Sunday, November 19, 2006

Is anyone counting?

Some more thoughts, then, on the whole "I don't know, kids nowadays, they can't even add up" business.

I'm not entirely disagreeing with these sentiments, but what frustrates me is that I know - know, dammit! - that the kids in front of me nowadays can actually do more in the way of mental arithmetic, or simply without a calculator, than they could when first I started teaching.

Y'see, when first I hit the chalkface, the exams in maths at school could all be done without a calculator. Now of course we did still teach pupils the basics of arithmetic, but they quickly worked out that if they were allowed to ue a calculator come the actual exam, they were going to darned well use the calculator in class too. We did what we could to stop them but, being mathematicians, we had to admire a grasp of simple logic. Naturally enough, quite a few pupils then started using the calculator for everything: why work out 6 times 9 yourself when the calculator will guarantee the right answer? (And - still the case today - why bother even considering if the answer seems reasonable? Would the calculator ever lie?) So it came as no small wonder that we were turning out a nation of somewhat less than numerate children back in the nineties.

Ah, but then. Then someone somewhere decided the Thing To Do was to give pupils exams which had to be done in two parts: one with our electronic chum, one without. Hurrah! we cried, and set about teaching percentages, fractions etc etc with renewed vim and vigour. All seemed well. All was well. I remember teaching a lower ability class in S3 with an S6 prefect helping out, and I well remember the prefect telling me that she didn't really know how to do half of the stuff these less able pupils were managing. Result!

So, dear general public, rest assured that we do teach tables; that the kids in class do know how to do a fair bit of what "we" used to be able to do standing on our heads.


Nevertheless, I have to agree, pupils emerging out into the world of work nowadays simply are less numerate. And I'm really not sure there's much we can do about it.


Well, as I've mentioned before, in this electronic age, there's simply little or no opportunity for pupils to use or practise these skills out in The Real World. I mean, when last did you seriously - seriously - have to add up some numbers, or do a long multiplication, or add (multiply??) fractions? These kids can do the arithmetic well enough to pass exams, but the skills then atrophy through misuse.

Like it or not most of us rely on electronic aids more than we'd care to admit. Those of us Of A Certain Age do still have reasonably high levels of numeracy, but only because (a) it was about all we ever did in school for the first seven years and (b) we did have to use these skills to a certain extent in everyday life.

Those days are gone.

It would be nice to think that this then frees us up more to concentrate on less mundane skills in maths - on more reasoning, for example - but it may well be that the ability to reason follows the ability to execute the basics with confidence.

To put it another way, we're screwed.

Or maybe not. Does all this matter in the larger scheme of things? And were we really so good at arithemtic back in the day? (Take written English for comparison: OK, so a lot of kids nowadays can't spell or use basic grammar, but reading other teachers' reports I do wonder if 'twas ever thus.)


Tuesday, November 14, 2006

It is indeed an honour

Well folks, take a look here at a posting from a while back, and a comment - just received today - from the good professor Howie himself! Well, he claims to be, at least, and I choose to believe him. Oan yersel', big man! etc.

(If anyone knows how I can get recent comments to appear summarised in the sidebar, do let me know.)

Friday, November 10, 2006

Assessment is for Learning - Revisited

Regular readers may recall a considered piece/rant from a wee while back, wherein I vented some spleen at the whole new thrust in Scottish education currently striding forth under the banner "Assessment is for Learning" (hey, I'm a maths teacher, so I can mix metaphors all I want).


Since then I've been in-serviced with current thinking in AIFL (I'd argue for AifL, but what do I know) - quite a good in-service, actually. And, secure in the knowledge that HMI have a gun to our heads on this matter, you can bet your life that the learning outcomes for my lessons are now regularly being shared. As in, I write them up on the board.

Hoorah! my class cry as they realise the overall quality of their education has just improved all but immeasurably.

Now in fact, I'm quite happy to admit that this AIFL stuff may well be more or less A Good Thing (though I reckon a little may also go a long way). I do wonder, mind you, quite how the pupils are going to take it all in once they encounter the same approach in all their classes, but who knows, maybe it's just what they want.


Two points:

  • I read a fascinating blog here recently, which looked at the notion of Accepted Solution Time in mathematics: the idea being that AST is the amount of time (and effort) a student is willing to invest in a problem before either getting the solution or giving up. The problem is, as the blogger points out, that AST seems to be decreasing, even for students supposedly "able" in mathematics. Well, if all this AIFL stuff is going to be breaking down the content of the subject into ever smaller pieces, isn't there a real danger that this is precisely the sort of approach which all but guarantees that students will become greatly distressed if ever they are asked to do something a little out of the ordinary or off-beam? "What's the learning outcome here?" I can hear them complaining already.
  • This leads neatly into my second point, which is basically that behind all this I think lies a philosophy that wants to reduce education to training; that believes that something as massive and amorphous as mathematics - even at school level - can be reduced to a checklist of "be able to". Oh jings, it's that Thatcher woman again isn't it?

Let me put it another way:

There are more things in mathematics than can ever be dreamt of in your learning outcomes.

Wednesday, November 08, 2006

It's not much, but...

Why did the chicken cross the Moebius strip?

To get to the same side.

Sunday, November 05, 2006

And finally, at number one...




Bit of a problem here, actually.

You'd think I would have known all along what I had in mind for the number one all-time bestist ever Scottish mathematics textbook, wouldn't you?

I mean, let's face it, leaving it 'til the end and hoping for inspiration - that would be pretty stupid, wouldn't it?

And, as I've said before, it has been a bit surprising to go for a wander down memory lane and find that so many textbooks let you down one way or another. Yes, even good old Blackie Chambers could get a bit weird on you every now and then.

So, maybe it's a copout, but I'll give you two options to choose from, in the hope that maybe one of them will feel a bit less like a let-down:

Option (a): there is no best ever textbook. How could there be? Isn't there always going to be a need for teacher input specific to the class in hand, which means that any textbook will only be of some use, to some pupils, some of the time? When will we learn that we need to focus more on what we need to teach in a lesson, instead of just turning to the next page of the textbook?
(Yes folks, this is the "educational high-ground" copout!)


Option (b): whilst not a textbook per se, any worksheet made with Banda fluid was always a huge hit with maths classes. Especially if they were fresh from the machine...

Accepting the award tonight on behalf of the Banda corporation is Malkie McAsbo, whose memories of maths at school are hazy to say the least, though he does remember colouring in some SMP booklets on "Rules and Formulas" in S2, which always baffled him on account of his grasp of plurals. Oan yersel', big man!

Red pen: newsflash

It's with great sadness that I have to announce the demise of my Faber Castell red pen (see blogs passim). For a while now I've been worried that it's been looking a bit sickly, and yesterday as I settled down to mark some Higher homeworks I heard the death-knell scrape as metal hit jotter; yes, the nib has finally worn down. Death is not far away.

Oh yes, I can still use the pen, more or less, so long as I keep the angle between pen and paper greater than 80 degrees... and I'm sure I will use it a few times more, just for old times' sake. But we both know it's over.

I'm not heartless, though. I'll keep the pen in my pencil case for a while yet, perhaps to be discovered later as I rummage through the case desperately looking for a pen of a certain hue. And when I do I'll think back to happier memories and smile.

But maybe the fairer thing to do is to just bin the pen right out; make a clean break; do the honest thing. Already I'm flirting with a red Staedtler 0.5mm pigment liner - she'll hate it when she sees us out marking together, I know.