Letters to my mathematics class, volume one

Dear class

OK, so you’re in shock, because this is what we call a “letter”… a special form of written communication. I doubt you’ll be familiar with it, but hang in there. It’s just like a text… though u have 2 cope with proper English, which I accept might not be gr8 fun 4 u.

So, you’re wondering how to improve in mathematics, eh? Well, OK, you’re not, but all the same, there are a few simple things you could do that might transform your mathematical ability. It’s not rocket science (that’s upstairs with Mrs McGinty in Physics – don’t forget your fire extinguisher, cos she’s getting on a bit), so why not give it a try.

First up, the equipment. Yes, that’s right Johnny, there are things that you are expected to have with you in your mathematics class. But don’t worry, I’ll explain them as we go along.

Item number one: the pencil

We use these to write with, for the most part, though a good chew on the end of your pencil can keep you going ‘til lunchtime if you’re getting peckish. You’ll have seen pencils before, because I’m forever bloody lending you one, but you know what? You can actually buy these from things called “shops”. They’re not expensive, though granted once your parents have forked out for a new X-box/mobile phone/Wii/pair of trainers, I can appreciate that there’s not much cash left for the non-essentials in life. Maybe you could ask your lawyer, sorry, Guidance teacher if you qualify for financial assistance. Or maybe you can just nick one off Nigel, like everyone else does (but get there early, for much as Nigel wishes his pencil case had TARDIS-like qualities, it doesn’t). But either way, get something to write with, specifically a pencil. Let’s face it, you’re going to make mistakes. So no pens, please. Specifically, no yellow, red, lime-green, scented, glitter dusted, honey-smoked, cinnamon flavoured pens, gel or otherwise.

Now I know what you’re thinking: why can’t you just borrow one from me, like you do all the fecking time? Well, it turns out there’s a limit to the number of wee pencils that your teacher’s allowed to steal from IKEA – who’d have thought it? – and with council cutbacks being what they are, it also turns out we have no money to buy them in ourselves. Yes, we do have funds to buy interactive whiteboards, but not pencils. Go figure.

I’ll sign off now, as I need to lie down, but don’t worry, I’ll write again soon, this time to tell you about the exciting technology we’re calling a “ruler”.

Letters to my mathematics class... coming soon

I see from a review in the Guardian here that the mathematician and writer Ian Stewart has a book out in paperback called “Letters To A Young Mathematician”. Nice idea, Ian! Way to go, etc.

But those of us at the chalkface (or interactive whiteboard face, if you prefer, though it doesn’t have the same ring and whiff of dust to it) know that this can be taken further. Oh sure, by all means write a book for young Nigel the maths geek… but what about the rest of the class? What about Wayne, who wouldn’t know a quadratic if it fell on him from a great height? What about Nikki (two Ks, two Is), who currently has her book upside down? And what about Lee, who has his finger up his nose?

Fear not, people, for the-proof-is-out-there is here to help. I give you… letters to my mathematics class. Enjoy.

(Posts to follow, honest!)

Higher musings

OK, late again, but better than nothing...

General consensus for this year's Higher Mathematics exam was that it was more or less OK, if a bit... meh. Kids found paper one (no calculators, folks!)** pretty straight forward, whereas paper two was more challenging. My first sight of paper two left me a bit concerned, but I think the questions looked worse than they actually were once you got down to it and gave it a go. But three questions in paper two on logs/exponentials? That's a bit weird.

Mind you, if you're going to make one paper harder than the other, at least they got this the right way round. If I was being picky I'd say paper one was too easy, but I suppose they made up for it later.

There you go.

(** unless of course you are allowed to use a calculator in the non-calculator paper... don't get me started, I'm saving this up for another time)

Jings, yet again...!

I've raised before in this blog the question of how important understanding is when you are teaching new methods in maths. I have a suspicion that for many people understanding actually follows rather than precedes the ability to carry out, say, an algorithm in multiplication. Does it matter if we don't understand the theory behind it? Well, some say it does, and in parts of the US new curricula are being developed that attempt to remedy this seeming problem.

I have to say I'm worried.

I thnk we've been here before, with the idea that pupils are meant to "discover" maths for themselves. Don't get me wrong, I like an investigative approach as much as the next mathematician... but there are surely limits to what can usefully be created in the time available. To put it another way, if you want the students to discover the maths, you'd better give us a lot more time in which they can do it. And besides, are the standard algorithms really so bad?

But hey, why listen to me on this, when you can see what I'm on about here.

So how was it for you?

Well, I suppose I can't really keep a blog on maths teaching in Scotland and not comment on the SQA exams, so it's probably time I gave my thoughts on the Standard Grade papers from last week. Feel free to disagree.

Overall they were fine, sort of, in that they were reasonably free from daft questions that are so non-standard that very few pupils will get anywhere with them. In years past there have been a few real beezers, the sort of questions where you despair of the setters, because you can't believe a teacher working "at the chalk face" wouldn't spot straight away that something was badly awry. This year was fine in that respect.

Relatively speaking, I think the hardest paper was actually the Foundation one (the "easiest" level by far), where the level of numeracy expected was quite challenging for the pupils concerned. (There's a real problem with maths at this level: in most other subjects pupils end up with grades better than Foundation, whereas we see kids actually failing at this most basic level. But that's a discussion for another day.) The General paper was a skoosh, and as for Credit...

Well, initially I was pleased because, as I've said above, there were no daft questions. But upon reflection I have to say now that I think the exam was just too easy - and believe me, I don't often say that. In particular, the level of algebraic skills required was way too low and there was no hefty manipulation (quiet at the back) which would help to really test a pupil's algebra at this level.

Now OK, maybe SQA will raise the cut-off scores to reflect an easier exam, but all the same I'm worried that we're going to have pupils with a Credit grade who don't really deserve it - and, these pupils are then going to attempt Higher next session, thinking they're doing well. Recent SQA statistics show that fewer than 50% of pupils with a grade 2 at Credit (the lower of the two possible pass grades) manage to pass the Higher in fifth year. I don't see how this standard of exam is going to change that depressing figure.

(Mind you, if my class don't get good grades come the results in August, boy am I going to be mad! Talk about setting yourself up for a fall...)

Key question: if we want to improve the standard of maths education in Scotland, do we have to award fewer passes - at least, to begin with?

Hmm.

Still alive...

You can't keep a good blog down... or something.

And so, after a 2 month hiatus, here we go again. Well, I've got to have something to do on exam leave, haven't I?

So...