the proof is out there

It's (not quite) the end...

2008-12-23T22:01:00.003Z

... for the moment has been prepared for. Get thee over to our new site/blog/whatever - Maths teacher goes to the movies. We have popcorn and everything.

Man bites dog

2008-05-29T22:52:00.004+01:00

... and other less than sensational headlines.

In today's Scotsman, an article on the introduction of (A) Curriculum for Excellence (apparently the A is optional... no-one tells me anything these days), telling us that confusion is about to reign.

Well, mebbes aye, mebbes naw. They are totally right to say that teachers want much more detail than we're currently getting, but it frustrates me to see union leaders grumping on again about lack of funding. Listen mate, it's not funding that worries me, it's the fog of fuzziness in the outcomes themselves. Give us some detail, for goodness' sake!

Math Wars: Ceasefire?

2008-05-26T17:34:00.004+01:00

Well, I'll have to do a whole lot more googling to find out how this is going down across the pond, but I was very interested to come across a US government report on the teaching of Maths, sorry, Math in the US. Very, very thorough. I'm impressed, initially at least, by the high standards the contributors set for assessing or including research in their considerations, and can't help but think it's a much more rigorous piece of work than we have seen from (say) HMIe of late over here. Also, just look at the detail included in their recommendations for the content of what should be taught at each stage of school life, and compare it to the jelly on a stick candy floss fare of "Curriculum for Excellence" and ask yourself... are we even on the same planet?

It's quite a read - even a quick flick takes a wee while - but I'm struck by their good sense on the Math War business of "teacher-directed" versus "student-centred" approaches. Basically they say that you need both, and that any program (sic) based solely on one or the other is just plain dumb. Ah, the sweet voice of common sense! They also put out an urgent call for quality research into the effect of long-term calculator use, which again makes a whole lot of sense to me.

Quite what this means for current teaching programs in the US, I don't know. I'd be interested to hear if anyone has any news on this.

I'm in love...

2008-05-26T16:46:00.002+01:00

After all these years, it seems that the search is finally over... I've long been a fan of the Pilot drawing pen, though frustrated that it's only available in black. But it's never felt quite right to me, for some reason, so I've vascillated between it and a few other makes when seeking a black pen for school work (Staetdler, I'm talking to you here). And what size nib to use? The 0.1 is elegant but feels a little too fragile, while the 0.3 feels a bit overkill.

And all the time the solution has been staring me in the face! Have Pilot been making a 0.2 nib for some time, or is it brand new? Either way, I stumbled across one the other day, and whahey, I'm in love! (Well, within acceptable limits of those of us with stationery fetishes, of course.) It's sharp, clean, and has all the depth and definition a jobbing sums teacher needs. Just writing with it, you can practically feel your handwriting getting neater.

Now all I have to do is persuade them to make models available in red and green... the campaign starts here.

Proof, if proof were needed...

2008-05-10T14:29:00.003+01:00

... that all is not entirely rosy in "Curriculum for Excellence" land. Here's Prof Lindsay Paterson, all round good egg, on how education is faring just now under our new Scottish Government (from this week's TES):

Lindsay Paterson, professor of educational policy, Edinburgh University
The SNP, like other significant parties, is constrained by the National Debate consensus. This does encourage durable, evidence-based policies. The class size reductions will gradually happen and work: teachers, parents, and rigorous research support them. Universal free school meals and the ending of the graduate endowment come under the same pragmatism, as perhaps may the school examination proposals. But the consensus is balefully anti-intellectual. A Curriculum for Excellence, veneration of the vocational, and a disregard for the achievements of liberal education will be challenged only by rather daring leadership. None of the parties yet provide that.

"Balefully anti-intellectual", "veneration of the vocational", "disregard for achievements of liberal education"... ouch! It'll be interesting to see if any of this stooshie is picked up elsewhere.

For what it's worth, I do kind of see what he's getting at.

It's That Time of Year Again

2008-05-10T08:20:00.003+01:00

Yes, once more by public demand (ahem), we here at TPIOT bring you our annual review of the Scottish exams, starting with part one: the Mathematics Standard Grades (Foundation, General, Credit - in increasing order of difficulty) which took place last Thursday in sweaty exam halls and school gyms up and down the country.

So, what's the skinny?

Well, I thought they were all pretty reasonable to be honest. Keen fans of this blog will recall that I was worried last year at the lack of testing of algebraic skills at Credit, and though this does remain an issue, I do think that they managed to produce a better paper overall. Last year's was just too darn easy, which has ultimately done no-one any favours, as a lot of pupils have ended up heading on to Higher this year when really they shouldn't have.

I've spoken with a few teachers at other schools and there are perhaps some concerns that some of the reasoning questions in Credit were a tad obscure, but I'm not sure I agree. It seems to me a pretty pathetic position to be in, when we expect every question in the exam to be one which pupils have seen before.

Meanwhile General and Foundation seemed very decent. I was pleased to see that the amount of reading in the F exam has been cut down, which is a good thing as often the less able pupils are disadvantaged by issues other than their mathematical ability when there is so much waffle going on. (I am happy to predict now, by the way, that we'll eventually be told that the worst done question was in fact the one requiring pupils to draw an angle of 80 degrees... which must have sent invigilators across Scotland scurrying to maths departments in a hurry to get yet more protractors.)

Final point: I couldn't help but notice that quite a few questions in the exams dealt with "real life" situations with a slight environmental or social tinge... that'll be SQA getting in on the "Curriculum for Excellence" jamboree bandwagon bunfight then.

Gasp!

2007-12-10T22:48:00.000Z

Well, michty me, would you credit it? The mathematics outcomes are indeed now available on the LTS website which you can find... och, away and google it yersel'. Not had much time to look in detail but... hmm... could be worse, I think, but I'll reserve judgment for now.

However I am amazed to see that a particular rumour is indeed true. The maths outcomes contain the numeracy outcomes (and extend them), so obviously it's helpful to be able to quickly see which is which in the full list of outcomes... and so step forward, A Curriculum for Excellence, for the first of our "Pure Mince, So It is" awards, for the sheer brilliance of deciding to... print the numeracy outcomes in green, and the maths ones in black.

Yup. Green. That's it. No italics, or different font, or even font size... just green type.

Did I mention that these outcomes aren't being published in paper form but are instead just to be taken from the website? And then freely copied and distributed to staff?

And they think this is going to happen in colour?

This one speaks the truth...

2007-12-10T02:42:00.000Z

Blimey, things have come to a pretty pass when we have to rely on the Head Teacher of a private school to speak up about the impending mess that is "A Curriculum for Excellence" (or Mince as I described it in a recent post). So fair play to the head of "Smellies", as the good people of Edinburgh might refer to the august institution that is (deep breath) Daniel Stewart's and Melville College, for doing just that, as reported by the Scotsman newspaper here.

Apparently the outcomes for Mathematics are due for release... today? I'll believe it when I see it. Even better would be for the ACE people to fess up and actually make clear precisely how we are meant to contribute our thoughts and opinions, as (scandalously) there seems to be no actual mechanism for feedback at all just now. To be fair, this is entirely in keeping with the so-vague-it's-saying-next-to-nothing approach taken thus far by the whole enterprise.

This is all very worrying.

Still breathing

2007-12-06T07:21:00.000Z

... more or less. I even saw a couple of films, but they were so meh I can't really be bothered writing much. "Elizabeth: the Golden Age" - avoid at all costs. "Lions for Lambs" - yawnsville.

And on the maths front? Well, a few good ideas, here and there. But for just now I suppose I'd better head into work...

But first: hey, let's hear it for the Pilot Drawing Pen 0.3mm black - very much my pen du jour. Why don't they make other colours though? Why?? Why???

Failed in the real world?

2007-11-10T08:47:00.000Z

Nice line in jokey ads from Armstrong & Miller, a patchy sketch show on the BBC. Take a look here (click on the clip on the right with the title above). Especially like the web address!

More to be found on YouTube, I'm sure.

Maths Teacher Goes to the Movies: Sicko

2007-11-05T19:23:00.000Z

Now bend over... this may hurt a little.

There's been an impressive amount of anti-Michael Moore stuff out there of late, most of which is, it's surely only fair to say, right-wing propaganda. It's also fair to say that Moore does play fast and loose with facts from time to time, but rare indeed is the documentary film-maker who doesn't arrange the facts in the way that best supports their point. Fahrenheit 9/11 was one hell of a movie, as was Columbine... heck I could probably still sing the guitar-riff theme tune from TV Nation, his TV series way back when. So, declaration of interest up front: yes, I'm a fan.

How was the movie?
Well, this is a bit odd. I was pretty depressed to be reminded just how awful US "healthcare" is, and I was moved to be reminded of just how great the NHS is, in comparison (yes, people have complained that Moore presents a sanitised NHS, but listen carefully and you will hear nothing that's a lie)... but at the end of the day I was just underwhelmed. Maybe it's because there's no clearly visible Big Bad to get angry at, though Bush and Co. do lurk in the background. Or maybe it's just because you can't see for one second how things are ever going to change over there. I'm not sure. But - oddly for me - I felt that this was one documentary I could have happily waited for on telly. Not enough laughs either.

How's the maths?
Gosh, I can't remember. There's a fair amount of figures and percentages flying around, which counts for something, but the only equation I recall is (desperately poor people) x (high insurance premiums) + (refused claims repeatedly) = (filthy rich capitalist gits).

Can I teach with it?
Well, wouldn't that be fun? Seriously though, if I used this with a class and analysed healthcare costs in the US in a way which (let's say) puts across a pro-liberal agenda, would that be acceptable? Or if I did the same with party political matters in the UK? "Hey kids, let's analyse which party is more reliant on private donors and look for a positive correlation with peerages!" Would that be part of A Curriculum for Excellence? I'm sure Alex Salmond wouldn't mind...

Man bites dog

2007-10-28T10:26:00.000Z

Wow... an academic (I think) is claiming that there is too much exaggerating of the figures for bullying in our schools - as in over-exaggeration. It seems that we are guilty as a society of wrapping our children up in cotton wool, instead of getting them used to some of the hard knocks which life will throw their way. (Hey, it's my blog, so I can mix metaphors all I want.) See here for the article in the Guardian reporting this.

FWIW, I agree a far bit. I'm impressed by how much is done to combat "genuine" bullying in schools (compared to in my day), but I do think that some parents can have unrealistic expectations of how much the school can do about "lower level" stuff - name-calling and so on - and how quickly the bullying tag can be applied to stuff which is more your everyday sort of sometimes-kids-can-be-wee-beggars. (Which isn't to say that name-calling can't be devastating, either, in some cases.) Encouraging kids to stand up for themselves is surely a good thing (that, and perhaps karate lessons).

Read 'em or weep

2007-10-23T22:45:00.000+01:00

What, can't a blogger go on holiday?

OK, so I'm back. And impressed by Channel 4's current week of programmes on literacy (I think you'll find it here). Can't quite decide yet if Ruth Miskin, the woman with the mad evangelical gleam in her eye for a particular style of teaching kids to read is mad or... well, no, she is bonkers, to some extent, I don't think that can be disputed but still... hmm... it's sobering and also inspirational stuff.

Of course this has nix to do with teaching maths - does it? Miskin's prescribing one method which should be used alone, to exclusion of all others, for teaching reading (called synthetic phonics, at which point I'm guessing she's asking for your credit card number) - one teaching method to rule them all, and in the darkness bind them, sort of thing.

And I do sort of see the point for the (non-PC language ahead alert!) less-able, even in maths. I mean, with my more able classes we can have a fairly interesting time discussing different methods or ways of setting out a solution to a problem, but I tend not to give that freedom to the less able, because they seem to thrive on the safety of knowing that this is how you're meant to do it. OK, so they thereby miss out on some of the vast richness of the subject but... if it means they can work out a percentage without a calculator, I reckon I'll take the trade.

I can't help but wonder if there's going to be a ground-swell of opinion in favour of teaching reading this way, on the back of such a high profile media campaign which (as far as I can see so far) backs it. It's a shame it has such a ring of "back to basics" about it though.

A Curriculum For Mince?

