triangles and sponges

I had my first real lesson 3 days ago, on triangles, objectives on the board and all. Writing those does not come naturally at all, and I think I will probably never actually write "TSW" on the board...I remember in 2nd grade, or around then, having to write the objectives down in our little notebooks, and thinking it was absolutely pointless. I keep recalling back to such experiences as a student, when strategy or ethical questions come up, especially in our afternoon class. For instance (in regards to not allowing students spend "free" time doing other classes' work) I have to say when I was in high school, I was always thankful when I got free time to work on homework or study for another class. It seemed like there was never enough time, and even a few minutes here or there could catch me up or get me ahead, knowing I might be at a 5 hour band/colorguard practice that afternoon (yes, I was a band nerd, saber captain in fact, and proud of it :). It certainly depends on what type of students are in the class, and I was usually in the honors classes with the "good" kids, so I'm sure we had more freedom. But what about that guy who's working from 3 til midnight after a full day of school to help his single mother get by, and just doesn't have time, or energy, to do his homework? What about the over-achieving student who needs a few minutes after she's done with my class's work to prepare for a test next period? Of course, the first example is more compelling, but you get the idea.

Going back to the lesson...now that we've been studying different learning strategies, I realize that it was more of an inductive lesson than deductive. I'm surprised that I accidentally did that, but I think I was just trying to get them to figure it out for themselves...which of course is the whole point. I won't go into great detail (since I explained it in class the other day) but I would rather share what happened yesterday in class. Ruth has joined Lee and I, and I must admit she has added a warm and friendly dynamic that was not there before. Lee is a bit more serious and methodical, Ruth is more spontaneous and witty, and I guess I'm somewhere in the middle, and she's loosening me up and allowing me to find more enjoyment in the whole experience. I honestly think it'll work out quite well since we've decided to help each other, but at the same time alternate teaching every 3 days so we have independent practice. So yesterday we were (again) going over solving for simple unknown variables. I had the idea of doing a "human equation," I suppose for the kinesthetic learners (not intentional I must admit, but I think it just follows from natural instinct...you want them to learn, whatever method you've gotta use), so Lee was the = sign, and we added/subtracted students, made them an "x", and solved for it. It went quite well, and the kids had a good time, and I think it at least helped enrich the understanding of a few... I hope...

So today, we had another interesting class. Ruth did her lesson, which went well (she can be a little snappy sometimes...or perhaps I'm just not strict enough) which was only 20 min., so the students worked on worksheets. We were all getting bored..."teachers" and students, so after the break (students with mountain dews, doritos, and slim jim's in hand) I attempted to teach a sort of make-shift lesson on divisibility rules, square roots, and LCM (least common multiple). I had gone through the book and took notes before hand, and it went pretty well...until we had to backtrack because Elizabeth (unassuming and vocal, but with very little confidence in math...she repeatedly calls herself stupid, in a halfway joking manner) did not know what a square root was...
"What does that sign mean? Does that meet it's an angle? Does that mean we subtract?"
Now how do you explain a square root? I was caught a bit off guard. Luckily, another student teacher from TMI spoke up, and said it's doing the opposite of squaring...so I expanded on that and eventually got to...
"Now Elizabeth, what times what is 36?"
"I don't know..."
"What is 6x6?"
"I don't know, " and with that, she took out her calculator...

I've gotta say, I'm so glad I'm getting a taste of this before this fall, of the huge division between those getting it, and those who just don't, even just within a class of 8 students in a month long summer school with too many teachers with too many ideas. (the teacher to student ratio is ridiculously large in our class, 7:8!...and no, that's not a factorial...ugh, math humor...) Every day I'm learning more, and it's usually at the times when I am not expecting to. As Brian and I both decided, we're just gonna be "sponges" while we're here, cuz I know we won't get it all, and I won't agree with all I hear or am being taught, but I'll soak in as much as I can.