Line symmetry:

I drew the left half of a cartoon butterfly on the whiteboard, right next to the seam between the two boards at the front.

“Did I draw the whole thing?”  (“No, duh”)

“Do we know what the whole butterfly looks like?”

“Okay, someone come up here and draw the rest of it.”  Girl comes up and draws – a few rowdy kids point out everything she’s doing wrong – ‘That part’s too small! That doesn’t look right!’

“Okay, so you were correcting her – how did you know that it was wrong?”

Students already know line symmetry, intuitively.  The only thing they need to learn is how to understand what they already know a little more deeply, so that they can apply it in less intuitive situations.  This has kind of turned into my theme for the geometry unit, actually.  Half of what I’m teaching them is stuff they already know without thinking about it.

3D Surface Area:

I pulled out the straws and tape for this one.  Groups of students built the five platonic solids and had to calculate the surface area of each one.

(The trick is to get bendy straws and cut along the short end of the straw, so that it can be pushed together a little smaller and tucked inside the long end of another bendy straw.  You can build the 2D shapes for each face without using any tape at all.  Then you just tape together the faces.)

This … kind of worked.  Students generally had no problem getting that the surface area is calculated by finding the area of each panel / face and then adding them up.  (One group had a moment of difficulty, but only because I brainfaded and said “length cubed” instead of “length squared” and confused them for a minute.)

I experimented with letting students choose their own group after having told them which shapes would be more challenging – sort of self-selecting a difficulty level.  I warned the “easy mode” groups that once they were done they’d be helping the harder groups finish their constructions.  Unfortunately, of the two harder shapes, one group blitzed through it and the other group was stubborn and wanted to do it themselves.  The groups were also a bit too large at 5-6 kids per group.  This might be worth trying again, but only if I can frame the tasks so that “easy mode” doesn’t also mean “takes a lot less time”.

Photoshop:

We have a collection of links to online tutorials that we use to get the students up to speed on most of the key tools available in Photoshop.  For the healing brush we send them to this one, where there’s a close-up of a guy’s face that they’re supposed to “fix”.

Students started asking me what they were supposed to fix on the photo.  “His nose?”  “There’s nothing wrong with his face.”

I had no way of explaining that one quickly without feeling like an accomplice to something horrible.  I had no choice but to pull up the Dove “Evolution” video and spontaneously add a new goal to my unit: to have them understand that the media around them, especially advertisements, are full of images that look absolutely nothing like reality.  I went just a little Adbusters-ranty on them.  I replayed the second half of the video a couple of times so that students could wrap their minds around just how much evil is done with Photoshop in the name of increasing sales.

I am now officially halfway done my practicum.

I am convinced that student teaching is significantly harder than regular teaching, aside from the fact that it isn’t a full year.  We prepare our lessons, all of which we are teaching for the first time ever.  We struggle not only with how much to mark, but how to mark, why to mark.  We’ve stepped behind the curtain and suddenly realize that tests, exams, notes and the rest of a teacher’s show are not solid but are shakily constructed from whatever materials can be found, whatever looks like it’ll do the job long enough to finish the performance.  You start to see that it didn’t have to look that way; it could have been built in at least a dozen other styles and still performed the same function.  All the while we wrestle with how to become an authority figure without falling into the trap of trying to prove that you’re in charge (because if you have to prove it, you’re not).

And all of this takes place in a room which is ours, but not ours.  We may have been lucky enough to be present at the start of the year, but our sponsor teacher is still the one who has set the tone of the class, the expectations, the feel of the room.  We can come in and try to create a space of our own, but whether that works is affected by how our presence contrasts with our sponsor; how we present ourselves in the first 15 min (the exact time when we have the least experience doing so); how the logistics of sharing space or jumping from classroom to classroom limit what we can do to remake things in our image.

Today sucked. Tomorrow, pro-d. Monday I don’t have to worry about yet.

Time to go home, celebrate a milestone, eat more cookies than is healthy (hey, I made them myself) and relax.

Then … catch up on marking.

My love for paper folding lured me into starting out my Math 9’s with Circle Geometry.  I’ll start off with the regular block this week; I’m a week into it with my Essentials / Remedial block.  I asked a LOT of them and then gave them a lot of in-class support.  I don’t want to apologize for that in principle, but I should’ve been bringing those lesson plans in halfway through the year, once they were comfortable actually working on things together.

I’m busy pillaging resources like Dan Meyer’s Geometry notes, but I wish someone had a cheat sheet on how U.S. math courses translate to our Western Canada course structure.  Still, it looks worth pillaging.

It’s reassuring to see that he also picked up on the reconstructing a circle from an arc exercise.  I was thinking of finding an actual stone circle of some kind or another and smashing it; instead I fudged it at the last minute by taking a hand-drawn circle, tearing it up into pieces, and handing out the pieces.  In retrospect I kind of like the drama of tearing up a piece of paper in full view, and I think I’d do it again.  I’ll just need to improve how I lead them up to that point next time.