2007-10-02T07:19:00.001+01:00

OK, maybe I'm being a bit harsh, but the much heralded "numeracy outcomes" for ACE (as those in the know call it) are now out, and boy, you might just as well try to nail jelly to the wall as get a grasp of these beauties. Those of you working in schools needn't dash off to find which member of the Senior Management Team has received the paperwork and is hiding it in a cupboard somewhere, as - of course - the outcomes are available online. (Is it just me, by the way, or is it not an appalling dereliction of duty and responsibility for major public organisations like LTS and SQA to unilaterally transfer the copying and printing costs on to already-cash-strapped schools?)

So, you can find them - and various other bits and bobs - here. Early response from maths teachers I know is basically "despair". We shall see. More to follow.

Maths Teacher Goes to the Movies: Atonement

2007-09-30T16:30:00.000+01:00

A bit late in getting to see this film, I admit, which is perhaps a curse rather than a blessing as I seem to have forgotten any negative reviews and went in with high hopes. And for the record, before we begin, I haven't read the book. So:

How's the movie?
Well, let's be fair and say that it all looks terribly, terribly nice up there on the screen - or should I say tahbly, tahbly ness, in keeping with the movie accents? There's some impressive cinematography, but by heck they want you to know about it, so it's hard to lose yourself and get really caught up in the story. I believe the book unwinds in a tricky manner that lets on from the outset that one of the central characters is telling the story, so it would be nice to think that what was going on here was that the film-makers were playing with the idea of someone making a film about the story... but that would be crediting them with more than they deserve.

The film hinges on a misunderstanding (wilful or otherwise), from which follows much woe - gorgeously cinematic woe, never fear - but to be honest it's hard to care over much, or not to feel at the end of the two hours that you really didn't need to bother. Whereas a misunderstanding offers much in the way of comic potential, there's not many laughs to be had here - although there were titters from the audience at one point in the film which I think was meant to be very erotic.

So anyway: go see it if you want. It looks nice; the actors do their bit; war is terrible; atonement is... well, what exactly I don't know and nor do they; and that's your lot. Can they have a Bafta now please?

How's the maths
Oh, dahling, I'm afraid everyone's far too frightfully posh or clever to talk about mathematics - don't be such a bore. Pass me another ciggie, won't you?

Can I teach with it?
Well, in the movie world time is seldom linear and much more a big ball of timey-wimey stuff, and seldom more so than here, as the scenes jump forward and back over (eventually) about 70 years. A chance then, surely, to apply negative numbers in context: let the initial scene have value t=0 (years), in which case (ooh, here comes a flashback) this must be t=-2, and then boom! it's Dunkirk so t=3, but wait now (blimey! it's Vanessa Redgrave) t=70... and so on.

However, be warned: the central conceit mentioned earlier does include a letter from one character to another, containing the use of a certain four-letter word (and not the one starting with f, either) ... and I think you can safely wave goodbye to your teaching career if you let that crop up during the DVD. All the same, I daresay the History department will happily borrow it from you in order to show that war is A Bad Thing.

Tum te tum...

2007-09-26T19:44:00.000+01:00

Jings but time flies, eh?

Those headlines again... um... I've been busy.

More on that story later.

Math wars - coming to a school near you?

2007-09-11T22:31:00.000+01:00

Well, OK, I exaggerate for effect. But by jings, this is all very interesting. Basically there's a war raging in the US over how maths should be taught. No surprises that it's a sort of traditional v modern thing, but the extremes are pretty extreme, and if reports are to be believed then there is a real question over whether or not students are being damaged in the crossfire.

See here
and here
and here
for a few details/comments/op-eds, though be warned that these are pretty one-sided (even if they do seem fair enough to me, but what do I know?).

I'll post my own thoughts later, but would be glad to hear any comments from colleagues from the US in the meantime.

Maths Teacher Goes to the Movies: The Bourne Ultimatum

2007-09-11T22:14:00.000+01:00

Well, in a summer of "threequels", finally a movie that does what it says on the tin. No more than that, mind you.

How's the movie?
Pretty exciting stuff - certainly never a dull moment. Lots of gripping set pieces, all filmed in shaky Steadicam (that's not-at-all-steady Steadicam, then), with fast editing in all the fight and chase scenes. Basically you have no real idea what's happening in these moments, but it sure is fun to watch. There's a visceral confrontation between Bourne and a hitman that'll leave you gasping for air. When the movie slows down enough to start to wonder about delivering a plot, it's maybe no surprise that it opts to rerun that of the second Bourne movie. But who cares? I mean, can you remember the plot for any of these, beyond the basic amnesia thing?

Rating?
In keeping with the Hollywood belief that hi-tec needs many decimal places to sound cool, I'll give the movie 7.00000000001 out of ten.

To be critical I would say that the movie could do with more warmth, in terms of human relations. Julia Stiles pops up again and does her best, but a brief hint of a romantic past goes unexplored and before too long she's off dying her hair in order to vanish from the baddies (meanwhile Matt Damon continues to look like Matt Damon, complete with Action Man haircut, yet the authorities never ever recognise him until he bursts in, guns ablaze) and the movie moves on apace to the next loud moment.

How's the maths?
Not too much on the go, though lots of hi-tec stuff kicks around and I suppose there's all manner of projectile motion going on, what with the guns and stuff.

Can I teach with it?
Well, morally, would you want to do an exercise on bullet trajectory with a class? Alternatively, maybe a brief probability study, with null hypothesis "the bad guys can't shoot for toffee" tested at varying degrees of significance.

Meanwhile, back at that press conference...

2007-09-05T17:41:00.000+01:00

The story so far...

Alert readers of our humble blog will recall that in a recent press conference with Gordon Brown, President George W Bush was asked the key question: what is 37 times 23? The good Mr Bush gave what can at best be described as an evasive answer (see here if you've forgotten). But we here at TPIOT are made of sterner stuff, and so we recently managed to sneak into a recent press conference, bribe the PR guy with several twinkies, and ask the question again.

Now, dear reader, read on...

(Transcript of press conference follows)

TPIOT: Mr President! Mr President!

GWB: Yup, the... um... the geek with the glasses. Yo! Whassup, dude?

TPIOT: Mr President, back in July at a press conference with Gordon Brown...

GWB: Yup, I remember. Scottish guy. Big. Not dour.

TPIOT: That's right... anyway, at this press conference you refused to give a definitive answer to the question, what is 37 times 23? I was wondering if, now you've had time to read the reports, you might have an actual answer?

GWB: Um... well, yeah, kinda. Me an' the boys bin kickin' this one round for a while. I mean, I'm no mathematician, right, but we called in the experts and I think it's maybe time to set the record straight on this one. We dun looked at this from all the angles, and though we're not prepared to say exactly what 37 times 23 is, we can reveal that the answer is... an even number.

TOPIT: An even number.

GWB: Bullseye! Now we ain't ready at this time to reveal just how big this even number is, but we at least hope that y'all will give us credit for the progress we made so far. Knowin' that the answer is an even number... well, sir, that kinda military intelligence takes years of hard work an' countin'. I mean, just getting' all them fingers in the same place, so we can count on 'em.... makes me proud to be an American. Next question?

TPIOT: But Mr President, isn't it generally accepted that, if you take an odd number and multiply it by another odd number, the result will be odd itself?

GWB: (audible sigh) Y'see, this is exactly the kind of... um... unpatriotic line of questionin', that makes me wonder if you even care about the war against terror. Oh sure, the liberal elite will tell you that an odd times an odd is odd, they've always believed that... but the rules have changed, son, the rules have changed. 9/11 put paid to that. An' y'know... this kinda talk, it's just emboldening the enemy, is all it's doin'. You gotta trust me on this one.

TPIOT: So, 37 times 23 is even?

GWB: Welcome to my world, son, welcome to my world.

Maths Teacher Goes to the Movies: Knocked Up

2007-09-05T17:26:00.001+01:00

Well, what do you know, but I finally managed to mark enough orange jotters to be able to take a night off and go see this... apparently it's been a big hit Stateside, and been well here too. What's not to like?

How's the movie?
Meh. I mean, it's OK and everything, but I really couldn't care too much about what happened to the lead characters, which is a bit of a downer in a romantic comedy. Everyone was a tad too self-obsessed, and overall the movie seemed to want to have its cake and eat it (or, perhaps, to have the bun in and on the oven?), in terms of portraying how empty our lives are when we are stuck in long-term relationships going nowhere (speak for youself, mister!), yet still give us the pat happy ending. And then all of a sudden in the midst of the angst comes an avalanche of bong-themed stoner jokes more at home in American Pie. In a word: confused.

Still, by the good Doctor Kermode's litmus test for a comedy: I did laugh out loud several times, so who am I to complain? But it's far from being a classic.

How's the maths?
Well, any number of variation on multiples of four weeks abounded, with a maximum being reached naturally enough at 36, more or less. But not much else.

Can I teach with it?
Lordy no! far too many swearies for that, even if you are a Biology teacher.

Well, hello...

2007-08-25T08:18:00.000+01:00

This, folks, is a certain Danica Mckellar, who may be known to people on the other side of the water in the US. She's an actress, and a mathematician. (She's also apparently released a yoga/meditation DVD, but let's pass over that in dignified Wittgensteinian silence, shall we?)

And she's written a book on maths. Sorry, math. (I recall an American friend and teacher saying to me, "yup, we only have the one subject in the US".)

And it's called... wait for it... "Math Doesn't Suck".

This has to be a good thing, surely. Ms Mckellar is apparently keen to reach teenage girls with the message that mathematics is a subject that can appeal to them - in a nutshell, I suppose (and trust me, I'm not being facetious, it really is her point): babes can do math. More details of the book etc can be found here.

Ms Mckellar, we here at TPIOT salute you, wish you well in your work, and are proud not to have descended too far into Leslie Phillips territory, despite an overwhelming urge to say something like "ding dong".

Oops.

Lemon-soaked paper napkins

2007-08-23T07:22:00.000+01:00

Jings but things have been busy. Nevertheless we here at The Proof is Out There wish to apologise for the hiatus in bloggery over the past week. Rest assured that we are working hard to overcome this problem and that normal service will be resumed as soon as possible.

In the meantime, here is some music.

Choose a job you love...

2007-08-16T07:11:00.000+01:00

... and you'll never do a day's work in your life.

Old Chinese proverb, apparently. And on a good day I absolutely believe this to be true. Worth recalling now I'm back at work.

Oh, and one other thing - it's also worth mentioning that ants dance a mean samba. How could anyone disagree?

Round up

2007-08-12T12:20:00.000+01:00

A few sites worth checking out... first up, Vlorbik is hosting the XIV Carnival of Mathematics here. This is a round-up of all manner of maths-related websites and I'm honoured (or should that be honored) that this humble blog has been included.

On the back of this mention, I'm chuffed to bits that the joke press conference (Bush & Brown) has now been linked to by some other bloggers too... see here for an American educationalist's take on the TIMSS business, and here for the sheer joy of this blog making it into what I think is the Dutch language. Dank U!

And finally, a mention of reel fanatic's movie-review blog here. Sure, the blogosphere is heaving with many such sites, but I like the choices, and admit to having a soft spot for Macon, Georgia.

Maths Teacher Goes to the Movies: Hairspray

2007-08-09T15:17:00.000+01:00

OK, I know it's remiss of me not to have seen this one earlier, but it's amazing how busy one can be on holiday. Anyhoo, finally managed to see this the other night and was surprised by how good business was - not quite a full house, but not bad for a movie three weeks or so after opening.

It's always interesting catching up with a film later on, because by then you've heard quite a few reviews and comments from friends, all of which can work for the film or indeed the other way. Going in, I knew the following: (a) it's a film of the musical based on the earlier Hairspray movie; and (b) it's got John Travolta in a fat suit playing a woman. (At least, I hope it's a fat suit... you don't think he did a Rene Zellwegger, do you? I mean, Mr Travolta's a man who likes a meat pie at the best of times but... no, surely not.) Oh, and just to clarify: I have not seen the original John Waters movie, though I know enough to be able both to bluff about it and to spot Mr Water's (very appropriate) cameo appearance in the new film.

How's the movie?
Well, it's not at all bad, so long as you don't mind musicals of course. It is loud (very loud) and colourful, but like so many musicals there isn't much variation in tone. Hard to know what you can do about this, to be honest. Musical theatre needs to play to row Z, so subtlety's not really an option. But I came out pretty happy, having "gone" with the movie. A few days later and I can only vaguely recall a couple of tunes, but it all seemed passable enough at the time. Newcomer Nikki Blonsky is very good indeed, Christopher Walken does his usual schtick (though not enough dancing, if you ask me), Queen Latifah gives it big laldy... and it's certainly nice to see Michelle Pfeiffer in a movie again.

