Changes are coming

So if you’ve missed it (which is pretty likely unless you happen to be a Victorian maths teacher), a consultation period for the new VCE Mathematics study design has just begun. You can find info on any of the maths study pages on the VCAA website. They have a draft of the new study design to start in 2016. That means the current 2006 study design will last ten years once we’re done with it. So it’s probably due for a refresh.

It’s probably a good idea to go read the new study design in detail so you can give an informed opinion in the online questionaire they have. Instead, I’m just going to glance at the changes and just blog about my gut reactions.

The only VCE maths I’ve taught is Methods Unit 3 & 4 (and for the last few years at that), so most of my comments will focus on it.

Also, if it isn’t clear, the new study design is only a draft. So don’t go crazy about it yet.

No more “(CAS)”

“Mathematical Methods (CAS)” is dead! Long live “Mathematical Methods”!

By that, I mean they’ve dropped “(CAS)” off the name of the subject. Which totally makes sense, really, since it’s been our only “Methods” for a while now.

For context, a while ago (2004ish? When I was at school still, anyway) CAS calculators were introduced into the curriculum by adding “Mathematical Methods (CAS)” in parallel with “Mathematical Methods”. But then the original was killed off a few years ago, leaving us with only one Methods subject with “(CAS)” tacked on the end.


OK, I might have gone on record recently stating I’ve never really liked stats, but I’ve always thought it an odd omission not having statistics in Methods. But it’s there now: Area of Study 4 is now “Probability and Statistics”. Specifically, Statistical Inference is added, following on from Discrete and Continuous Probability Distributions.

Not only that, but Specialist Mathematics now has a “Probability and Statistics” area of study too. It’s been strange that up to this point, the only way to study statistics in Year 12 was in Further Mathematics, which not many of our high achieving maths students would do (though I hear there’s also a lot of stats in Psychology).

Of course, to make room for all the lovely new stats, something else has to give …

Where’s my matrices at?

So the list of topics removed from Methods includes:

  • Markov chains/sequences and transition matrices
  • matrix representation and solution of simultaneous linear equations

And while not in the official list of changes, I can’t find any mention of transformation matrices in the draft either. While this makes me somewhat sad (I loved linear algebra at uni) it’s somewhat understandable. The old treatment of matrices was a little unusual: we had to explain what they were for these three tiny parts of the course, but there was never really room for proper coverage of them.

Though I have one concern over their removal, from my personal experience. I went to school in Victoria and got my VCE, but I went to univeristy in South Australia. My very first lecture freaked me out – it was on matrices, and I had absolutely no idea what they were! I borrowed a SACE maths textbook from the library and got myself caught up pretty quickly, but by removing matrices from VCE again, are we making this situation possible once more?

As far as I can tell, the only mention of matrices in the draft is in General Maths. My small school isn’t big enough to run multiple General classes, so we usually only use it as a feeder into Further, so we’d be unlikely to cover matrices at all.

Honestly, the other removals from Methods seem sensible to me: topics that are interesting, but probably not essential when you’re trying to trim down a subject.

No more tests!

There are only three SACs set down for Methods now:

  • One “Application Task” over 1-2 weeks in Unit 3.
  • Two “Modelling or problem solving tasks” (the old Analysis tasks, probably) in Unit 4.

Missing are the two tests from Unit 3. Of course, there’s nothing stopping a teacher from setting their own non-graded tests, revision quizzes, or whatever you want to call them. My students are going to hate me…

New subject!

Specialist Mathematics Unit 1 & 2 is now a thing. I don’t really have anything to say about that yet.

There’s also got to be other changes I haven’t even noticed yet. I’ve already written a lot more than I intended, so I’ll leave it here for now. Again, these are just my first reactions, I might completely reverse my opinions in the coming days. If you’re a VCE maths teacher (or English for that matter, I think they’re being reviewed too) don’t forget to look through the draft yourself.