Also, paper was fun, but wow I need to get my hands on a digital projector, fast.

It’s impossible right now for me to ignore the parallels between my lesson planning and my love for game design.  I think this is because there’s actually something going on between the two (but we can’t rule out the possibility that I’m just obsessed).

Today I taught my second math block in my official practicum term.  I gave students a significant challenge, but it may have stretched too far too quickly.  I’ve been giving them open challenges rather than easy answers, and trying to structure things in such a way that they can work it out.  I’m learning that accessibility is a key factor.  You could say I need to work on my intro levels to build up the skills and awareness of ‘verbs’ that they have on hand already.

I’m also finding it really hard to sit down and write here, as much as I want to contribute to the larger teacher-blogger community.  There are already a number of math / science teacher bloggers who are feeding me a constant stream of inspiration, and I want to give back to that.  When I sit down to write, though, it’s a struggle to pick out the bits in my head that are sharable vs the bits that are not.  Anything I say about my class has the potential to reflect publically on my students.  When things go wrong with my lesson, I know that my delivery, my preparation, and my knowledge are not the only factors involved.  Students’ lives are just as messy and complicated as mine, and they’re not mine to share to the world.

Still, I’ve seen too much awesome being blogged out there to ignore.  I need to do this.

Right now I’m faced with a problem: my budget is incredibly tight, I’m bored of all the music I own, and I’m a stickler for copyright ethics.

On the bright side, I live in Canada.  This means that the filthy major record labels already have more of my money than I gave them for music purchases, due to the blank recording media levy.  I’ve bought a few stacks of blank CD-Rs over the past few years that I’ve used for data, not music, but I’ve still paid the 21 cents per disc.

So how do I translate that to mp3 downloads?

Arguably, I could say that the levy is in support of personal copying, and then go on and leech as many mp3s as I want.  Legally, this is a possible defense but it hasn’t been tested in court as far as I know.  Ethically, I don’t know that I want to go there.

I don’t have a solution, but my gut feeling is that it should be arguable for me to download a small number of mainstream albums based on levy fees that have gone to their record labels already.  (Fees are distributed based on commercial radio airplay, which means indie labels and artists don’t see much of this money.)

This is pretty tempting to turn into a numeracy lesson.  The math is there, it doesn’t require any difficult techniques, and there isn’t one clear right answer.  I could hand them data on levy amounts, on average CD costs in physical and digital stores, and maybe to stir things up include data on the breakdown of how much money from each CD sale goes to various parties (distribution, publisher, artist, marketing, etc).

Wolfram Alpha has launched.  Wolfram has coupled the symbolic and computational math power of their Mathematica software to an extensive collection of curated databases, on topics ranging from chemistry to socioeconomic data to sports statistics.

While the ability to do your high school math homework has some people either very happy or very worried, I’m much more interested in using it to access meaningful data in a way that I could use in a math classroom.  A one-step resource for good data coupled with the ability to easily do computations could be fantastic for bringing real-world problems into a math class, or for student-driven projects.

So with that in mind I’ve been poking around at what sort of data and data analysis can be extracted from Alpha.  The results are promising, but still a bit clumsy.

Playing around with socioeconomic data seemed promising.  But then I tried to ask for the standard deviation of GNP.  Alpha completely failed to understand that I meant the set of all GNP data by country, and instead thought I was asking for the SD of a single value for the total world GNP.  Is there a way around this?

Another weird oddity was looking at the country data for Canada, specifically the results for languages.  English and French are obvious enough, but Plautdietsch at third place nationally?  I like my vereniki and farmer sausage as much as the next Mennonite-farming-immigrant-descendant, but Stats Canada shows Chinese at third place as of 2001 with 2.9% of the population.  In fact, the results seem to miss not only all Asian languages, but all European ones other than English, French, and the oddball Germanic mix.

It looks like a great math tool to have on hand, but with data this rough around the edges it’s hard for me to simply take “Wolfram|Alpha Curated Data” seriously as a primary source just yet.

For the last few months I’ve been busy in a B.Ed degree program at Simon Fraser University.  It’s a 12-month, second degree program, so come next January I will be officially marked as insane enough to want to teach high school kids.

This blog sort of formed out of a desire to learn more about game design.  I still like overanalyzing games that I play, and I still poke around a little at small freeware game development every now and then.  But overall it’s no longer the foremost thing on my mind worth talking about.  So I’m re-generalizing this space to write about whatever I need to get off my mind in a way that I think could be worth reading.

On the other hand, I’m also signed up for Ian Schreiber’s Game Design Concepts summer course that he is excellently offering for free.  I’ve tried my hand at teaching game design myself briefly; it went okay, but had all the rough edges you’d expect from a new course taught by a new teacher who was making up a new curriculum.  I don’t know if I’ll go back to trying to offer a standalone course in that way again, but I suspect I may integrate game design basics into high school IT courses if there’s enough interest in basic game development as, say, a project option.  So I may end up blabbing about game design a bit more, but in a shifting context of integrating it into my teaching practice rather than as an aspiring indie developer.