However... let it be said the really wrong note in the film is the afore-mentioned Mr Travolta himself. Oh dear. First up, his accent is absolutely all over the place, though no matter where it wanders I can't help but think he is channeling Dr Evil from the Austin Powers franchise. Nor can he sing particularly well. And I'm sorry, but in a film which is at least in part (it seems) about challenging society's views of (ahem) fat people, what the hell's the point in then simply inviting us to laugh at JT padded up and out as a fatty? In the original film this part was played by the cross-dressing transexual Divine - who was that size - which perhaps also allowed the movie to touch on even wider societal hang-ups, but no such allusion is possible here. A case of Hollywood (if not JT) wanting to have their cake and eat it, I suppose.

How's the maths?
Zip, zilch, nada. Nothing to see here. Move it along folks.

Can I teach with it?
Well, if you teach History or Modern studies, this movie could lead into a discussion regarding issues of race in 1960's America, but you'd be brave to try it, because apparently all we need to do is to get down and boogie. Or something.

Results, results, results... part two

2007-08-07T17:24:00.000+01:00

OK, settle down, this might be a long one.

A quick recap: first up, the structure of Scottish education, exam-wise. In fifth year (a bit like year 11 down South - the first year of the two year A Level?) able pupils will sit Highers; in sixth year pupils can then choose to sit Advanced Highers (very much like A Levels, though probably a bit harder to be honest... I would say that, being Scottish), or perhaps more Highers in other subjects. or a mix of both.

But! according to the news today (see here, for example), the number of students choosing AHs is down on last year, much to the (apparent) consternation of universities. How can this be?

Well, two reasons, both of them pretty accurate if you ask me:

1. It's the universities' fault
It's a bit rich of the universities to complain about this situation, given that they use the Higher (NOT the AH) as the benchmark for university entrance. When the structure of our exams was changed a few years back and AH introduced (in place of the old "Sixth Year Studies"), the unis had a perfect opportunity to back AHs as precisely the sort of course which students should have to do. But they didn't. Oh no. Why not? Well, I hate to be cynical here, but if they had gone for AHs instead of Highers, then they wouldn't have got so many students through their doors... which of course means less money.

And so the status quo reigns. If a student does well in their Highers in fifth year, they can do bugger all in sixth year and they will still get a place at university. So why should they knock themselves out studying a harder course like AH? (We have to do a big sell in my school on how difficult it is to cope with a Maths degree if all you've seen is Higher work, which is true beyond words I can offer here.)

But there's more: when asked, universities will actually advise students not to bother with AHs and go off and do some more Highers instead. I can offer a personal example here: a student of mine once applied to study Maths at a Scottish university and did well in his Maths Higher (an A), but less well in other subjects. This lad was clear that he wanted to study Maths so in his sixth year he studied two Maths AHs (Pure and Applied, if you will), plus Higher Accounting. Now his Higher results weren't so strong that he was going to be offered an unconditional place, but we were pretty pissed off when the unversity in question made him an offer conditional on him getting a B in Accounting and completely ignored the far more relevant (surely?) Maths AHs.

So if universities really are so gutted at the drop in AH uptake, it's high time they started treating it as at least equal importance (if not more so) than the Higher.

2. The schools can't afford to run them - or aren't willing to
Now I don't want to get personal here, but let me say this: for most schools, for most subjects, the number of students who will want to study an AH will be small (easily fewer than ten), and for the management of most schools, that's not a cost they are willing to meet. Far too expensive. Classes of single figures - how ridiculous!

However... I do like to point out that the most able pupils in our schools tend to be taught in the largest of classes from first to fifth year (up around 30 in a class, maybe more), whilst the less able get targeted help and support in smaller classes. So, in a sense, the more able subsidise the less able. Is it so ridiculous to hope that we might view AHs in sixth year as some form of minor payback?

-

So there you go. It would be nice if, say, the new government in Scotland could throw some money at the problem so that schools could more readily afford to run AHs (though I sense this isn't terribly high up their agenda), but it will take more than a few crocodile tears from the universities if we are really to do something about the problem in uptake.

Results, results, results - part one

2007-08-07T10:19:00.000+01:00

So, the exam results are now out in Scotland, though I've yet to see any mention of pass rates etc in mathematics. But the papers are covering two "stories": one, the online results service offered by SQA; two, the decrease in the numbers of students studying Advanced Highers.

So, the first one then: yes, indeed, for the first time ever across Scotland, students were given the opportunity a while back to sign up for an online (or text) results service, which meant that they could log on a day early and find out their results (that would be yesterday) before the actual envelope containing the results dropped through the letterbox (that would be today).

Meh.

First up, it's amusing to see that apparently a large number of students couldn't access the results because they had forgotten their passwords, and apparently some parents are complaining about this, like it's the SQA's fault. Ah, parents, how we love thee...

But taking a more serious look at this: this must have cost some money, right? And no university or employer or whatever is ever going to accept a printout of a web-page as evidence of exam results, right? So we can never get rid of the need for the paper copy - the exam transcripts, as I believe they are referred to - right?

(You see where I'm headed?)

So basically this expensive (I'm guessing) results service is pretty bloody pointless and a waste of money - right? I mean I admit it's nice for the students to find out a day early, but it's hardly life or death, is it? Is it honestly worth spending a lot of money on? Is it cynical of me to think that SQA are doing this just because it's a (supposedly) funky sort of use of technology, which must therefore be A Good Thing?

Just how much money has it cost, I wonder?

Suggestions, please!

2007-08-05T21:26:00.000+01:00

Here's the thing:

Up here in Scotland quite a few schools are getting excited about "early presentation", which means getting kids to sit some exams (say) a year early in order to allow more time for the "big" exams (here we're meaning the Highers, which are typically sat in fifth year of secondary education, ie the penultimate year assuming you leave school around 18).

I confess I'm not a big fan of this myself, as I worry that we try to cram too much in too soon, and there seem to me to be developmental issues regarding the maturity of pupils for sitting such exams in the first place. BUT! I am keen to see more able pupils being challenged with appropriate work, so here's the question: what work? In particular - say, from a university perspective - what sort of ideas, concepts, methods etc would you say are pretty darn fundamental to being able to cope with further mathematics?

In a way I guess I am asking for people to come forth with their pet hates, ie. where undergraduates tend to go wrong in big ways, and that is part of it. But I'm happy for the net to be cast wider. (I have asked a colleague who works in Electrical and Electronic Engineering and he offered work on logarithmic and exponential functions as being worthy of early coverage, and I see his point.)

Without giving away too many details, this coming session I'm going to have a class in third year (aged 14 ish?) who will be working towards an exam in two years' time. They are a bright bunch and I'm confident I have a lot of time to get through what they need to know AND to cover a good deal more besides, but I need to decide what exactly this bonus DVD material should be. For example, I'm pretty sure I want to cover work on vectors (even though, scandalously IMHO, they don't need to know it for the exam) - but what about, say, matrices?

(BTW, if you're interested in knowing more about the content of maths curricula in Scotland, I'd suggest you look at the SQA website where content can be viewed: here, for example, is the arrangements document for Higher Mathematics.)

Contributions most welcome: you may now start grumping. (And yes, I will be covering fractions!!!)

Well, it could happen...

2007-08-03T09:25:00.000+01:00

I see here that the US has apparently withdrawn from the TIMSS programme, which is an international study designed to allow comparisons between the relative mathematical abilities of students in different countries around the world. (This also allows newspapers to print stories about how poorly Scotland is doing compared to England, or the other way about, according to our positions in the "league table".)

Interesting. Is the US withdrawing to spend the money more usefully elsewhere, or is the government scared of the negative publicity which may ensue if such data does become available and is less than flattering? Discuss.

Meanwhile, surely there's a better way to compare countries: why don't we just make our political leaders sit the tests for us instead? Just imagine that press conference...

Question: what is 37 times 23?

Response from George W Bush (US): You know, I’m getting’ kinda tired of being asked this question all the time. People keep askin’ me, what’s 37 times 23? When will you finally give an answer? And all I can say is, I refuse to set terms and conditions on what 37 times 23 is, or to give a deadline for that solution. I mean, if I give what’s meant to be some kinda definitive answer, that’s just gonna embolden the enemy. But we’re workin’ on this. You gotta trust me on this one.

Response from Gordon Brown (UK): I'm happy to announce that under a Labour government, 37 times 23 is much more than it ever was under the Conservatives.

Question: differentiate sine x with respect to x

Response from George W Bush (US): Now I'm no expert on math, but I believe we do need to show respect to x. I believe all letters should be respected, not just x, but also y, and zee, and... um... all the the other letters, alphabetically speaking. And as for this business of sinex, well, let me be clear that we do need to differentiate on this matter, 'cos if we do nothing about sinexes then we just end up emboldening the nasal passages. And that's just what the enemy wants. So I'm calling on Congress to support our troops and join with me in this battle on terror. We need to differentiate the sinexes and smoke 'em out.

Response from Gordon Brown (UK): It's important, I believe, to identify the role of the United Nations in ensuring differentiation, according to the Newton/Leibniz protocol originally agreed in 1673. It would be easy to give an answer to this question of how we differentiate sine x, but we have to be able to meet this answer within the context of financial jurisprudence, which is why...

(That's enough politico-mathematical satire - Ed.)

The psychology of marking

2007-07-29T21:30:00.000+01:00

So, how do you mark work then?

Yes folks, it may be the holidays but nevertheless I found myself marking a pile of homeworks this morning... if this sounds like dedication, then it's not really; more a case of not having got round to doing it during term-time.

Anyway, it struck me that marking a pile of jotters can be done in many different ways. It's almost like the Cadbury's Creme Egg "how do you eat yours?" advertising campaign.

Confused? Well, let me explain. You may think that teachers simply mark the jotters in the order that they have the jotters in, which will probably be rather random (having been schlepped home first). But not necessarily. When I first started teaching I was given the advice to try and mark the best homework first (ie dig out the work from the pupil you consider the best) as this is a good way to check that you haven't made any mistakes in your marking scheme. Good advice. But... this may mean that you end up penalising rather minor errors (we dont' want anyone do get 100% too easily, do we?), and then when you get on to weaker pupils you're then struggling to give many marks at all. So care is needed.

Nowadays I do actually mark jotters more or less as they come, until I get down to the last ten or so. Then I have a quick look through the names of those remaining, and save a few good ones for the end. I like to finish on a high note...

I've heard of other equally idiosyncratic approaches taken by maths teachers, and am happy to hear of any more. Own up now to your petty foibles!

(I haven't mentioned here the modern approach of "mark less to achieve more", or "comment only marking". Blimey but I have reservations about this. Apparently when (for example) a pupil makes an error in calculating a gradient, I'm not meant to mark this as wrong, but somehow at the end of the piece of work I'm meant to make some kind of constructive comment instead. Aye, that'll be bloody chocolate!)

Maths Teacher Goes to the Movies: The Simpsons Movie

2007-07-28T20:32:00.000+01:00

Finally, a movie that isn't a sequel... er, except I suppose it is of sorts.

How's the movie?
Well, I enjoyed it, but the bar is set pretty high when it comes to the TV show, so I can't help but feel a tad disappointed overall. I mean, it's way funnier than Shrek the Third, but you'd expect that. Plenty of laughs but oddly enough it ends up being the plot that gets in the way, particularly towards the end of the movie. And why so few guest stars? Overall it feels a little like a single episode stretched out, and I'm absolutely certain that the TV show could "do" this plot in 20 minutes, and that it would be more enjoyable for it. By all means go see it, but there are times it's a bit... meh.

Then again maybe I'm being too harsh. It may well be the funniest movie I'll see all year. And they still manage to have a go at Fox Television. But maybe that's part of the problem: the TV show is brilliant at playing with and subverting the medium of TV (if you will), whereas the movie doesn't do the same for the film medium, excepting gags at the start and close of the movie. (One word of advice here: don't leave until the credits have finally finished or you'll miss hearing Maggie's first word - a very funny moment.)

How's the maths
Well, there's an amusing example of Arnold Schwarzenegger coping with very basic arithmetic - encouraging to see he knows that if you double two, you get four.

