Teaching Math in Ontario

Ontario has – well, “had”, because it was just ruled unconstitutional – a Math Proficiency Test for new teachers. Which has been quite a topic of discussion around here, as my daughter is just finishing teachers college, and my future daughter-in-law is currently teaching.

In another version of my life, I thought I’d be a math teacher. I’d be that cool teacher who gets the kids excited about math (and also directs the pep band.)

so I woke up this morning and I thought, you know what would be fun? Why not try the practice test and see what this is all about?

You can try it too .

Perhaps this is an odd definition of ‘fun’ but I enjoyed going through the test.

71 questions. 2/3 of them are on math, and 1/3 on pedagogy, and then there’s an optional questionnaire. I believe 70% is a passing grade. For the past year or so, all new teachers were required to pass this, but the future of the test is up in the air at the moment.

plunging ahead

This, believe it or not, is one of the actual questions. (I got this one right, phew.)

Sample Question

What on earth is going on here? Is this an attempt to catch bots, or people who always answer “B” to every question, or a test to see if you’re reading, or was there originally some question that they later decided was inappropriate?

the math part

I did not have much trouble with the math part. Some of the questions let you use a calculator but as a show of mental toughness I decided to try doing all the questions in my head. Got one wrong – dumb arithmetic mistake that I’m sure I would have caught if I used the calculator.

Some of them are unbelievably basic, like (paraphrasing)

In the number 470,253, the digit ‘7’ represents what?

  1. 70
  2. 70,000
  3. 700,000
  4. 7

Others require you to evaluate a little expression using BEDMAS (“What is 16 – 2 * 3 + 5 * 0”, that kind of thing) which if you’ve been on Facebook any time in the past year, you’ve seen some idiot version of this which has fourteen million wrong answers in the comments.

And at one point I had to pause for a moment to try to recall the formula for the area of a parallelogram – one question showed you a parallelogram, gave the lengths of the sides, and said “if you divided this into two congruent triangles, what would be the area of each” and, well, there’s a button in the test that takes you to page showing all the formulae for things but you know what I REMEMBERED HOW TO DO IT WITHOUT LOOKING IT UP phew.

You could answer a lot of the questions that required calculation by just doing a rough estimate with rounder numbers – can I quickly come up with something that’s within 25% or so of the right answer? – which was often enough to rule out 3 of the 4 choices. This is also a useful skill. You don’t always need to do an exact calculation.

So, good news, I passed the math part with flying colours. I should hope so. I have two degrees in math, which honestly is two more degrees in math than anybody really needs.

the pedagogy part

The last section was pedagogical questions. This sort of thing. (I got this one wrong, I think I mixed up “of” and “for”.)

Pedagogy Question

My daughter commented – Yeah…I mean that question would be very easy for someone who’s taken a pedagogy course…but yeah that’s the level of minutiae.

She’s right, this pedagogy part just seems to ask you to repeat the buzzwords you learned in a course. It’s a test of memorization, not of math and logic.

The first part of the test seems like a pretty reasonable way to evaluate if somebody remembers what they were taught up to about 9th grade math. I think that’s a reasonable thing to ask of all teachers. They’re not asking you to do calculus, they’re just asking you to apply some general principles. I heard it said once that All teachers are teachers of language, and I think you could extend that to basic math numeracy too.

But the pedagogy part. That would really trip up people whose first language isn’t English, for one thing. And what’s it doing in a test about math proficiency?

having said that I am delighted to say I got 17/20 on the pedagogy part with some educated guessing, which is also a useful skill. I’ve been lucky to work in the education division of my employer so I’ve been around teachers for a while.

And Cathy reminds me “Didn’t you actually go to teachers college?”

Well, yeah, I did, for three weeks; I am a proud dropout of York University, after a brief, unsuccessful midlife crisis experiment a while ago.

It turns out some of this is hard.

the questions I hoped it would include

Math is a wonderful thing!

Get off your ath and do some math!

Six times a billion is …?

so should there be a math proficiency test?

Yes. Yes there should. Math is a universal language. It is the foundation of truth, and beauty, and has a standard of proof higher than that in any other field of human endeavour.

When we send satellites out of the solar system, hoping they will some day reach a distant galaxy, we engrave plaques on them with math symbols to prove that we are an advanced species. Prime numbers, in particular, are such a fundamental idea that if you can just list them in some language-independent way, like this –


that that’s a good start at demonstrating where you are. There is no conceivable universe where 7 is not a prime number! We have to agree on that with whatever aliens are out there!

The first radio message beamed out to the stars from the Arecibo Observatory in 1974 was sent as 1,679 binary pulses.
Why 1,679? It’s the product of two primes, 73 and 23, and if you can figure that out, you might realize you could arrange the binary pulses into a 23 * 73 graphic like this (colour here added by the Wikipedia article with all the details- but can you see the patterns in there?

There’s a human (red) and a representation of our solar system (in yellow) – notice how the 3rd dot is offset, that’s where this message originated. And more. How much of this can you figure out? Here’s the details.

