Unbelievable commitment

It's 6:49 pm, I'm finishing up the dinner dishes, and my phone rings. Now, I don't get a lot of phone calls-- maybe 25 a month. I fish out my phone, don't recognize the number on the caller ID, but it's a local number, so I answer it.

On the other end of the line, is Arne Duncan, CEO of Chicago Public Schools, and the first thing he says is, "I heard that you were involved in the incident on Friday, and I want to see if there's anything I can do for you."


For those of you in the corporate world, imagine that you work for a company with 45,000 employees at over 600 offices, serving 420,000 in-house clients, with an annual operating budget of $4.4 billion. That's, for example, about twice as big as Apple, Inc. Now imagine that the CEO calls you, at home, at 7 on a Tuesday night, to say, "Hey, man, heard you had a rough day last week. How you doing? Anything I can do to help?"


Mr. Duncan and I had a really good conversation, for about 10 minutes. I was very frank about my perspective, what I think the school needs in order to feel secure. He was really easy to talk to, and I tried to give him ideas about what's on my mind, and what the talk around the lunchroom is (he was surprised, for example, to hear that the faculty are nervous about the prospect of the school closing-- it wasn't even on his radar, and hadn't occurred to him that it'd be on our minds). At the end of the conversation, he made sure I had his email address and his direct phone number, and invited me to follow-up if I have any more thoughts that I'd like to share with him.

So, people can say what they want about the guy-- the dedication he's shown right there, his concern for me as a teacher and his interest in making sure I get my need met (especially given that he recieved my suggestions with enthusiasm) has just made me his biggest fan.

One for the team

I was thinking, during my lunch break, about writing about something to do with teaching stuff-- earlier today, I think I had some ideas about that.

Then, all hell broke loose, the school went code red (yeah, we literally have codes, one of which is red, which means lockdown, no students move, nobody in the hallway). We had, I think, something like 30 police officers (also, 6 firemen, treating injuries) before things were made sufficiently safe to gradually dismiss students and clear the school out.

Towards the beginning of the extended series of mob actions, I encountered a student of mine, who was apparantly trespassing (he's suspended from school), behaving erratically. I tried to talk him down, as did a number of other adults who were around, but to no avail. Before it was over, he shoved me three times, and put his hand on my throat.

I wasn't too worried about my physical safety, throughout any of the day: the student with whom I had the physical confrontation is a big guy, but he was out of his head, and I was in control-- not a real threat, there. Shortly later, I confronted another group of students and corralled them back towards where the authorities were (they had their cell phones out, and were discussing which of their associates they should call-- this is apparantly a recurring theme: gang members call in their soldiers when it jumps), and my conversation with them got a bit tense-- I was aware that I was on my own, without any nearby backup, but a quick assessment made it clear there was really only one fighter in the group. Still, that was the closest I came to feeling that I was in danger.

I'm not sure where I'm going with this-- I think I'm just dumping data at the moment-- but I can't help but notice that my earlier plans to think about my teaching practice are now utterly washed away.

Conceptual problem with prisms

My sophomores have taken easily to the volume of a rectangular prism (V=lwh), but other sorts of prisms have given them a lot more trouble. Yesterday seemed to help: I gave a presentation of building a prism by "stacking up" congruent shapes, and pointing out that each piece had the same surface area (a neat connection to volume of solids of rotations, which I'm doing with the calculus class right now-- again, calculus is the geometry of curves!)

What was interesting was this: when I gave them an isometric view, with the instructions to "draw the top, find the area of the top, then mulitply by the height" that got some traction-- but a LOT of students had trouble removing the height from their drawings and calculations of the top. That is, I was continually pointing out that "that number represents how far down below the table your shape is."

Neat bit of discovering misconceptions, anyway.

Settling into a decent routine

So, as the second semester dawns, I'm making some pretty significant changes in my regular classroom routines, which is worth documenting.

Last semester, I did a lousy job of staying on top of grades, mostly I think because I was buried in it: I tried to grade everything the students ever did, and it was just way, way too much.

Recently, I was reviewing the teachers guide to the unit we're doing now (Key Curriculum's Interactive Mathematics Program, which is a wildly different curriculum than the traditional math textbook), and I noticed that, right up there in front, it says "Because you will not be able to read thoroughly every assignment that students turn in, you will need to select certain assignments to read carefully and base grades on. Here are some suggestions:" This is followed by FIVE assignments, in a unit that is paced for 29 classroom days-- like, SIX WEEKS of class, FIVE assignments to grade carefully.

