Some Thoughts on Teaching Math and Computer Science

Two unrelated thoughts about teaching math and computer science that I came across today.

Tau the line

First, today is π day, celebrate mathematics and the beautiful wonder of nature!  But could π be…wrong? π of course, is the ratio of the diameter of a circle to this circumference and a snazzy number to throw out in Divinci Code-esque thriller novels.  It has an air of magic and mysticism which mathematics is actually full of.  But only a few such numbers and equations break through the collective consciousness to the general non mathematical public: π, E=MC²,  imaginary numbers

So that’s why tau manifesto is so interesting. It’s a very well written and entertaining piece about geometry, history and π. It lays out the case that π is actually not the most natural number to use for circles. It’s not that π i

s wrong, its that its awkward and that in fact τ, pronounce ‘tau’, is actually more natural.  τ is simply π times two.  This simple change actually simplifies a lot of what was tricky about advanced geometry in highschool and it has implication for how formulas are written in many fields of science given that π shows up in a lot of equations about the working of the universe.  So, after reading the whole thing, I’m a believer, if only for how it might make teaching geometry a little less painful for students. So while Pi Day is nice, on June 28 I’ll be celebrating Tau Day too. And like the author says, if you enjoyed the baked pie on Pi Day, you’ll love Tau Day, it has twice as much pie!

Big-O No!

The other teaching topic I thought of today is probably one someone has already done.  If you are a computer/physics/math nerd you owe it to yourself to be addicted to the great XKCD webcomic. It’s really got some great stuff and almost all the jokes or comments require some significant knowledge of math, programming, statistics or science.  When teaching computer science it is very easy to get separated from the reason we are teaching various theoretical concepts, algorithms and analysis techniques. It usually can be grounded down to preparing students to be better programmers or modellers or to give them the grounding needed to understand other courses later on where they can get computers to do truly cool things.  However, it’s often difficult to make that connection for students before they actually know how those cool things work

But how about these learning goals? They are fun, easy to evaluate and provide clear goals to students in that they are total gibberish before the course and funny jokes afterwards.

1) After successfully completing this course on optimization you will…understand why this is funny.

And be able to explain why its funny, or at least supposed to be funny.  We won’t deduct marks if you don’t laugh, but we will judge you 🙂

2) After this course on complexity theory you will understand why the following comics are funny:

3) Unix Tools:

I’m there are lots more. If you can think of one put it in the comments <XKCDNumber> : <Course Topic>


What does 42 mean to you?

This is a call to all geek bloggers out there. This upcoming sunday is 10/10/10 no matter which way you order your Gregorian calendar which is 42 in binary…. If you don’t know the significance of that number you can stop reading now, sorry for wasting your time.  It’s not my fault you aren’t interesting in the answer to the question about the Life, Universe and Everything.  It’s not even my fault that you have such a self-important view of our scrappy little piece of dirt called Earth that you don’t care about all the news going on in the rest of the galaxy.  That’s so like humans. No interest in anyone but themselves.  That’s why nobody gave us a ring to let us know about that bypass the Vogon’s were building right through our front yard.  They knew we didn’t follow the local interstellar planning council motions, and they didn’t even give us a call.  Well I hope they’re happy.  What happened to that bypass anyways? Oh well, maybe that was a different universe.

Anyways.  The point is, this sunday is Pan-Galactic 42 Day.  So how should we bloggers celebrate or mark this occasion?  I have a proposal, and don’t worry this one doesn’t have anything to do with political parties making bold and visionary (thus highly unlikely) agreements like most of my proposals.

This proposal is simple. This sunday, on your blog, release a post to be added to that most remarkable of all books ever to come out of the great publishing corporations of Ursa Minor, The Hitchhiker’s Guide to the Galaxy.  The post should be on the topic your blog normally discusses with the aim of opening the eyes of the shortsighted humans on Earth who usually have no interest in galactic matters.  I will, of course, be writing a summary of the many different, and surprisingly progressive, democratic systems used by other planets in the galaxy and beyond.  How do the Silastic Armorfiends choose their Senators?  How do the sentient matresses of Squornshellous Zeta select their chief negotiator for the next year’s mattress culling?  What kind of voting system allowed Zaphod Beeblebrox to become president of the galaxy? And how many sub-triplicate forms do the Vogons needs to fill out to exercise their franchise?  All this and more will be revealed on Sunday.  And you should get writing your own poignant H2G2 entry for 42 Day as well,  this might help .

