking at the quartic regression slide, one of the boys (let's call him Fred, because he'll be back!) brought up the idea of Myspace, which I had intended to address as well (thanks to @DaveLanovaz last night, who made the same comment!). Someone else questioned why the logistic regression equation didn't give a correlation coefficient. I told him I didn't know why; I'd looked into it last night and couldn't find out. Fred (who is taking AP Stats) told us that the correlation coefficient is found by taking the log of something (he lost me here) to turn the equation into a linear equation. Because the logistic equation had already been taken a log of, you couldn't do it again. Hence no correlation coefficient. Or something like that. (@druinok let me know (late!) last night that maybe my regression equations weren't the best as the calculator uses least squares regression which would affect the vertical aspects of the equation. I decided that instead of redoing all of my slides I was just going to let it slide. Ha. :) )
@JackieB!) was to find the area between f(x) = e^x and g(x) = ln x in the interval [1/2, 1]. We talked through strategies... plot some points, draw a graph, cut up the shape into shapes we know to find their area. Fred kept referencing integrals (I kept putting him off), other ideas were a trapezoid and a triangle, a big rectangle minus two triangles, and two triangles. Then I let Fred talk. He's a great kid - the kind who is constantly running up to the board to do his "thinking". He's very very interested in all things mathematical and is currently taking AP Computer Science, AP Stats, and Honors Physics (in addition to Honors Precalc). He explained the "idea" of integrals (dividing up the shape into smaller trapezoids of which you have an infinite number of pieces) and was very theoretical. Then another girl (who had asked me yesterday if this was an integration problem) came up to the computer and talked through something more "concrete". She showed an integral, made up a function, showed exactly what it was she was finding in terms of the area, and found her area. Did I mention she's a sophomore who's come up through college prep and was just added to my class a few weeks ago because the trig teacher thought she needed more of a challenge? And did I mention that she takes extra classes on the side because she likes math? Anyway. The other kids in the class were stunned. Some totally tuned out because they had no idea what was going on and some were interested and amazed that they were seeing a classmate do this.
3. New stuff - modeling exponential functions. Not so exciting, but I was able to get the rest of the class to tune in.
(A year ago this never would've happened because I wouldn't have given them the opportunity to think this way. Shame on me.)