Can I teach with it?
A large part of the plot concerns a dome placed over the town of Springfield, so there's a few opportunities to pose questions on hemispheres, and maybe even centripetal motion if you're feeling really brave. But the most interesting thing here is how direct proportion doesn't apply: the movie is roughly equal in length to three TV episodes, but I can't help feeling there's more laughs to be had in the latter than the former.

Overall score?
Well, bear in mind it's always difficult to be precise when giving movie ratings, and that any attempt to quantify creativity or enjoyment is doomed to failure... so overall I give this movie e + 1 out of five stars, which rounds (up) to four stars.

Two pi or not two pi?

2007-07-27T16:27:00.000+01:00

Hmm... this is interesting, though it's been linked to by others far earlier than me. Basically the author points out that way back when it was decided to define pi as being 3.14..., we would have been much better off defining it as 6.28..., that is to say, two times our value of pi. Apparently a lot of formulae would work out looking a whole lot neater if we did, and radian measure would be much easier: 360 degrees would be pi radians (whole circle = all of the pie!); 180 degrees would be pi/2 (half circle) etc... I can see the attraction. Though it wouldn't clear up the misconception that many students have, when they suddenly decide that pi equals 180 in the middle of an integration question involving trigonometry.

Of course the actual definition of pi as a ratio would need tweaking, but that would be easy enough.

Oh well... missed opportunities, eh?

Maths Teacher Goes to the Movies: Harry Potter and the Order of the Phoenix

2007-07-26T11:07:00.000+01:00

Yup, I'm on a roll... shame that it's such a summer of sequels though.

Anyway, on we go for Harry Potter and the Order of the Phoenix, or HP5 if you prefer.

How's the movie?
Well, you know what, I quite liked it. Very dark and not much in the way of action until the end, but I thought the director caught the atmosphere of the book well - and additional kudos for keeping the running time down, given that HP5 is the longest of all the books by some way. Imelda Staunton completely runs off with the film for her performance as Dolores Umbridge - impressive to end up so scary whilst wearing pink - whilst the lead actors acquit themselves pretty well. I mean yes, of course they look too old, but we're well into suspension of disbelief territory here anyway, so I can go with it.

The weirdest thing of all for me was seeing the film in an old style cinema which insisted on having an intermission... very much not appreciated.

How's the maths?
In Harry Potter? Are you serious? A shame I suppose not to see "Harry Potter and the Simultaneous Equations of Doom", or indeed to ever meet a maths teacher. Do they even have them at Hogwarts? Maybe Snape teaches sums in his spare time...

Can I teach with it?
Back to sequel-itis here. You could compare the length of each movie with the respective length of each book, I suppose, and see if there's a connection. This could be as simple as drawing some nifty bar charts, or (further up the road) as complicated as doing a statistical test like the... um... can't remember which one would work... the ummm... "hingummy" test, perhaps?

Overall score?
I'm happy to award the movie four out of five stars (two stars from Gryffindor and one each from Hufflepuff and Ravenclaw - no stars at all from Slytherin, obviously).

Maths Teacher Goes to the Movies: Shrek The Third

2007-07-25T12:09:00.001+01:00

(oh that it should come to this...)

Well, heck, what else is a maths teacher to do with their holidays?
And besides, who says maths teachers can't take an interest in popular culture? (I mean, who else kept the fashion flame burning for cardigans and corduroy jackets, if not us lot?) So every now and then, I'll be offering some movie reviews - from an educational perspective, obviously.

How's the movie?
It's fine. It's been pretty harshly reviewed as far as I can see, so I did go in with low expectations. But if - like the good Doctor Mark Kermode of Radio 5Live - your measure of a comedy is that it should make you laugh out loud at least five times, then this movie more or less fits the bill. Obviously there's a law of diminishing returns at work with most sequels - and indeed "threequels", and that's probably the case here. But I was never that much a fan of the first Shrek anyway, to be honest. I mean it was fine, but it wasn't that good. And it's the same here. Don't go in with high expectations, and you'll pass the time reasonably enough. Not exactly a ringing endorsement, but there you go.

How's the maths?
Well, I didn't really see much, which can't be much of a surprise. I guess the title of the movie is worth approving in that at least it doesn't do the silly "Alien cubed" approach. But disappointingly few mentions of differential equations... what is the world coming to?

Can I teach with it?
Well, I daresay a few teachers of other subjects will chuck this in the DVD to keep a class quiet at Christmas. But for maths teachers? Hmm... maybe a little project on the diminishing returns of sequels in terms of quality as mentioned earlier: find a formula for the quality indicator of an "n-quel", where n is a positive integer(*). Is the relationship one of exponential decay? Is it linear? Does Hollywood even care, when the cash register keeps ringing?

(*) Blimey, just realised, what with the business of "prequels", I suppose n could be negative too... and I suppose "Die Hard 4.0" introduces the idea of sequels being rounded to one decimal place. And I've sat through any number of irrational sequels...

I'll get my coat.

On holiday

2007-07-10T10:29:00.000+01:00

Jings, crivvens and help ma boab, but this blog is almost a year old. There's a thought. Started last year whilst bored during the holidays, and now here we are again. Not that I'm bored. heck no. Just recharging the old batteries, and kicking back. I mean to say, is there a better time of year than the end of July, when hairy Scottish teachers get paid for a month of not working?

By the way, if you are ever bothered by friends complaining about the amount of holidays teachers get, don't bother trying to explain how hard you work at other times/how stressful the job is/etc etc - just say "yes, I know, it's terrible isn't it?" Believe me, it's much more annoying that way.

Stuff

2007-06-23T17:46:00.000+01:00

My, but there's a lot of blogs out there in Maths-land! For someone like me - who ends up saying "times" instead of "multiply" on a bad day - the maths can be rather high-powered, but all the same there's some fascinating material out there. When I remember how to add links to this site, I'll list a few.

Meanwhile, this leads me nicely into linking to an amusing maths video link here - scroll down to the second clip. Made me laugh.

I might even try to show it to some of my classes this week, as they begin to demand that they be allowed to play games etc as the end of session approaches. After all, they've been watching DVDs in History and RE for ages now... but never fear, we maths teachers are made of sterner stuff, and keep the little darlings busy to the end. More or less.

-

Letters to my mathematics class, volume two

2007-06-16T10:56:00.000+01:00

(With apologies to Dr "Bones" McCoy of Star Trek - "dammit Jim, I'm a doctor, not a bricklayer!", this is more of a postcard than a letter... but any teacher will recognise the sentiment.)

Dammit class, I'm a teacher, not a branch of WH Smiths!!

-

Hands up, baby, hands up...

2007-06-02T07:31:00.000+01:00

(Apologies for quoting terrible lyrics from way back... the blog goes tabloid!)

So, someone somewhere in "the government" has issued advice, apparently, telling teachers not to ask pupils to put their hands up to offer answers to questions, because (apparently #2) some pupils get left behind if you do this.

Hmm.

Well, some initial thoughts.

First up: are we talking UK here, or Scotland? I can't be too bothered to try and find out, but given that I heard about this on BBC 5Live, methinks this is probably south of Gretna. In which case we can just ignore it.

But honestly, chances are, this is yet another media misrepresentation of a small part of advice to teachers regarding the importance of varying their techniques for Q & A sessions (or "direct interactive teaching", if you're writing your cv).

Getting pupils to put their hands up does have its place. For one thing, you get a quick idea of how much pupils are understanding (or how many of your class are still awake - all useful stuff). If you only ever have a couple of hands up, then you need to vary this, 'cos something is clearly not right.

For example, I sometimes use a calculator to throw out a random number, then ask the next question to the pupil corresponding to this number in my register. Keeps the class on their toes, I can tell you! And if this sounds cruel, well... (a) yes, and your point is? (b) who says I'm honest? I know my classes well enough that if I think wee Johnny can't answer I'll either ask a different question or just say another number has come up. (The key thing here is to generate the number away from the gaze of the class, and ask the question AFTER you've seen who's in the firing line.)

There are loads of other ways of assessing pupil understanding, but asking for hands up is hardly a criminal offence.

It really gets my goat when certain people (maybe the media, maybe even teachers) seize on one aspect of teaching and think this is or isn't the definitive answer to all our prayers.

Let's be sensible.

-

Letters to my mathematics class, volume one

2007-05-27T15:03:00.000+01:00

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

2007-05-27T14:39:00.000+01:00

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

2007-05-25T08:35:00.000+01:00

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...!

2007-05-14T18:52:00.000+01:00

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?

2007-05-11T06:52:00.000+01:00

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...

2007-05-07T13:05:00.000+01:00

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...

How To Be Good

2007-02-20T22:21:00.000Z

Maybe it's because elections are almost upon us here in och-aye-the-noo Bonnie Scotland, but by jings there's a fair old whack of stuff being written and proposed by our lords and masters about A Curriculum For Excellence, the keystone, lynchpin and corner... er, stone of the new education thingy.

Only trouble is trying to nail down precisely what we're meant to be doing, but let's leave that be for once and concentrate instead on some of the perfectly laudable aims of the document. We are, it says, in the business of trying to produce weans who are (now, let's see if I can get this right - I know there's four of 'em):

- effective learners

- confident individuals

- somethingy somethingy contributors

- and, er, something else about citizens.

(You may be less than impressed but let me assure you, I'm batting higher than most teachers here.)

Anyway, the thing is, most teachers tend to concentrate only on the first of these: getting the wee beggars to read, count, whatever. Fair enough, cos this is the business we're in, after all.

"Aha!" say the powers that be, "But that's the point: what about the other three things you should be doing, eh? What about them?"

Well, indeed. Y'see, what I'm interested in/worried about is, underneath this is a perfectly decent desire to turn out young adults who are... well, let's not beat about the bush here... who are "good". Good, in the sense of having morals, principles, caring about others etc etc.

And the really really really big thing is: will someone please tell us how you do that?

How do you teach someone to be good?

Honestly, any ideas?

I hate to be wishy-washy here, but the best I think we can hope for is to be good ourselves, and hope it sort of rubs off. (Define "good", you ask? Now that's another entry entirely.)

I don't think goodness is a subject you can teach; nor do I think that knoweldge necessarily makes one good. As George Steiner is fond of pointing out, the guards at Auschwitz really loved their classical music...

To be fair, a working document on citizenship has been released which I think does a good job of a difficult area. But... it's quite something to try and promise to an electorate, isn't it?

Watch this space.

Jings, crivvens, help ma boab

2006-12-16T09:34:00.000Z

Well at least the guy's not Scottish... listen here for an actual recording of a phone call with some truly astoundingly bad mathematics...

Alive and kicking, honest

2006-12-09T09:39:00.000Z

Jings! Nothing gives you a quicker "kick up the z-axis" (as a friend of mine likes to say) than realising that you haven't blogged in a while. So, this is a holding entry, just to say hello to whoever may be out there and reassure you that some form of normal service will be resumed - maybe after I've finished marking S4 prelims?

In the meantime, many thanks to the student (I think) teacher who has commented (twice!) on the entry "extreme excitement for maths teachers of a certain age": yes, indeed, these are much loved books and still in use across the country, albeit behind the scenes. (We tend to get a bit embarassed about using them as class sets, but a bit of illicit photocopying never did anyone any harm!) If you have a complete set, guard them with your life. Or perhaps a small first-year pupil. Whatever.

When first I started this blog I had wondered about peppering it liberally with advice for newbies - is there a market I wonder? Well, let's find out. Some thoughts on discipline - oops, I mean classroom management! - coming next week.

Is anyone counting?

2006-11-19T12:24:00.000Z

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.

But.

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.

Why?

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.)

Discuss.

It is indeed an honour

2006-11-14T19:35:00.000Z

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.)

Assessment is for Learning - Revisited

2006-11-10T17:23:00.000Z

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).

Well.

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.

But.

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.

It's not much, but...

2006-11-08T20:36:00.000Z

Why did the chicken cross the Moebius strip?

To get to the same side.

And finally, at number one...

2006-11-05T19:49:00.000Z

Um.

Er.

Ah.

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!)

Or:

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

2006-11-05T10:52:00.000Z

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.

Number two unveiled

2006-10-31T21:41:00.000Z

Here it is, folks!

First up, let me reassure you that I am in no way connected with the publication of this tome, just in case you suspect this is a puff piece. But by heck, if I was, I'd be pretty proud.

