A little more background, this time from the Calgary Herald rather than my second-hand knowledge from email listservs:

University-bound arts or humanities students who once struggled to complete high-school math requirements may find help when a new math curriculum begins for Grade 10 students next year.

…

Mathematics 20-1, 30-1 and 31 is meant for students who wish to pursue math-intensive subjects while Mathematics 20-2 and 30-2 has been created to prepare students for post secondary studies which would not require higher-level math training.

Arts students, for instance, could learn to interpret statistics and to complete math research projects, assignments which aren’t included in the more science-focused math class where the emphasis would be on calculus.

“It’s not easier math, it’s different content you are studying,” said Henzel.

That last line is the kicker.  This isn’t just a watered-down version of calculus prep, this is a completely different teaching target.

The article ends with a mention that the U of Alberta and U of Calgary will be “aligning” with this curriculum in a few years.  The devil is in the details, though, and they aren’t giving any details yet.  Hopefully they take a more reasonable approach than UBC.

My first job interview for a Teacher-On-Call position happened last week, and it went pretty well.  There was only one question that caught me off-guard.

I’ve been looking over your resume and your background.  So why the switch from computer programming to teaching?

In retrospect I don’t know why I didn’t anticipate that one, since I’ve had dozens of people ask me over the last year or two.  It’s not really that surprising a question, but I have a long and messy history with it.

I had one interview for a tutoring position a year and a half ago with a private tutoring service where the woman interviewing me asked me exactly that – except with more confusion and shock.  I gave my answer and she followed up with, “But, you do engineering – engineers make more money than teachers. Why would you be a teacher?”  Which I had just answered, but since my answer didn’t have dollar signs on it she apparently couldn’t understand. I am not even making this stuff up.  I teach math – I’m pretty sure I can add up that this isn’t a quick route to getting rich.

The interviewer I spoke with last week was far more reasonable, but the question is loaded with so much personal stuff that it still made me laugh a bit.  Switching from software engineering to teaching hasn’t been easy.  It took me a while to shed the layers of cultural, peer, and personal expectations around “being an engineer”, even without looking at the dollar signs.  It took even longer to let go of the layers of baggage around being (having been) a video game developer.  If that’s hard to imagine, here’s a quick cross-section: childhood dream job / engineering pride / coder pride / need for vindication after layoff / dream to succeed as an indie dev / need to have creativity recognized / being “the man” and bringing home the big(ger) paycheck.

But when it comes to the original question, my answer can’t be that different than any other sane teacher out there.  I do it because I love learning.  I love watching people get something they didn’t get before.  I like being helpful (although not too helpful).  And working with kids is fun – they have less stuff in the way of getting to know who they are than grown-ups do.  (Yes, even teenagers.)

This is how I like to sum it up:

“Teaching might be nuts, but it certainly isn’t boring.”

Alt: “Making video games for a living was too boring, so I went into teaching instead.”

From Dan Meyer’s report on the “Thoughts On Rationalizing Algebra In Ways That Serve Kids, Not Universities” session from a recent math conference:

The day before CMC-North I was trading notes with our lead counselor, just swapping stories about kids, when she mentioned a student who was at the end of her turn at the local community college. She’d be transferring to a state college to complete a liberal arts degree if it weren’t for a failing grade in Algebra II. Because she can’t yet perform long division on polynomials, she’ll have to postpone her degree in (just guessing here) linguistics a full year.

Stories like this drive me crazy.  Mathematics has been positioned as the primary gatekeeper for post-secondary education.  What’s worse, thanks to early streaming of math education (in the name of helping students achieve success!) that gate is often locked for students the moment they step through the doors of high school.

Now, my problem in writing this is that I so desperately want to hammer out a harsh rant and lay out exactly what’s being done wrong and how to fix it; except that I just finished my practicum with a cross-section of Grade 9’s in both a “Math 9″ and “Essentials of Math 9″ block.  I know there is no easy solution because I’ve seen at least half a dozen of any category of student you want to think of: underachievers, overachievers, those crippled by poor self-efficacy, students with learning disabilities or global delays, students not actually flagged as LD or delayed but quietly falling behind those who are… the list goes on.  I don’t have a single solution that wouldn’t leave at least half a dozen of those students worse off than they deserve.

But what’s truly frightening is the thought that no amount of educational reform at the secondary level is going to remove that gatekeeper effect.

Western Canada’s provinces and territories are currently adopting a new secondary math curriculum from grades 10 – 12.  This new curriculum has been designed to provide two possible streams leading to post-secondary education.

• Pre-Calculus prepares students for STEM programs.
• Foundations is designed to prepare students for liberal arts programs.
• Applications and Workplace is the “easy” stream, but is notably more challenging than the previous “Essentials” stream. It covers the basic Trig and Geometry knowledge needed for trades work, as well as general life skills math (personal accounting, taxes, etc).

The programs were designed in consultation with post-secondary institutions in Western Canada, and all sounded great.  Then UBC released their basic entrance requirements for students coming to them through this new curriculum:

Either

• Foundations 11 and 12, or
• Pre-Calc 11

The effect being, for students who aren’t going into STEM fields and simply want to do enough math to get to their goal, the Foundations stream will mean taking an extra course.  Naturally, many math teachers see that as a death knell for the Foundations stream as it was designed.  (How many English-majors-to-be want to sign up for two math classes when they can get the pain over with more quickly?)

All of this just highlights the real problem: universities and colleges want a gatekeeper.  They want that extra way to filter admissions, because they have to do it somehow.  Worse, they don’t want to be seen as the “easy” school to get into, because this lowers their respectability.  (This also drives me crazy.)  So they demand gatekeepers, whether or not those gateways are actually a more useful math education for their students.

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).

This last couple of months has been all about getting to really see progressive teaching techniques in action, especially in one of my math-education classes.  I’ve finally been getting firsthand experience of a lot of the buzzwords that have caught my attention lately – co-operative groupwork based in problem solving and discovery learning.  Also, a lot of fun and not a lot of listening to someone lecture.

A common thread that’s come up now and then during my education program is this whole idea of keeping students challenged enough that they’re actually thinking, but not so challenged that they hate you and the course.  Sounds awfully familiar if you’ve looked at game design.  The number of different catchphrases and terms I’ve heard to describe this concept is growing: flow, challenge, “don’t help them too much”, or zone of proximal development (I want to snark about that one, but do I blame Voygotsky or whoever translated his work from Russian?).

But I think my new personal favorite came from the prof of the above-mentioned math class:

“Comfortably frustrated“

Which, as he described it, is when you go “ARG! Okay let me try that again”, instead of “ARG! I HATE THIS I’M LEAVING!”  (paraphrased, but not by much)

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.