400px Arecibo message svg

Isn’t that cool? Yes, yes it is.
Math. It’s everything.

But the pedagogy part. That needs some thought. That belongs somewhere else.

Apple + NeXT, 25 years ago today.

Apple and NeXT Announce Merger

25 years ago today, I was a field systems engineer for NeXT, one of three NeXT employees in Canada – and our family was in Scranton, Pennsylvania, introducing a three week old baby to his grandmother.

Nobody had reliable cell phones back then, so most messaging was done through a voice mail system called Audix, and somehow I still remember the number. 1-800-345-5588. I dialled it the other day. Number not in service. But I can still dial it quickly.

So anyway, we got a sudden Audix message. Urgent. Everyone must dial in at 2 PM. I went looking for a reliable land line for the call, not having much idea what it was about, and somehow wound up on a pay phone at the Steamtown Railroad Museum. (which I kind of wanted to visit anyway.)

And there, we learned that NeXT had agreed to be acquired by Apple for $400,000,000.

In retrospect, the tech involved in the merger wound up being so one-sided that many people say “NeXT actually bought Apple for negative $400,000,000.” A few years later, something like 70% of Apple’s VPs were ex-NeXT people.

I was floored. I didn’t expect this at all.

NeXT was struggling. Our founder, Steve Jobs, seemed to be spending all his time at his other company, Pixar, and although we just just eked out our first quarterly operating profit (mostly based on selling WebObjects, a Java application server) we weren’t exactly setting the world on fire.

Here’s the sort of thing NeXT was selling at the time – a press release from three weeks before the merger, touting CyberSlice, a revolutionary new system for (get this!) ordering pizza from your computer. (WebObjects was also powering the Disney and Dell online stores, and Steve had even demoed using it to buy a plane ticket through a web browser. Heady stuff for the mid-1990s.)

“CyberSlice has enabled any small or large pizza provider to get online,” said Steven P. Jobs, Chairman and CEO of NeXT Software. “NeXT is excited to provide the enabling technology to CyberSlice, which combines fun with an innovative business concept. The success of CyberSlice shows the versatility of WebObjects in creating and deploying consumer web applications that are both sophisticated and original.”

It must have been killing Steve Jobs that his vision of a revolutionary new workstation and operating system for higher education hadn’t panned out and that he was now reduced to selling enterprise server software for $50,000 a copy.

Apple was seemingly caught in a death spiral too and was getting awfully close to running out of money.

two weeks earlier

Two weeks earlier, I’d got a call from a former NeXT colleague Barb, who’d gone to work for Apple. She wanted to know if I wanted to come along.

“No thank you”, I replied politely, when what I was really thinking was “What, that bunch of losers? Why would I go there? They’re the only company going out of business faster than WE are.”

But the merger happened anyway, and Barb called me about a minute after it was announced to say “Well, we really wanted to hire you, so this is the only plan we could think of.”

I always wondered if the message of “We really need to hire Steve from NeXT” got garbled somehow.

shortly thereafter

Barb called and invited me to visit Apple’s office in Markham to “show us what the heck it was we just bought.”

What Apple was most interested in was NeXT’s NeXTSTEP operating system that originally came with the NeXT cube but had been ported to run on Intel systems as well. I wasn’t even using that day-to-day any more; most of my work was using WebObjects on Windows NT. But I managed to reinstall NeXTSTEP on my Toshiba Tecra, and took that up to Markham for a demo to the Apple team.

I remember struggling to get my laptop to work with their weird mutant boardroom projector, and thinking “geez, I hope this works.” and I wasn’t just thinking about the projector.

Ultimately we got it to work at a cramped 640×480 resolution and I was able to show off NeXTSTEP, Unix, Interface Builder and (horrors) the Terminal program, which was pretty much the opposite of what Apple had been providing.

Everybody at NeXT was so unclear that this merger was going to work that we all handed out our NeXT business cards for as long as those phone numbers and emails still worked. (Remind me to write up my “I was steve@next.com” story some time too.)

eventually all was well.

It worked out OK, though. The merger happened at a historic low point for Apple, and once Steve Jobs came back as CEO, an incredible technical and business turnaround began.

NeXT’s software and hardware became the foundation of everything Apple made. The NeXTSTEP operating system – which NeXT was just about to shelve, until a midlevel NeXT guy John Landwehr (hi John! How are things at Adobe?) cold-called Apple’s CTO Ellen Hancock to ask if they needed a robust operating system because Mac OS was really shaky – became the foundation of Mac OS X; NeXT’s Project Builder and Interface Builder became Xcode; NeXT’s love of the Objective-C language eventually created Swift.

And, all that technology that I started learning when I bought my $11,000 NeXT cube in Indiana in 1988 now runs on my phone. And my watch! On my wrist. Objective-C and NeXTSTEP runs on my wrist today. Crazy.

And here we are. It’s been a pretty amazing run.

The three week old baby turned out to be a fine young man too.