The book in question is "Heinemann Higher Maths, a textbook published by, er, go on, guess. (Since when did we decide the publisher's name should be part of the title, eh? Let's hope it doesn't catch on... Penguin 1984, anyone?) It's designed to be used for Higher Mathematics, one of those Scottish qualifications which so baffles anyone south of the border, and in particular with the relatively newly redesigned, "unitised" Higher (don't ask). The authors are a team of Scottish teachers who have done a good job, on the whole.

Complaints? Well, some of the maths is dodgy - eg talking of a function y=3x+2 (say) when they should call it a function f(x), then define y=f(x) if they really want to. But that's forgivable, if a sign of the times. No, what's a real bummer is that the answers at the back are notoriously unreliable. To be fair, Heinemann fessed up to this and published an errata, as well as updated newer printings... however, this seemed to throw up wrong answers elsewhere. So, if you're using the book (and it's the one I would choose above any other for the Higher right now), be aware that the solutions sometimes aren't (solutions, that is).

But hey, I come to praise the book! So on the plus side... well, it has investigative approaches, particularly to the earlier parts of chapters (hoorah!), which most teachers miss out (boo!); it includes questions from actual Higher exam papers (always a hit with the kids); it has a lot of content, with more questions than anyone could really use (ideal for differentiation within a class, aka keeping the clever ones quiet); it has very useful revision chapters for each of the three units; in short, it's firm, meaty nourishment. And, whisper it quietly, a gazillion times better than the "other" textbook, which I shall mention not.

It makes teaching a whole lot easier when you have a textbook on which you can base a course, and one that you don't feel you have to fight against. Take a bow, HHM, for a job well done.

Having said that, the vectors chapter is pants.

Number three...

2006-10-29T21:12:00.000Z

OK, this is a bit of a cheat. Didn't I say that I was looking at the top ten maths textbooks? And yet here I am giving plaudits and big thumb-uppery to a book on the business of teaching (not a textbook then), and one that's not even maths-specific.

Ah, but.

This wee journey through memory (old and new) has actually been a bit of a surprise to me, as I've been forced to re-evaluate a fair amount of books; often, these have been found wanting. But I can honestly say that this book, "The Craft of the Classroom" by Michael Marland, is an absolute belter. No other book has affected my teaching more, I can safely say. Of course, I was fortunate in that a teacher friend recommended it to me way back before I started at my very first school; I spent a good while reading the book over that summer and jings, crivvens and help ma boab, I realised I'd struck gold.

I see the latest edition is subtitled "A Survival Guide", presumably because these types of books are selling well to anxious newbies. Well, fair enough, but Marland's approach is more positive (balanced?) than that. He has a lot to say about a lot of things, and seems to have a brilliant knack for alerting you to potential problems - and well thought-out solutions - before you've even come anywhere near them.

For some people he maybe comes across as old-school, but who cares? He's absolutely inspirational. So I hereby award him honourary mathematics teacher status, to go with his Summy.

Nearly there...

2006-10-29T15:47:00.000Z

Jings but this has taken a while... sorry and all that. Spot the teacher who is now back at work!

So, number four... and time to pluck yet another oldish textbook from the realms of obscurity and hold it up as a shining example of what a good, solid textbook should be. No piccies, I'm afraid, as it's been a long time since I set eyes on a copy.

A long time ago when Standard Grade was in its infancy, a teacher called Isobel Vass wrote a series of three textbooks called "Foundations in Maths", designed for use with Foundation Level pupils. Isobel went on to become a Maths Adviser - this was back in the days when these essential (dammit!) posts still existed - and from there on to even greater heights, so she may well be surprised to find these books hailed as one of her crowining achievements, but there you go.

What was so good about them? Well, they were well written with a lot of real-life examples, and were a step above your "hundred questions all the same" stuff, in that they managed to contain challenging questions which were nevertheless achievable by kids with pretty low abilities on math. Nice one, Isobel!

Sadly the books were never very popular - I guess most preferred just to keep the Foundation kids happy with the mathematical equivalent of colouring in - but hey, since when did the popularity of a book mean it was any good?

Three more to go... over by the weekend, I promise. And if anyone out there has suggestions or comments, please do lob them in. You don't need a blogger account, as you can comment anonymously. Go on, you know you want to...

Extreme excitement for maths teachers of a certain age

2006-10-25T21:11:00.000+01:00

OK, it's not the full set, but I stopped short of that for fear that older maths teachers would pass out from excitement and/or jealousy. Hopefully this will be enough to keep you going while I get to work on the top four...

Number five is...

2006-10-22T18:47:00.000+01:00

Nearly there... and at number five, I'm going slightly quirky and choosing an old textbook that probably came out in the early 80's if not before: "Algebra and Number Systems" by Monk et al. Ah, memories! This is a book that was used back in the original days of CSYS, for the "Pure" paper, which was Paper I, though in the revised CSYS it became Paper II, and now of course in the days of Advanced Higher it... er, doesn't exist. Oh sure, the new AH contains a bit of complex numbers and a smidgeon of proof by induction etc, but back in the day we had one helluva Pure paper, and this was the book that came with it.

A fiendishly difficult book, I might add. When I was teaching it, there were quite a few questions I spent many a happy hour over.

To think that at one point, we offered - in school, mark you - a paper that dealt with group theory, rings and fields (topics now covered typically in 2nd year university mathematics)... gosh, it makes me (a) proud (b) nostalgic (c) sad (d) all of the above.

So here's to you, Professor Monk (I think) and yours: solid, undiluted, pure mathematics, just for the hell of it. The joy of sets indeed.

Numbers seven and six unveiled

2006-10-20T08:23:00.000+01:00

Yep, double posting - amazing how busy one gets on holiday!

So, at number seven: the SPMG series of textbooks. That's Scottish Primary Mathematics Group, don'tcha know. Pretty ubiquitous and in use across much (most?) of the country towards the end of the century. I confess that my knowledge of the scheme is a bit hazy, but liturgybuff was kind enough to suggest it, and who am I to disagree?

Number six is a bit similar. For a lot of youngsters not long out of school, the words "Maths In Action" will be well-known. MIA is still going strong, having been reborn as "Mathematics In Action"... hang on, it may be the other way round now I think about it. Whatever. But in days past MIA had near total dominance in the Scottish market for years S1 to S4 in particular. Are the books truly great? Well, no, to be honest, but they got a fair amount right (except for their two attempts at Higher Maths books, which didn't impress me one bit) and I can't help but reward their popularity. MIA tend to be good for the more able pupil, but their efforts for the lower end leave a lot to be desired, so that's why I'm keeping them out of the top five.

Accepting both awards is Bert McBert, chairman of the Bert McBert Committee on och I can't be bothered with this I'm off to bed.

At number eight...

2006-10-18T21:03:00.000+01:00

A reminder: the task in hand is to come up with my top ten, best ever maths textbooks, from a Scottish perspective (of course).

So, number eight in The Summys:

Jings, but this is proving difficult. Maybe it's no surprise, given that UK publishers regard Scotland as a curious creature, and insist on mailing Scottish maths teachers with exciting news of forthcoming English titles that will guarantee effective delivery of KS3 or KS4. Like we have even the slightest clue what that means. So, genuinely Scottish texts are pretty thin on the ground.

Well, let me get both indulgent and mysterious here. I'm awarding position number eight to a textbook that I don't know the name of, but which nevertheless kept me good company throughout my formative years. I'm talking about the series of textbooks which I used at Primary School and I trust you'll forgive me for not having noted down the ISBN at that point (this would be back in the 70's).

This book was probably one of the first to atempt anything like "friendly" maths, though I do think a hefty dose of set theory was in there too... but my main memory of the text is that there was a wee character called "Abe", who was made up out of bits of an abacus (Abe, geddit?), and who popped up at the side of the page almost as often as that hugely bloody annoying paperclip does in MS Word.

Were the books really up to scratch? Who knows. But just like old Proust confronted with a Jaffa cake, I only have to see the slightest glimpse of an abacus or a Venn diagram to be transported to la recherce du mathematiques perdu.

Unfortunately Abe can't be here tonight, having only recently checked into the Jessica Rabbit Rehab Clinic for Fallen Comic Characters, but accepting the award tonight on his behalf is Marcel himself. What a trooper!

Number nine in The Summys is...

2006-10-17T21:12:00.000+01:00

Tricky one this... so let me throw in a mention for the "Teejay" series of textbooks and worksheets etc, produced by (I think) a couple of Scottish teachers and now much in use over the country. Over the years these books have become more sophisticated in terms of their presentation, but at their best the books solve a common problem for your typical maths teacher: that of not having enough questions. 'Cos boy, do these ever!

OK, there's a certain lack of sophistication, the maths can be clunky and ill-defined, and the actual maths methods outlined are sometimes false short-cuts (see my earlier comment here), but these books do have an honest, down to earth quality about them which makes them attractive to those teachers all too weary of books which look nice but have little in the way of work to offer. The Teejay books are great for "borderline" pupils as they don't major on really complicated stuff, though that is a potential weakness too, as they don't challenge and extend reasoning skills as much as I'd like.

But all the same, well done guys and keep it up. I'm picking the seminal tomes "Credit Maths/Intermediate 2", which address a well-known problem in Scottish maths education (latter too easy, yet supposedly on a par with the former) and couldn't really have been produced by anyone else.

Accepting the award tonight is Shuggie McShug, who has finished pages 45 to 48 and so doesn't have to do any homework.

At number ten...

2006-10-16T12:46:00.000+01:00

OK, so on with the top ten proper (the afore-mentioned Blackie Chambers books have now been given the maths teacher "Lifetime Achievement Award" for services to snotty-nosed Scottish weans of the last century and so are ineligible for the actual top ten).

Every day this week (guess who's on holiday) and beyond (guess who can count) I'll be unveiling my choices, in reverse order of course, for the much-coveted "Best Maths Textbook Ever" awards, aka "The Summys".

So, at number ten: Euclid's Elements. OK, so it's not flying off the shelves these days, but all the same, you have to recognise what was surely the first proper textbook, and one that exerted an influence on UK maths education even into the 20th Century. It's even mentioned in Shakespeare: I am undone/With queftion number one/And have no clue/As to queftion number two (line famously cut from Hamlet, just before the prince wonders which pencil to use for his art homework).

Unfortunately Euclid can't make it tonight, but in his place the award is received by Major Lam-Wham von Psycho-Tippler, spokesman for the "Back to Basics: Keep Britain Greek" campaign.

Tune in tomorrow for number nine.

All time top ten maths textbooks

2006-10-13T06:56:00.000+01:00

Well, if Channel 4 can get away with recycling endless variations on the theme of "top ten"this and thats, why can't this blog do the same? Many's the departmental meeting which has been enlivened by healthy debate, considered arguments and occasional fisticuffs concerning the topic. A sort of "Desert Island Textbooks", if you will.

First up, let's acknowledge the total domination of the Scottish market by a particular series of textbooks in the years 1970 to, well, the present for some, but let's say 1990 for argument's sake. Yes, I am talking about Blackie Chambers seminal tomes "Modern Mathematics for Schools", also known as "those ones with the cube on front". Man, what a textbook (sighs nostalgically)!

Nowadays the notion of "modern" maths is pretty quaint, with primary kids no longer required to draw Venn diagrams or wonder what the heck the Universal set was when it was at home (or, for that matter, why it was denoted by the letter E). But what was so great about these books - speaking from the heart - was the absolute rigour behind them all. These people knew their stuff. Nowadays textbooks are written by teachers rather than university lecturers, which makes sense I suppose, but they can contain some real howlers mathematically.

And, any attempts to put maths into context (a regular holy grail) were pretty reasonable, as opposed to the "stick a drawing in to keep them happy" approach we see now. I mean, does anyone really give a toss what the equation of a paperweight is? Puh-lease!

Oh, and another thing: questions. In abundance. These books had loads. We maths teachers love lots of questions. It's the equivalent of "silent reading" in English...

And finally, to finish this reverie: the books were small and well-nigh indestructible. Yup, after a nuclear war the world may well belong to the cockroaches, but they'll be crawling over MMFS books 1 to 9 when it does. Teachers have been known to kill for a complete set.

So do I have them still? You betcha.

(OK, I got carried away on these books, so the rest of the top ten will have to wait. And if asked to pick one from the series of 9, I'm going to be controversial and go for book 7. An under-rated classic with a strong ending.)

Is it a good thing to pass exams?

2006-10-10T20:53:00.000+01:00

OK, daft question, I know. Or not...