What if only one side of the earth faced the sun…

Today my VCE Unit 3/4 Maths Methods class was preparing for the test we have tomorrow, but we became distracted for a while. At the time I was disappointed in myself for letting that happen, but reflecting on it now, I’m actually pretty excited about it. Let me explain.

We were talking about circular functions, reviewing how to determine maximums and minimums, as well as sketching their graphs, just by looking at the functions. I mentioned that we’d seen a lot of functions that look like sin(π•t/12), which they realised related to cycles with a 24 hour period (hooray!). So far, still relevant.

Then one of my students mentioned that they’d seen a lot of questions about tides, but we remembered that tides have a period of 12 hours. That led us to talking about why, which led to talking about the Moon’s motion around the Earth, which led to me mentioning that the Moon is tidally locked with the Earth (that is, we only ever see one side of it).

Which led to someone asking this question:

What would happen if the Earth was tidally locked with the Sun?

So we talked about this for a while, and decided:

  • Each side of the Earth would be uninhabitable for being too hot or too cold. But hopefully there would be a zone in between which could sustain life (which would be in some kind of permanent sunrise/sunset).
  • Solar energy would be a lot cheaper and easier – solar panels could be in the sun all the time, and we wouldn’t have to change their direction.
  • We could build houses that rotated slowly so each side would get the same amount of sunlight. The rotating motors would be powered by our cheap solar energy.

This is where we ended the conversation, because we had revision to do, but I wish we could’ve kept going. Because what we had been doing really was maths in disguise. Well, kinda…

We had started with the statement “The Earth is tidally locked with the Sun” and followed that statement to a logical conclusion. We were thinking about the consequences of that statement in order to discover new truths. And isn’t that, if nothing else, what mathematics is?

Yeah, I know I’m stretching the definition of maths past the point of breaking here, but this is why I don’t think my ‘distraction’ was a waste of time. If we can teach a student to take an idea (be it mathematical or otherwise) and think “What if?”, isn’t a lot of our work already done?

I’m not suggesting we throw out our current curricula in favour of talking about silly ideas all lesson, and we did get back to sketching curves and differentiating functions pretty quickly (we have that test tomorrow, after all, not to mention the exams at the end of the year). I guess I’m just excited to have a class who’s willing to think through problems both creatively and logically, even if that means following Mr Carter on the “What if?” crazy-train every so often.

BTW: If you’re not already reading What If? by Randall Munroe (of xkcd fame), well, you should be.


Statistics Questions

I’ve never really liked statistics.

I know that’s a terrible thing to say as a teacher, but it’s true. Stats has always seemed too messy and too tedious to me. Compared with algebra, with it’s clear “it’s either proven or it’s not” results and elegant working, statistics is all over the place. (I majored in pure maths at uni, if you couldn’t tell).

But I think I’m actually starting to get a soft spot for stats now. I’ve realised something: statistics (and all maths and science, for that matter) is most interesting when it tells you something about the world that you didn’t realise before. Or maybe when it tells you something you already thought, but could never justify as true. I think I already knew this, but hadn’t bothered to actually put it into words before.

Statistics has a function that no other area of mathematics can really cover. Whenever we have a logical statement that we want to prove as true or false, algebra has our back. But for those questions that we don’t really know the answer to, that we have no real way of proving but want to have a crack at finding out anyway? Time to reach for the stats toolbox.

This is the key thing to convey to students about statistics – stats is how we answer those questions that seem, at first, unanswerable. So my Year 9 class started our statistics unit by asking a question. Learning from last year, I put a couple more restrictions on what the question could be:

  • The question had to be interesting. In my experience, some groups start with simple, obvious questions because it fits their need to complete any set task as quickly as possible. They don’t realise how bored they’ll be later in the project. I had to reject questions from a few groups, which annoyed them at the time, but I think their new questions were a lot more interesting.
  • No survey questions. I wasn’t letting my class interupt every other class in school. I think I was the most hated teacher in the staff room for a while last year.