My NeXT Badge

My NeXT badge, and over my shoulder, my NeXT cube.

the people

At the time of the merger, NeXT had about 400 employees, and Apple had only a few thousand. Today. Apple has 160,000 people. I’m curious how many of the NeXT crew are still here. I know about a dozen, and I’m sure there are more. 100 maybe? Who knows. We’ve all been incredibly lucky.

PS. This is a photo of the last ever gathering of NeXT employees before the merger was legally finalized. To my great regret, I was not able to get out to NeXT’s HQ in Redwood City for this picture, but it sure brings back a lot of memories.

Very Last NeXT Team Picture No Logo

Orchestra Wee Wee

In 1999 the Hamilton Tiger-Cats managed, somehow, to win the Grey Cup, a feat they have not accomplished since but they’re going to try again next Sunday.

In June of 2000, the team held a banquet at which the players were awarded their Grey Cup rings. And since the team had a sense of humour, they actually contacted, us the arch-rival Argonotes, the Toronto Argonauts Band, to see if we’d pretend to be the Ticats band for this event.

(Hey, they offered us food and beer – and T-shirts – how could we say no?)

So here is Orchestra Wee Wee, the temporary Hamilton Tiger-Cats Pep Band, at the Grey Cup Ring Presentation Ceremonial Dinner


As far as we could tell, nobody noticed that the band looked kind of familiar, but we gave it our best shot and played the Tiger-Cat Marching Song multiple times. Our band has a long history of playing that song in Hamilton and wondering if anybody recognizes it.

The Ticats, recognizing a good thing when they hear it, briefly set up their own pep band and we were delighted to confront them at Ivor Wynne Stadium at a game in 2003. Here’s a joint picture of the Massed Bands of the CFL East Division at the Labour Day Classic in 2003.

P1010022 1

That too didn’t last but it sure was fun.

here’s an email I sent to Argonotes after our rousing success as Orchestra Wee Wee –

From: Steve Hayman
To: Argonotes
Subject: Orchestra Wee Wee!
Date: June 30, 2000

I want to thank the 14 members of Argonotes who became Orchestra Wee-Wee, the Hamilton Tiger-Cats Band last night for Hamilton’s Grey Cup Ring Ceremony dinner. Over 800 people were in attendance to see the Ticats presented with their championship rings, and as far as I can tell nobody managed to put 2 and 2 together and realize that some of the music they were hearing sounded very familiar!

We got off to a shaky start. Weather caused the mother of all traffic tieups on the QEW – *three*hours* from downtown to downtown –
and everyone (including Premier Harris) was late, and when we started playing we had a whopping four people on hand, but once we all got there, they hustled us up to the balcony overlooking the banquet hall and had us play the Alleged Former Ticat Song (“We love those Cats,
those Tiger Cats ….”) over and over and over again while the players were being introduced. I imagine we played it more timesin that one stretch than it was ever played at Ivor Wynne Stadium in history.

We did a nice, tight, post-banquet show outside the hall as well. It’s amazing how good you can sound with the right 14 people
in place!

We got a picture or three of the band, in our souvenir Hamilton TiCat shirts, with the Grey Cup, and I’m sure it will be featured prominently on our “other” web site, www.ticats.com, as soon as yours truly gets his scanner fixed.

Thank you again to saxes Clem, Steve and Trevor, trumpets Alex, Gary and James, trombones Richard, Ian and Deb, tuba James, and percussion Bud, Angela and Tina. I really enjoyed doing this and I thinkwe did ourselves and Argonotes proud. Fundamentally I think we are all CFL fans as much as we are Argo fans, so if we can do the odd thing to help Hamilton, it will be good for the league, and maybe it will even shame Hamilton into actually organizing an actual band.

They’re already looking forward to having us visit for the Toronto at Hamilton game on Friday October 13. Game time is 7:30. based on what we saw of the traffic yesterday, I think we should all plan on taking the GO train.

Have a great Canada Day and we’ll see everyone at our next ARGO game, Tuesday July 11 vs Montreal. Meet at 6:30 at Front and Simcoe. More details later.

Oskee-wee-wee—excuse me, that should be
Argos Rule,

P.S. The Fan 590 has inquired as to whether we might be available for some sort of parade on the 11th from their downtown studio to the dome. It’s intended to celebrate Toronto’s home teams and will involve both the Jays and Argos, and a double decker bus which we might be able to ride on. I think, unfortunately, it’s during the day but if it’s at lunch time we might be able to find enough people. I’ll let you know the plan, if there is one, when I find out more details.

P.P.S. Yesterday I got a call from someone wanting to hire us for a Canada Day parade. (As you might expect the answer is “No, even if we did do parades, don’t you think we would have figured out something for July 1 before June 29?”)

P.P.P.S. I got another invite for a parade later in the year in Mississauga. Here is how this kind of thing usually goes. They tell me that they’ve got the Argonaut cheerleaders, so they figure they could get the band; however it usually means they have 3 of the 30 cheerleaders, and while that works great for the cheerleaders, if we had a turnout of 3 people it wouldn’t be quite as great, soI usually politely turn this sort of thing down.