You see, in my time as a teacher I think I've got a whole lot better at teaching (well, you'd hope, wouldn't you?), and as a consequence I reckon that I'm able to present at least some of the material in a way that makes it more accessible to less able students. Fair enough.

But let's to put it another way: if I think back to my very first Higher class, I can see that the older, more experienced version of me would have been able to get considerably more of them through the exam.

But! is this a good thing? At what point does getting kids through an exam (the Holy Grail of all our masters, though they'd deny it) become something along the lines of irresponsible? What happens when they leave school and head for courses or training where it's assumed they actually understand the subject, when in fact all they have a motley bag of tricks and half-remembered methods that just about adds up to 50% in an exam on the day?

Should we be worried?

OK, I'm not advocating that kids should be taught badly - that would be ridiculous. But so much of school feels like an exam factory these days, I have to at least consider the question.

Heigh ho... soon be the holidays!

The joy of marking

2006-10-02T21:05:00.000+01:00

It comes with the territory, this marking malarkey. I’m not complaining, but by heck there are times when marking homework gets you down. And that’s even with my new classy Faber-Castell red pen (still going strong and now very much my pen du jour).

So, besides the ever-present glass of red wine, what else can be done to help pass the time while doing battle with the old orange jotters (half-centimetre squared, natch)?

The first bit of advice I’d offer is: don’t take it personally. By this I mean that, as you are marking, you’re bound to get a tad… let’s say, annoyed, at the number of numpties who have insisted on doing the wrong thing, time and again, despite all your best efforts to persuade them otherwise. Examples? Well, brackets with a negative multiplier springs to mind. Ah yes, negative 2 multiplied by (x – 4) – that’ll be –2x – 4 then, won’t it? Aaaaaaaarrrrrrggggghhhhhhh.

So, don’t take it personally. And this is why you’re marking after hours: cos you’d reach across and thump the wee b*gger if it was in class.

If I have the usual number of jotters – around 30, say (insert cheap gag about practical sets and other subjects here) – I’ll sometimes separate them into piles of, say 10, in order to get some small sense of achievement once I get through a pile, so to speak. You could even set up a reward system, I suppose: “once I get these ten done I’ll have a chocolate biscuit” sort of thing. It might work. Or you might end up saying “sod this for a lark”, taking the whole packet and heading off to watch some trashy telly.

Other advice? Well, some folk say you should mark the best kids’ work first, on the grounds that this way you’ll be able to check your marking scheme. If you get two thousand and fifty-six and they get 36.8, you’ll want to check that working, mate.

This is fair enough, as far as it goes. But I say, leave some of the good ones until the end, to cheer yourself up – because you’re probably going to need it. Yep, no matter how good a job you think you’ve done in class, you’ll still find some topics where you’ll begin to question whether or not you even taught the flippin’ thing… so hopefully you get a nice wee surprise at the end when good old Tarquin and Jemima reassure you that at least they were listening. (Or at least that their tutors were.)

Of course, under this whole new assessment is for learning thang, there’s folk who’ll tell you that you shouldn’t give a mark at all for homework, but rather write a wee essay telling each pupil how well they’ve done: “I liked the bit where…”. Aye, and that’ll be chocolate. (“I liked the bit where you said that 5 divided by zero was zero – man, I laughed like a drain at that!”) Let’s get this straight: big, solid homeworks exist for two reasons: one, to get the kids doing some work which includes regular revision of old material; and two, to let you know what stuff has sunk in and what hasn’t. So, OK, the mark maybe isn’t that crucial at the end of the day – but it’s useful that the pupils clearly think it is. And you do build up a picture of pupil ability and effort: always useful when a parents’ evening comes along. And finally, if people honestly think you’ve got enough time to write all these mini-essays, then they really need to get back into the classroom, wake up and smell the pencil sharpenings.

An apology

2006-09-27T19:11:00.000+01:00

I'm reliably informed that my last posting was "a bit of a rant". A good rant, maybe, but a rant all the same.

Sorry.

I didn't mean to, honest. I was trying to offer a cogent, concise, thoughtful op-ed on the problems of demonising - however inadvertently - the very people who make a good school what it is. But I did get rather carried away.

I'm off to write a few lines by way of a "punny".

In praise of the staffroom cynic

2006-09-26T22:38:00.000+01:00

There's been a lot said recently about so-called "staffroom cynics", mostly by Peter (where's my baseball bat when I need it) Peacock, the hairy Scottish Education Minister, who's come over all tough and rough - in a pre-election year, jings, who'd have thunked it? - regarding poor teachers. As in, not very good ones. Pistol-packin' Pete is clear on the matter: it's the end of the line for these varmints, dagnabbit!

Well, there's many points I could make here. For one, any "rubbish" teachers will quickly be replaced before you can say "How Good Is My Toilet Roll" by any number of och-aye-you'll-do newly qualified teachers pouring hurriedly out of our esteemed colleges of education. And they'll all be fabby, right?

But what's getting my goat - and not just Pete's natty goatee either - is that he's having a go at staffroom cynicism. You know the sort: teachers who insist on asking questions about new initiatives in education, rather than hurrying off to buy some new highlighters so they can pretend they've read the latest policy document. Hey, Pete, that's all that keeps some poor beggars going, mate!

Don't get me wrong, there are teachers who are, for whatever reason, no longer up to the job, and this is a real problem. But, there's also any number of really good teachers who long to get on with the job free from the political kick-around which passes for educational policy these days. Yes, they are cynical at a great many "new initiatives", and often with good reason. For one thing, they've seen how today's brave new idea gets a kicking from HMIE a few years down the line when fashions change; for another, they've seen careers made on piles of keech and a fancy cv; but most of all, maybe - just maybe - they know a steaming pile of poo for what it is. If it looks like it, and smells like it... and worse, if someone somewhere is making a pile of cash out of running consultancies offering self-help schucksterism and join-the-dots psychobabble, your average staffroom cynic knows that somewhere down the line, they'll be picking up the pieces.

So, for once, let's hear it for the staffroom cynic. You know the one: the one that's first in the door in the morning, gets on well with the kids, drags them through exams, stays after school for hours on end to help them with their work or to take part in after-school activities, BUT who thinks that QIO is a BBC2 comedy quiz show with Stephen Fry and loses the will to live when asked to fill out a self-evaluation form. How dare they.

And you know what, Captain Peacock? They weren't born this way. There was a time when they weren't cynics. So, what made them this way?

Proofs out there

2006-09-18T10:58:00.000+01:00

Well, if I'm going to call this blog "the proof is out there", and then come across this, then I'd better share it.

Made me laugh, at least.

And, for any actual maths teachers out there, how about this fabulous resource for all manner of mathematical goodies?

Value for money, I tell you.

This business of teaching

2006-09-16T17:36:00.000+01:00

It's a funny old game, isn't it? I suppose we teachers must sound like those sportsmen and women we go on about their respective sports: "that's the beauty of snooker/cricket/all in mud wrestling, Clive, you never know what's going to happen next", sort of stuff. And so with the business of teaching. Seldom dull, you have to admit.

Heard a good one today - every now and then a colleague will pass on an anecdote that has survived the telling in countless staffrooms the land o'er - about a pupil working in "techie" in the old days (pre Health and Safety legislation). I hope it's true - and even if it's not, it tells a truth all the same.

The teacher explained how they were going to make a coffee table, the first step being to take a given length of wood and cut it into four equal parts for the legs.

Well, as you can guess, when Sir gets to wee Johnny he finds he has three pieces of wood roughly the same length, and one much shorter. "No, Johnny, they've all to be the same length, remember?" says our intrepid teacher.

To which comes Johnny's reply, thereafter to live on in teacher lore: "Aye, and the plank wisnae long enough for them a' tae be the same length, wis it!"

Told well, this is funny - I hope - but it also sums up a truth about teaching, about teachers and about students which I think every teacher "gets" as soon as they hear it. I'm not sure I can quite put it into words... so, for those that have ears to hear etc, on you go.

Och, but it's a great job

2006-09-11T20:52:00.000+01:00

OK, this'll have to be quick... "Hell's Kitchen USA" is on in fifteen minutes. (I do appreciate swearing when it's done with the finesse of Gordon Ramsay... actually, I didn't used to swear much at all, now I come to think of it. Do you reckon this teaching lark has something to do with it? Discuss.)

Anyway, time surely to say why I absolutely love my job. After all, I did start off trying to be in some tiny way inspirational in my bloggings, but looking back I see I'm reaching for the rant button a fair bit. So: teaching. Jings, but it's fabby. Love it. Love it love it love it. And despite all the best efforts of managers, politicians, (parents? surely not) etc etc, the whole you-and-the-class-learning-together thing... och, but it's great.

There you go. Almost rant free; swerved close to ranting in the middle bit, but I think we can all agree I recovered.

It's not for everyone, of course. So good luck to all you student teachers out there, wherever you are, buying your new satchel and wondering how to look grown up (don't worry, even if you're 21 the class will think late twenties minimum - sad but true). I hope this is the beginning of fabby fabness, career-wise. And if it's not, but is a year of hell instead... well, trust me, it's better to find this out sooner rather than later.

And the holidays... hey, somebody's got to have 'em.

Assessment is for Learning

2006-09-08T06:58:00.000+01:00

Now, I hope I know what you're thinking, if you've never heard this phrase before. You're thinking "Eh?", or perhaps, "Whit?" - and who can blame you. I mean, is the phrase even grammatical?

Y'see, it's an initiative, so grammatical requirements are sidestepped - because the numptys who write these things would barely know a grammatical statement if it bit them on their bums (or bum's, as they might put it).

Anyways, "AifL" - as we call it in the trade - is an initiative designed to get schools thinking about how best to use assessment to improve learning. I nearly said "enhance" there, rather than improve - jings but this jargon is catching. The idea as I see it, is that assessments - for which too many of us immediately think "tests" - are too often used at the end of a process of learning, when it might be a whole lot better to look at ways to use less formal ways of assessing to see how much kids understand during the learning, and act accordingly.

Now at this point let me be clear that this is, undoubtedly, A Good Thing, as far as it goes. For one thing, the burden of marking in Maths is a bit of a killer, so any way we can reduce this gets my vote (there's only so much red wine I can drink of an evening...). And for another, isn't this what good teachers should be doing anyway?

And there lies the rub. I don't mind someone coming up with an initiative - fair play to them, and I'm sure they get a real kick out of designing little diagrams based round triangles that purport to show the three corners of assessment - but I wish to hell they wouldn't make out that they've come up with the bloody Theory of Relativity. And worse yet, I wish they wouldn't then go on to maintain that this is the blueprint for all lessons forevermore.

Y'see, it's now apparently expected by the Inspectorate (HMIE as they are to their friends) that all lessons will begin with teachers - get ready for this - "sharing learning intentions criteria".

Oh for goodness' sake! I mean, is it just me, or should whoever first committed that phrase to paper not be forced to endure a thousand paper cuts as punishment?

People: education is not a business. We're not producing widgets. We're dealing with kids who deserve to be challenged, motivated, heck, even inspired... and if you honestly think that having every lesson in the entire sodding land begin with the teacher outlining these "criteria" is going to transform education for the better - well, all I can say is, you must be a crap teacher.

Now of course there's a place for making it clear to the weans what we're up to in a lesson. And of course, all too often, our lessons start with a bit of maths dumped on them from a great height with no explanation or context to help kids get the picture. But, but, but... is this one-size fits all "sharing learning intentions criteria" really the answer? And to take but one example: if I'm going to introduce calculus to a class that's never met it before and have no understanding of the term, how in heaven's name am I meant to get across these sodding criteria? I'm like quite a few teachers in that I introduce calculus by lookng at graphs and talking about gradients and the like, before then using graphing software to begin a quest to find a rule for the "gradient function" - so the last thing I want to do is give the game away by saying what the rule is. Whereas, presumably, someone who comes straight out with the rule at the start of the lesson and witters on about learning intentions is somehow delivering a better lesson? Aye, that'll be chocolate!

On a good day, I'm ready to believe that our lords and masters don't see things so simply, and that it's just the (poor) interpretation of their suggestions that makes it down to us mere mortals. Well, here's hoping...

Short and to the point

2006-09-04T20:31:00.000+01:00

Parents.

That's all I'm going to say.

The Evolution of a Maths Problem

2006-09-03T21:53:00.000+01:00

OK, this is lazy, but if I don't blog then I don't exist, so here's an old gag which might raise a smile:

The Evolution of a Maths Problem

1950:A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is his profit?