And I thought, "Yeah. One a week, I could do". So that became a basis for my new plan. There were some great in-class conversations, with students giving me some great ideas. Here's what we settled on:

Homework continues to be assigned on Monday, Tuesday, Wednesday and Thursday only (no homework on Friday)-- but everything gets turned in on Friday. POWs (taken from NCTM) still exist, but are not optional for extra credit. I'll be adding mandatory POWs from the IMP curriculum, about two per unit. The first day of each week starts with a review of the Big Picture from the past week, and an overview of the objectives for the new week. Each Friday begins with a 10-minute ungraded quiz (we're calling it a "check-up"), where students take on the week's Big Picture goals. During that 10 minutes, I walk through the room, marking up
the homework, just to see who's done it. We then go over the check-up answers, and the class gives me "thumbs up" or "thumbs down", to indicate if they understand that goal and are ready to move on, of if we need to continue with that idea next week.

After that, I drop the homework answers, so that students can tell, again, if they got it right or not. They mark one assignment of the four to be graded carefully, and if there's any time left in the Friday, we can either go over the stuff they didn't get yet, or move into some extensions on the Big Picture from the week now ending.

So far, I think we're all excited about this. From my perspective, I love the use of formative assessment and metacognition. Pacing might be hard (four days a week of new material), but by consolidating all the homework check-up and such to the end of the week, it frees up more class time on Mon-Thurs, which should pay dividends in terms of getting stuff done on those days. And, it makes it much easier for me to stay on top of grades: the administrative overhead is much smaller (I enter one grade for homework each week into my grade book), and I'm recruiting the students to keep pressure on me to stay up with it-- they're under orders to bug me mercilessly if I don't return their work on Monday...

Baby's first gold tooth

Yesterday, I came up with my first "hook". Okay, maybe not exactly my first, but definitely my best, meaning my most useful, most engaging, and first that isn't really a languistic trick.

(I also came up with a new linguistic trick, see below).

Systems of Equations:
So, I have this ball in my hand, and I'm eager to show it to you, because I don't know much about it yet-- it's all wrapped up inside my fingers-- but I think I can unwrap my fingers, and, yeah, there: a ball.
This is kind of like unwrapping an equation: 2x + 5 = 11 -> 2x = 6 -> x = 3 and now you can see the ball, I mean the unknown, x.

But, what if I have two balls in my hand? Now, when I try to unwrap it, I'm liable to drop one, which just messes up the whole thing. (Dropping one ball). So, if I want to show them to you, they've got to keep moving (starts juggling two balls in one hand). This is like this equation: l*w = 12. The two balls could be 3 (timed to one ball rising) and 4 (the other ball), or else 1 and 12, or 2 and 6, or 8 and 1.5, or -3 and -4, or anything. If one ball moves, the other one will too. So, in order to stop this whole thing-- I need another hand.
(Taking one ball into each hand), And then I can show them both to you.

This is how equations work, too: if I have two balls in one hand, they have to either keep hidden, or else they're both going to be moving (or at least, movable). But once I add a second equation (w = 6), then I can stop the whole thing, and tell you what is what.

Try it with a volume problem, now: You have a square-bottomed rectangular prism. It's twice as tall as it is wide, and the total Volume = 54 in^3. How tall is it?
So far, I have just one equation (V=54 in^3), but I can add another one really easily, because I know something about volume: V= lwh.
Now that's TWO equations (hold up both fists) with FOUR variables (show that there are two balls in each hand). Not so good. I need more hands-- I mean, equations.
The bottom is a square, so l=w. That's THREE-- just one more now. The height is twice the width: h=2w.
Now some algebraic substitution, and V=lwh becomes 54=(w)(w)(2w). Solve that, and w=3, so h=6.


So far, this skit has worked really well with two classes. It helped to review algebra... I've always liked that "algebra" is from the Arabic (al = the, gebra = change). I love telling my Latino students that they have an advantage in learning math, because so much of it makes more sense in Spanish. This is a great example. In English, that direct translation isn't so good. In Spanish, I'd translate "al gebra" as "el cambio", which is great, because "cambio" captures more of the idea of replacement or trading, which is a huge concept in algebra (substitution of equivalents).

So, the big linguistic breakthrough today? The Currency Exchange two blocks from the school has a neon sign in the window: "Casa de Cambio". So, in English, don't translate "al gebra" as "the change". Translate it as "the EXCHANGE". Emphasize that this is synonymous with "the SWAP" or "the TRADE".

Maybe it's just me, but I saw a lot of lightbulbs over heads today. "And there's another swap..."