So questions like “What’s the favourite AFL team of our school?” and “What type of music do teenagers like?” were out. These are the actual questions asked (and to be answered!) by our class:

  • Do pink marshmallows cook faster or slower than white marshmallows?
  • Does closing one eye affect the ability of a person to shoot a basketball or a netball?
  • Which types of biscuits go soggy in hot drinks first, and are they affected by adding milk?
  • What effect do TV shows and movies have on the heart rate of the viewer?
  • How is the cooling rate of boiled water affected by the container it’s kept in?
  • How do different web browsers (Chrome, Firefox, Internet Explorer) compare in terms of Javascript speed, when run on different devices?

(I apologise to any of my students if I got these wrong, but I wrote that list from memory.)

It was last week when they chose their questions. They performed their actual experiments today, and I’ll share a bit more about that once they’ve written up their projects.

But I’ll share one preliminary result: the heart rate group chose me as one of their test subjects. I really stood no chance keeping my pulse steady: they showed me a scene from Doctor Who. Not only that, but it was the Tenth Doctor’s regeneration!

Then they showed me a scene that I found out afterwards was from High School Musical. Let’s just say that my choice to never watch that movie was the right one.


Blogging in 3, 2, 1…

OK then. This is the start of my blog. Not the most exciting start. I guess I should introduce myself…

Hi. I’m Shaun, a maths teacher from Australia, rural Victoria to be more precise. I’ve been teaching for four and not-quite-a-half years, at a small P-12 school (combined primary and secondary), though all of my classes are senior secondary (well, this year anyway). I also teach IT and sometimes pretend I know something about Physics.

OK, I’ve actually taught a bit of Physics over the last few years. It’s just, who really wants to teach Physics when they could be teaching Maths? 😉

I’m planning to use this blog to share teaching ideas, and maybe just ramble about anything else that catches my interest (typically fairly nerdy stuff). That said, who knows how that will actually turn out?

I’ve been following a number of mathsy type blogs for a while now, so I thought it was about time I jumped in on the action. This is also the first year I’ve introduced a new ICT class ‘Web Development’ as a year 9 & 10 elective, so I thought building a website was a good way to update my own skills.

For that reason, I chose to build this site myself, rather than going with a service like blogger or I’m using ghost as the backend, but I wrote the theme myself; if you really feel the need to look at my code, please ignore the fact that it’s a complete mess at the moment. I’m pretty sure there’s a lot of commented lines that I haven’t gotten around to deleting yet. I really am an amateur at this stuff.

So about the name. I realise already that it wasn’t the best choice of a domain name, as the US (and a fair chunk of the rest of the world) doesn’t spell ‘factorise’ the same way we do here. So that doesn’t make it all that easy to find.

And to be honest, I don’t really know myself what it means. Number Theory was my favourite course at uni, so I guess that’s what I chose a reference to? But who knows what ‘The Prime Factorisation of Me’ is supposed to be about. Is it possible to factorise a person? Maybe it’s saying that by breaking the different aspects of me and my teaching practice down into my simple prime parts, I can build them up together to become a more awesome, composite, teacher? Or maybe it’s the first available domain I found and now I’m just sticking to it.

(For the record, just as the default theme for Ghost is called ‘Casper’, I’m currently calling the theme of this blog ‘Composite Human’. I thought it was appropriate.)

Also, it’s less than ideal, but I don’t have comments yet, because Ghost doesn’t support them. I’m still figuring out how to do that one. Maybe Disqus? If you have any suggestions, maybe you could leave them in the … oh, right.

So that’s the awkward first post out of the way. Maybe next time I’ll actually have something interesting to say.

EDIT: So to address the whole no comments thing, I’m now on twitter: @theshauncarter.

EDIT 2: As you may have noticed, I’ve decided to give Disqus a trial run. Was really quick to set up, but it seems to act a little weird. In theory I’ve allowed guest comments, but it doesn’t seem to be working.

EDIT 3: My bad, guest comments are working fine.