1960 (traditional maths):A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price, or in other words $80. What is his profit?

1970 (new maths):A lumberjack exchanges a set L of lumber for a set M of money. The cardinality of set M is 100, and each element is worth $1. Make 100 dots representing the elements of set M. The set C is a subset of set M, of cardinality 80. What is the cardinality of the set P of profits, if P is the difference set M\C?

1980 (equal opportunity maths):A lumberjack sells a truckload of wood for $100. His or her cost of production is $80, and his or her profit is $20. Your assignment: Underline the number 20.

1990 (outcome based education):By cutting down beautiful forest trees, a lumberperson makes $20. What do you think of his way of making a living? In your group, discuss how the forest birds and squirrels feel, and write an essay about it.

1995 (entrepreneurial maths):By laying off 402 of its lumberjacks, a company improves its stock price from $80 to $100. How much capital gain per share does the CEO make by exercising his stock options at $80? Assume capital gains are no longer taxed, because this encourages investment.

1998 (motivational math):A logging company exports its wood-finishing jobs to its Indonesian subsidiary and lays off the corresponding half of its US workers (the higher-paid half). It clear-cuts 95% of the forest, leaving the rest for the spotted owl, and lays off all its remaining US workers. It tells the workers that the spotted owl is responsible for the absence of fellable trees and lobbies Congress for exemption from the Endangered Species Act. Congress instead exempts the company from all federal regulation. What is the return on investment of the lobbying?

Shortcuts and dead-ends

2006-08-31T21:33:00.000+01:00

Time, surely, for some mathematical musings.

Here's one: to what extent to teachers follow teaching methods prescribed in a maths textbook, just because they are there?

I don't mean to knock those who write textbooks, because by and large the quality isn't too bad. But sometimes you come across a prescribed method and think, "wait a minute, this is pants!". Or at least I do.

Now I'm not going to name the textbook, but here's a famous example: I wonder just how many pupils doing Credit maths in Scotland have been taught to expand brackets using the "FOIL" mnemonic just because it's in the pages of a very popular textbook? (Technical alert: you might want to look away for a bit...) Basically the book suggests that to expand, say, (x+2)(x+3), you multiply the first terms (x multilpied by x to give x squared), then the outsides (x multiplied by 3 to give 3x), then the insides (gives 2x) and finally the last terms (gives 6). F O I L - geddit?

Well, yes, but why do I need it? Is expanding using the distributive law - to give x(x+3) + 2(x+3) - really so tricky that we need a mnemonic? Strangely enough, the book starts off with the distributive method before offering the FOIL shortcut. But surely the shortcut is a dead-end, not a shortcut? Because all the student ends up remembering is "FOIL", which means they get well-stumped when subsequently faced with expanding a linear and a quadratic factor, eg (x+2)(xsquared + 3x +2), having forgotten all about the distributive law. Worse yet, the FOIL method seems to hide rather than highlight the distributive law. And yet this is still a very popular method, as far as I can tell.

So, stuff this FOIL business, I say! And let's start questioning more closely the methods suggested in textbooks, and chatting about them with colleagues. You see, having ranted to fellow teachers I've discovered they feel the same way - but none of us has ever said. (Mind you, that's probably because we're too busy scoffing chocolate biscuits...)

Of course, this all raises a fairly key question in maths teaching: to what extent does a student have to understand a process, in order to be able to use it? Does understanding always precede the ability to carry out, say, a successful calculation? Or can you do something without really understanding what's going on? And if you can, is that a good or a bad thing?

More of this to follow.

Anoraks of the world unite!

2006-08-28T19:34:00.000+01:00

What is it with maths teachers and the sheer, unfettered joy of keeping lists or ordering things? Or is it just me?

Och, we complain about paperwork - and rightly so - but, you know what, give us a list of marks to write up, or papers to put in order, or a good bit of solid filing to do... and we're in heaven. Maybe it's to do with always looking for order and reason, or maybe we're just control freaks. Mind you, I bet the truly gifted mathematically are probably less inclined to get out the coloured A4 dividers and go crazy filing old Higher homework solutions....

What's all this leading to, you ask? Well, jings, crivvens and help ma boab, have I not found the perfect website for... sorting out your library!!

What's that? "Why would I want to bother?" Well, see what you think: have a look at www.librarything.com and see if you can resist temptation. I'm in there somewhere, happily cataloguing and rating books. Feel free to drop by and say hello, if you can find me!

And yes, it's free.

We can call him Al

2006-08-27T22:58:00.000+01:00

Caught a bit of BBC News 24 today (hey, I have to have something to watch while doing the Sunday ironing): they were reporting live from the Edinburgh TV Festival and had an interview with Al Gore. Al's in town plugging his film "An Inconvenient Truth", which is in the Film Festival, and he seems to be doing all the other festivals he can too.

Anyway, I only saw the end of the interview but I did hear a superb soundbite from Mr Gore. Asked if he had any concerns about how unpopular his message about impending global warming and climate change was, he said this: "The truth will find its own constituency."

I like it. I really like it.

Dear maths teacher: your questions answered

2006-08-24T23:36:00.000+01:00

Those letters just keep coming in. First up, a query from Miss Markitt, an NQT in Scotland-shire. She writes: "Dear maths teacher, do you have any advice on the best way to get through the mountain of marking that comes with the job? Night after night I sit down to mark more and more jotters, and it's getting me down. Help!"

Well, Miss Markitt, you're right to point out that maths teachers the world over are busier with the red pen than most of their counterparts, but it sounds to me like no-one has yet told you the best way to get through the long dark night of the ticks. I'm referring, of course, to the use of performance-enhancing substances. Yes, I'll say it if no-one else will: just as no-one can seriously expect a Tour de France cyclist to go the distance without the occasional furtive visit to Superdrug, so too does your maths teacher need a little extra to get him or her through the evening. Heaven forbid that you should think I'm referring to illegal drugs, mind, because that would hardly fit our image. No, rather we say hello to The Glass of Red Wine. No maths teacher would think of marking at home without it.

Now, let me stress here, I'm not advocating you should mark jotters while squiffed/steaming/legless - though it might be fun to see the results, you have to admit. But one or two glasses of a well-chosen red, and trust me, that red pen will start to flow more freely. And, when you see someone forgetting that a negative times a negative makes a positive for the twelfth time in as many jotters, it won't seem quite so bad as it might otherwise.

Experienced teachers know that it's best to choose the wine to suit the class. For example, marking a Higher Ink Exercise is to become part of an age-old tradition, so obviously a decent Cotes du Rhone brings sufficient gravitas and helps you feel you belong. Marking a first year test, by contrast, is a lighter affair, well-suited to a cheeky Beaujolais Nouveau. (There being no famous Australian mathematician to speak of, by the way, maths teachers tend to reject New World wines as young upstarts that should be left to the Media Studies department, or PE.)

If, however, you ever face the prospect of having to read your School's Improvement Plan... well, get yourself a decent Islay Malt Whisky, a large tumbler and a pillow, and the pain will recede eventually. Failing that, call for Doctor Macallan...

Who's counting?

2006-08-23T21:51:00.000+01:00

First up, thanks to liturgybuff and covenanter who have both recently posted comments; as user-friendly as Blogger seems to be, I can't quite work out yet how to show recent comments on the sidebar, though I'd like to. Bear with me...

Anyway, here's the thing: how often do any of us have to do basic arithmetic these days? It's hard to find examples from real-life - and the old answer of "when you're shopping" doesn't really hold up under scrutiny in these modern times. Do you see people keeping a running total as they shove the trolley round? No. Do people work out a rough total? No. Does the shop assistant? No. The computer on the till does the work, and maybe - just maybe - you have to count out some notes, but more likely you hand over some plastic and cross your fingers. (And if you need change, the assistant doesn't work that out either.) Does anyone check the computer's calculations? Hardly ever.

Y'see, speaking as a teacher, we do teach kids the basics, honest. And things are a whole lot better now that the main exams have parts where you are not allowed to use a calculator, unlike in the 80's and 90's, when kids were welded to their calculators. So in theory at least kids should be getting better at the basics.

But, but, but... surely the important difference nowadays is that there's hardly any contexts where they then have to use these skills. Whereas for those of us who lived in a time before computers could do all the work, it was pretty important to be able to do the maths, or rather arithmetic, and you weren't short of opportunities so to do.

And this throws up a question of precisely what we should teach these days under the banner of mathematics. If it's just for personal finance, then as far as I can see kids need to be able to do the four basic operations, understand percentages and maybe just a tiny bit of fractions, though you could maybe get away without that. Under current guidelines this content would be covered and understood by a notionally "average" 14 year old. Meanwhile, maths is compulsory roughly to age 16.

Should we let kids get away from the subject early? Am I talking myself out of a job?

Trust me... this stinks

2006-08-20T22:51:00.000+01:00

Courtesy of the wonders of digital TV (and a subscription fee, I might add), I caught up with a TV prog yesterday which was originally broadcast on Friday night, 7pm, BBC2. "Trust me... I'm an economist" purports to demonstrate how the science (?) of economics can show us how to live more successful lives. It's presented by I-can't-even-be-bothered-to-look-it-up in a manner both smug and incompetent - always a winning combination. And what do you know, programme one was on "love", and did indeed try to use the language of economics to tackle such problems as how to meet the right partner/how to be sure marriage is the right step/how to decide whether or not to have a child.

The audacity of this programme was breathtaking. And disturbing. Quite the worst thing is, it struck me as a programme almost entirely devoid of any sense of morality. I shudder at the memory.

Naturally the programme maker had occasional equations flitting across the screen, cos hey! this is a science, right? Which makes me wonder what any of my pupils would make of this stuff. I think I trust them to call it for what it is.

Let's hear it for Howie

2006-08-20T22:04:00.000+01:00

Big splash in today's Guardian about government plans to beef up the content and difficulty of GCSEs in Maths and English - which doesn't apply north of the border, of course, but may end up being an indication of the way the wind is blowing, metaphorically speaking.

Anyhoo, there's a comment by Baroness Warnock which you can find here, and I've got to say, the old girl could be talking a lot of sense. I know that a lot of teachers and educational thinkers were disappointed when the government turned down the recommendation of the Tomlinson Report, and it does get me vaguely nostalgic for the Howie Report which came out in Scotland... ooh, ages ago. Basically Professor Howie - the guy's a mathematician, which has to count for something - said we needed to do something about the Higher exams, which are taken mainly by fifth years, who then get a university place based on their Highers, provided they do well enough. Which means they then do... er, what, exactly, in sixth year? "P*ss about!" I can hear the teachers saying in frustration. Well, the Prof suggested we go for a Baccalaureate thingy, which more academic pupils could get by the end of sixth year, which would (a) keep them studying (b) be a nice European way of doing things and (c) insist on students studying a reasonably wide range of disciplines. Less academic/more vocational pupils meanwhile would study for a vocational qualification, with exit points at the end of fourth, fifth or sixth year.

Not a bad idea, I thought at the time - though no-one asked me. But this was not great news to a couple of groups of people. Firstly, to the universities, who insisted that they wanted the Highers (fifth year, remember) to remain the benchmark for uni entry. And why would that be, exactly? Anyone? Well, that way you get more people through the door, of course. (Well, duh!) Which has to be a good thing, surely? See Baroness Warnock for thoughts on that argument.

And the second group? That's the group of people who go wild-eyed crazy when they see someone venture anywhere near the phrase "more academic pupils" like I did above; who complain that there can be no division between "vocational" and "academic" study, and who think that suddenly we're talking about reintroducing the 11-plus (which we never had here anyway). These people are more politicians than they are teachers, believe me.

It's weird: most of the pupils who leave for university see it as part of the process of training for a better-paid job, which is what the polytechnics and colleges used to do so well. So maybe that's Mrs Thatcher's legacy (always blame Mrs T, remember, though by jings Tony and chums don't seem keen to change things): polytechnics get to call themselves universities, and universities get to do the job of polytechnics. Orwell would be amused, at least.

In-service days and how to survive them

2006-08-16T22:23:00.000+01:00

In-service days, or ISIS days ("In-School In-Service" apparently)... ah, the joys of days in school with no kids around.

You'd think.

Time to tidy up the room, do that filing you meant to do at the end of last session, organise the jotters and books and folders and rulers and protractors and etc etc before the weans arrive fresh-faced the next day.

