Internalization

Right now our math class is working with algebra tiles, fun little manipulatives that help with concepts like combining like terms, solving equations, and the distributive property. They're basically a set of squares and rectangles of different lengths. There are "ones" tiles that we use to measure everything else, but some lengths don't measure easily. So we call one unknown length "x" and the other unknown length "y." Each tile is named by its area, so the x tile, for example, has length x and width 1, while the x-squared tile has length and width x. I've never seen anything like them in algebra, and I really like the way they offer a tangible way of looking at variables.

The tiles hve different colors on each side. The pink/blue/green side (depending on the shape) denotes a positive number, while the red side denotes a negative. So for example, an x tile with the blue side up and a y tile with the red side up represents the expression x-y. However, when we draw pictures of the tiles on worksheets, assignments, etc. we can't use the actual colors, so the algebra tile people just use shaded/black or unshaded/white pictures to denote positive and negative. Guess which is positive and which is negative?

If you're like most people, you guessed that unshaded/white is positive and shaded/black is negative. But the algebra tile people flipped the script and declared that shaded/black tiles would denote positive numbers while the white/unshaded ones would be the negatives. I have to admit that this really confused me at first. The same was true for our kids. They complained about how difficult it was to interpret the pictures. "Why isn't white positive and black negative?" they wanted to know.

"Why wouldn't black be positive?" we asked. "Black is always negative," one student told me. How fascinating that in a classroom where there are at most three white students, the entire class would resist blackness representing something positive. My difficulty getting used to this system definitely made me reconsider my own internalization of racist attitudes, not to mention what this must mean for the identity development of all my students. I appreciate the thought that went into creating the algebra tiles and their notation--what an interesting and surprising way and place to challenge kids' ideas of race.

Unconvinced that this has anything to do with race? For more examples of the ways we equate blackness with negatives and whiteness with positives, check out pages 52-54 of Dean Keith Simonton's "Greatness: Who Makes History."

Downsizing

When the school year started, my CT told me that we were guaranteed no more than 24 kids. Because we teach freshmen, they wanted to provide small learning environments where the kids could get used to being in high school and really get some personal attention (not that this shouldn't be happening in ALL classes, but unfortunately that's just not an option). So we moved out all the extra tables and only prepared for 24 at the most.

Then came the first day. 24 kids showed up. Then more, then more, and then some more. We had to call down for extra chairs in the middle of class. Each day for the next few weeks we had new kids walking in with a schedule that had my CT's name at the top. We added two more tables. By the end of the first month, we had 32 in one class and 33 in another. The problem was that the district had predicted a certain enrollment, but way more actually enrolled. So until the 10-day count took place to show just how crazy things were, we were working with a budget that covered teachers for about 800 teachers when really the enrollment was more like 950. You do the math (and then thank your math teachers).

Of course ours wasn't the only class that was overcrowded, so the administration went on a search to hire a new math teacher and a new English teacher. Finally, 8 weeks into the school year, they started today. Last week we spent agonizing which kids we were going to switch out of our classes, and then agonizing some more about how to tell them. The poor kids--can you imagine having to start over with a brand new teacher so far into the school year? And emotionally it was difficult to give up all these kids who I really like, and know that they're going to resent us for it. It's not like you can tell a kid that you've moved them out of your class and expect them to not have hurt feelings.

But all the pain paid off almost instantly. Today we were back to six tables and only about 20 of them showed up. Our first period class was silent during the warm-up for the first time ever. The whole-class discussions actually involved the whole class, and we spent more time actually talking about math than telling kids to pay attention. I can't wait for the rest of the year.

And there are really questions about what to fix in public education? Of course reducing class size won't fix it all, but if my class can transform literally overnight, can you imagine what kinds of changes we'd see if every class in every school was under 25?

Golden

In the past year or so, I began imposing on myself the rule that when possible, I would not buy foods that were not produced nearby. In New Zealand, that meant foods from Australia and NZ; now it means mostly from the USA's West Coast and maybe Mexico or Canada. Basically, I'm trying to reduce my carbon footprint (international shipping waste and all that) and also eat foods that I know are fresher because they haven't traveled as far. Of course there are downsides like no winter strawberries having to scour Napa for savignon blanc that even slightly resembles the deliciousness of Nelson Marlborough vinyards, but overall it's working pretty well. In winter I eat oranges and I just bought a bottle of California wine this weekend that's touted to "make the New Zealanders shake in their kiwi fields."

But then I was at the market this weekend and there they were...
GOLDEN KIWIFRUIT

Golden kiwifruit, for the uninitiated, is like regular kiwifruit, but with superpowers. They've got the same flavour and sweetness as the traditional green kind, but are less acidic, so you can eat bucketloads without your tongue going raw. Plus, they have softer flesh so they're easier to eat with a spoon. I had never seen the golden ones until moving to NZ, and had never heard of them being sold in the US.

I picked one up, praying that it would miraculously say "California" on the sticker, but no, there was the "New Zealand" label. What to do? Indulge myself at the expense of the ozone layer, or stick to Washington red delicious apples as my snack fruit for the week? Admit a failure of willpower, or declare triumph over my temptations? I chose the latter, and there is now a pile of furry little brown gems sitting in my fruit bowl, disappearing one by one.

In order to avoid further on-the-spot moral compromises, I decided to come up with a list of exceptions to my rule, so I know that next time I see them at the supermarket, I'll suck it up, buy them, and not drive my car as much for the week.
-Tim Tams
-Kumara
-Kapiti Ice Cream (preferably golden kiwifruit and pavlova flavoured)
-Griffin's Malt Biscuits (for making lolly cake)
-Pods
-Toffee Pops

Hey Godzone dwellers: I can think of a really good way how I could get all these things ethically imported (except the kumara maybe) AND get a chance to see you at the same time...

Absent Minded

When my CT told me at the beginning of the year that part of her grading system included points that kids couldn't make up if they were absent, I was kind of stunned. What if they're sick? I asked. What if it's an excused absence? Her response was "Too bad." I quickly understood her reasoning. Our kids are unbelievably truant, and a lot of those are excused absences from the parents. We had one student miss class all of last week being sick. We have other students who have to take care of siblings. Some kids miss for doctor's appointments and court dates. Others go to the Wellness Center practically everyday. And that doesn't even include the kids who are skipping class. Even though I was nervous about being unfair to the kids who have legitimate reasons (which a lot of the above reasons are), it ends up that if you're only missing class once a marking period, it's not going to hurt your grade. In the end, it comes down to the simple reality that kids can't learn when they're not in class.

Here are some other reasons I didn't think about to explain just how important it is that they come to school. Note the mention of Mission in the 10th paragraph!
http://www.sfgate.com/cgi-bin/article.cgi?file=/c/a/2007/10/07/INBJSHURJ.DTL

Milestones

Today I taught the entire 100 minute class period by myself. I know, it doesn't seem like much, especially considering it's what real teachers do every day. But for me it was a big step. It did not go so well in the first class I taught, but I corrected my more serious mistakes for the second class and I felt much better about it. On the one hand, this is a sign that I can learn from mistakes (which I will continue to make a lot of). But on the other, it's disappointing to remember that there's always that first class that has to be my guinea pigs.

Another big first that happened today: the first time a kid told me "F--- you" to my face. It took six weeks for that to happen? I must be doing something right.