On the surprising chance that anyone reads this and actually does it I’d be happy to add links to your 42 day blog on this page, but you probably stopped reading this when I got to the Armour Fiends.  Stupid humans.

42 Day Blogs

A nod is as good as a wink to a blind bat

Another day, another justification for dropping the mandatory long-form census by the Conservative government.  Today’s argument comes from Finance Minister Jim Flaherty; he basically argues that because a bunch of policy wonks came voluntarily to a meeting when invited by the Federal Finance Minister that most Canadians will fill out a 40 page census form if they receive one, as long as we ask them nicely.  Flawless little bit of logic, that.  Because, you know, most Canadians are very similar to those people he met this week.

Even beyond the astounding ignorance of this statement there was a more subtly offensive idea in his point.  He asks us to dismiss any rational attempt to use rigorous methods to analyse the state of our nation.  He implies that somehow, ‘Canadians being nice’ will compensate for the statistical bias they are adding to the census.  Can the Finance Minister quantify how ‘nice’ Canadians are and how willing they are to fill out 40 pages of questions if they don’t have to?  Even if he’s right, the census will be biased towards ‘nice people’ who do something just because they are asked, and who have the time and leisure to do so.

The Damage is Done

This brings up something I haven’t heard anyone mention yet.  The damage is now done.

You see, the original problem with dropping fines for not filling out the census (I never had any problem with dropping jail penalties, since this was never enforced it seems a non-issue issue) was that it would create a huge difference in returns from previous census’ and drop the number of people filling it out in an uneven and unpredictable way.  The new problem we face now, even if the government completely reverses their decision, which seems unlikely, is that the government who is collecting this data has been undermining it and badmouthing the very collection process all summer.  That’s going to influence a lot of people.  I would predict that even if the census were mandatory next year that the number of people not filling it out will actually skyrocket because the government is essentially handing it out to people while winking and whispering ‘nawww, don’t fill it out, it’s all a sham, we have to give it you, but we don’t really want to’.

So Flaherty’s assertion that Canadians will fill out the census if you ask them nicely doesn’t fly, because he’s not asking them at all.  No matter what happens, Statistics Canada is going to need years to rebuild their credibility with any Canadians who have believed the current government’s statements.

Called Out by Nature

In other news (well other census news, ok I’m obsessed) the Conservatives were called out by Nature itself this week.  Not Mother Nature, although I’m sure she’s upset at the Conservatives too, she’s just not very, you know, vocal.  No, the esteemed scientific journal Nature this week put out an unprecedented editorial slamming the Conservative government for scrapping the long form census and undermining statistical data that researchers in Canada and around the world rely on.  This isn’t Maclean’s calling them out, it’s not even some pop science magazine like Scientific American.  This is Nature. This, along with the journal Science, are the big scientific journals for general science.  Every scientist in the world of any stripe will hear about this very soon and shake their heads.  Now, scientists are usually a hard lot to pin down to agree on anything. Look how long it took them to definitively state that human’s were causing global warming. But there are just a few things they ALL will agree on if you ask them (in no particular order)

  1. The Earth goes around the Sun
  2. Human’s and Apes have common ancestors
  3. The entropy of any closed system will inevitably increase over time AND
  4. We always need more data, not less; and collecting data without controlling for relevant variables makes that data completely useless

Like asking Canadians, nicely

Please fill out these 40 pages of detailed information, but you know, we wish we didn’t have to, and its kind of intrusive don’t you think? Sorry,  so, try to return it whenever you can, if you feel like it. Thanks

The New Conservative Government of Canada
The Government of Canada
— Statistics Canada

A Concession

This week Prime Minister Harper did made a concession on the census but its one that indicates all their arguments are nothing more than diversions.  They added a couple of questions on Quebec language to the still mandatory short census.  This was only hours after a Quebec court agreed to hear a Quebec language group’s complaint that undermining the long-form census would violate laws meant to protect French language rights.  By caving in on this issue the Conservatives are indeed demonstrating that statistical somehow voluntary census collection is fine for most information unless it happens to relate to a voting group that the Conservatives are afraid of or want to get votes out of.

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