You'd think.

Well, OK, let's be fair, there is a certain amount of time available for this sort of stuff. But! there are also Meetings. Lots of Meetings. And these Meetings are Important because they are organised by our managers, and because... er, hang on, I'll get back to you on this.

Don't get me wrong, we do need to meet with colleagues, whether that be in departments or as a whole school. But (whisper it quietly) do so many of them have to be so boring, I wonder? What is it about standing in front of staff that makes a teacher - a teacher, for goodness' sake - go off the scale in the bore-o-meter? I've heard people deliver the most bahookie-numbingly dull talks, about how inspiring we should be as teachers. I'd like to say they were being ironic, but no.

So, this session, let's be radical. Here's to creative meetings; to a chance to discuss teaching and learning with our chums; to actually talk about how to teach maths. It could happen... but! we need to learn how to talk the talk first. Don't say "we're going to have a chat about how best to teach factorising quadratics"; rather, say "we'll be discussing proactive ways in which we can enhance the provision for accessing key algebraic skills and concepts, with opportunities provided for both individual and group learning and discussion". And keep a straight face while you're saying it...

Be careful out there

2006-08-13T21:15:00.000+01:00

Cruel as it may seem, tomorrow sees the start of schools returning for the new session, in some poor authorities at least. Some others get to wait until towards the end of the week, while others yet get to wait another week... but wherever we may be, we can hear the bell tolling (or maybe the bleeper bleeping, in newer schools) and we know the holidays are not long for this world.

So, wherever you are, whenever it is you're back out there, let me wish you good luck and - in the never-bettered words of Hill Street Blues - "be careful out there".

Good luck especially to all the newbies (sorry, NQTs), and to any student teachers out there - won't be long now.

Och, I'm getting all emotional...

(Those of you not in the teaching profession may, of course, wish at this point to mutter astonished comments along the lines of "six weeks holiday - what're they moaning about?!" Go on, you know you want to...)

Do the maths...

2006-08-10T23:16:00.000+01:00

Well, the SQA results duly came out on Tuesday and I have to say there didn't seem to be too much of a fuss made about them by the media. Most went mainly for the human interest angle, following some pupil somewhere as they opened their envelope to find out their results - though I do wonder: have the schools in question "spilled the beans" in advance to the press, guaranteeing a decent set of results for the kid in question? It can be done... and if it is, what's the legality - to say nothing of the morality - of such practice?

Anyway, the only other thing they fixed on was that the pass rate for Higher English has fallen by a couple of percent (can't recall exact figures offhand, but somewhere in the 60%s). This was put down to a tricky exam, but it does strike me as odd that no-one ever takes a more considered view of such a statistic. For a start: how many people actually sat the exam? Was it more than last year, in which case in theory it's possible for more people to have passed Higher English than before? After all, many pupils do sit the exam against all professional advice, at the express wish of their parents. How many? Difficult to say, but at a rough guess, I'd say that easily two-thirds of those who failed will have been expected so to do.

I haven't seen any comment on Maths results (perhaps tomorrow's TES will oblige?), so I don't yet have a fix on how my school's results compare with elsewhere. Everyone knows that you get "good" and "bad" year groups, of course, but that doesn't count as an excuse to the powers that be, and newspapers like The Scotsman are still publishing "league tables" based on results.

Still, at least as a mathematician you can get away with waffling on about means, medians, sample sizes, confidence intervals etc etc and hope that you don't get found out. It's worked so far...

(At this point I can't help but repeat an anecdote I once heard about a Headteacher demanding to know of a particular PT why more pupils hadn't got above the average mark...!)

Search for a red pen: update

2006-08-08T17:02:00.000+01:00

Out browsing today and came across a model of red pen I hadn't seen before, so before you could say "stationery fetish" I bought myself one. After rigorous roadtesting, here are my thoughts:

Make: Faber Castell
FC are well know in the art world but this is the first time I've seen them venture for a wider audience.

Model: Finepen 1511 Document

Price: £1.70 ish

Colour of ink: red
Quite a bright red, actually. There 's no colour stated on the pen, but I think it is what we call in the teacher trade "scarlet displeasure", perhaps with a hint of "vague encouragement".

Appearance:
Reasonably thick without being chubby; large pen lid. The body of the pen is a dark green (with a red end indicating colour), so I worry that after a heavy day I may inadvertently grab it thinking it's green rather than red. Time will tell.

Taste:
The pen top is chunky so should survive a good chewing, if you're given to such nervy behaviour. Phenol tones dominate on the palate, with an aftertaste of burnt sugar, lavender, pomegranate and wellies.

Nib width:
Not written on the pen, but a width of 0.3mm is apparently claimed. Electron micron measurement reveals a precise width of 0.324mm, which is fine by me, as the extra 0.024 always comes in handy for hefty ticking.

Bleed through:
Reasonable on a standard 0.5 square centimetre jotter, though comments written in anger ("NO!", "ugh!", "Show your WORKING!!!" etc) fared poorly - perhaps one to use with a more able class?

Performance:
The pen was road tested by first computer generating 100 basic arithmetic questions and answers, which I then marked under standard teacher conditions, ie at 11.30pm after consumption of two-thirds of a bottle of cheap red wine. The pen felt good on the ticks, with a free-flowing action, but on the crosses there was a tendency for deposit build up on the second stroke. To be fair, this is a well-recognised problem in assessment, and to the pen's credit, it did manage to write reasonably well on wine-stains.

Underwater performance:
Fair, but the jotters did get soggy.

Performance at altitude:
In order to check the pen's ability I took a long-haul flight (for greater altitude); the pen performed reasonably well but did smudge some jotters marked in economy class. To be fair, this may be because I'd dropped my mini-bread roll on the page earlier.

Works in zero gravity?
A delay to the space shuttle launch leaves this question pending. For wider space travel, however, it's worth mentioning that the pen worked well in a Type 40 Time Travel machine, though it didn't unlock any doors, so a sonic device remains a safer bet in such an environment.

Overall score: 6.83/10.
Not a classic by any means, but shows promise and may age well. Use now to end of term two.

A plea from the heart

2006-08-06T21:46:00.000+01:00

Only about another week to go now, and it'll be back to school. So what better way to spend the time remaining, than to sort out the maths teacher's wardrobe - we wouldn't want to be out of step with fashion, would we? Time, surely, to rummage through those drawers, cupboards, wardrobes and make sure everything's OK. Failing that, a quick visit to Matalan and all shall be well.

I love how, as soon as the holidays have started, shops like BHS or M&S have "back to school" displays... not after a couple of weeks of holiday, no, but straight away. Thanks for reminding us, guys! But these displays are always of weans wearing vaguely schoolish clobber; why not push the boat out and have a display of teacher wear instead? They could display the latest Harris tweed bullet-proof number, complete with leather elbow patches. Mmm - very Jude Law.

Anyway, on to the plea from the heart. Now I'm no fashion guru, but there are quite definitely things that should not be done. So, to all maths teachers everywhere, here's my wish list for the coming session... follow this carefully and thou shalt not be too tragically unhip:

Stop wearing the following ties: Wallace & Gromit; the Simpsons; Doctor Who, or basically any character based paraphernalia. Do you really want the world to say "Hello, Grandad"?
Give up the comb-over
Yes, early onset male pattern baldness is a terrible thing, but think Sean Connery, think Jean Luc Picard... or think Gregor Fisher in the Hamlet cigar advert. Your choice.
Put those pants away, madam
Your class does not want to see them, trust me. Or if they do, they won't be getting much work done.
"Non-iron" shirts and trousers
still need ironing.
Jeans
don't need a crease.
A smart suit
indicates a desire to join senior management. Before you know it, you could find yourself supervising lunches - is that really what you want?

Always remember that, historically, maths teachers have tended to operate within a narrow band of the fashion spectrum, unlike (say) art teachers who can wear almost anything in the name of creativity; though you could always go for the ever-popular "mad professor" look, but it's hard to pull this off because the moment you start trying to dress eccentrically, you're doomed.

One final tip: some pupils apparently have difficulty seeing red or green colours when used at the "blackboard". Theoretically this should mean that if you dress in red or green, you will become invisible to such pupils. It's worth a try, surely?

The calm before the storm

2006-08-05T23:10:00.000+01:00

You wouldn't know it to listen, watch or read the national media, but up here in hairy Scotland the examination results are due early this coming week. On Tuesday morning, the SQA will deliver the official verdicts on pupil abilities via the traditional letter through the post. (Though apparently there are plans to send them via text messaging next session - can you imagine it: "Maths not gr8"?)

I'd say good luck to one and all, but it's all decided now. It's a strange time for a teacher, but let me also say that it's one of the real joys of the job if you are able to go back to work in the new session and meet pupils in your care who have done well. And, of course, to sympathise with those who haven't - well, provided they worked hard, that is, otherwise you can let the unspoken "if only..." hang in the air.

Of course this also means that - in the Scottish press, at least - on Tuesday we the teachers get some form of verdict delivered unto us as well, in that we'll waken up to headlines either along the "standards falling: what can be done?" or "exams get too easy: what can be done?" variety.

I wonder which one it will be?

Aaarrrrggggghhhhhh!

2006-08-03T22:58:00.000+01:00

I'll say it again: aaaarrrrggggghhhhhh!

Yes, tonight I enjoyed that fabulous bit of entertainment, so loved by so many of us: kids misbehaving while their parents do nothing at all to stop them.

I'll spare you the gory details, but basically for the best part of an hour I had to put up with two wee brats running more or less riot in a train carriage, while parental figures (one per child) looked indulgently on.

Did I say anything? Did anyone else? Of course not. Who does, these days? We just did our best to ignore them. But since I was sitting directly opposite them, this was no mean feat, and I eventually sought refuge in the Proclaimers, played loudly through the headphones of my mp3 player. This almost worked.

A question well worth asking is, is enduring such behaviour harder for teachers than for the general public? I get frustrated for two reasons: firstly, that most teachers can get 30 kids behaving better than such parents can manage with 1; secondly, I can't help but wonder how these kids then behave when they get to school, if this is the measure of structure and control they are used to.

Or, to be blunt: I blame the parents.

OK, this is what teachers always say, so of course it can't be the whole truth, but by jings we're talking high percentages here. I've got pie charts and graphs and everything to prove it. Somewhere...

So, what's to be done?

Heck, who knows? We certainly seem to have reached a tipping point, where it's just not the done thing for anyone to comment on kids' behaviour when the parents are around (for fear of causing offence) or even when they're not (for fear of getting abuse from the kid in question, if not actual physical violence). How do you get back to the good old days, assuming they ever existed? How do you "untip"?

I will say this much: that a lot of the problems we have now are caused by the rise in the cult of the individual; the idea that there's no such thing as society. So, who am I to complain about how your kids behave? They're your kids and that's your call. Apparently. And who is the school to tell you that your kids are wee monsters? You know your kids, and they're lovely. And if you know one thing, it's that they never lie. Apparently.

I suppose, to be fair to parents (it won't last), teachers have access to a "big" picture at school - the behaviour of a class, or a year group - while they don't. We need to appreciate their point of view more, I can see that. But if we collectively decide that parenthood gives us a right to say "stuff the bigger picture", well that worries me. That way lies parents lying about their place of residence in order to get their kid into a "good" school, and then justifying their behaviour on the grounds that they're doing it for their child so that makes it OK.

We're already there, let's face it. And I don't like the look of it.

Cheery stuff, eh? Still, for any new teachers out there, remember: it's the parents fault. Failing that, blame Mrs Thatcher. Works for me.

[One final point: I have experienced contact with parents who, when faced with evidence of inappropriate behaviour on the part of their child, then go on to ask me if I have children myself. I have always refused to answer that question, and I'd suggest you do the same. It's entirely beside the point, whatever the answer.]

The campaign starts here...

2006-08-01T22:41:00.000+01:00

OK, bear with me 'cos I haven't thought this through fully yet, but all the same, enough's enough.

I've been mulling over my earlier posting on maths in the media generally, and I think I've located a central problem. Carol Vorderman. Now don't get me wrong, there was a time when our Carol brought a general sense of happiness and well-being to many maths teachers, back when Countdown was in its infancy. But by heck that time has long passed. Now it's all 30-day detox and Carol's book of Sudoku and put them away woman and and and those flippin' loan adverts. Enough already! No wonder people aren't studying maths much anymore...

Now, leaving aside the issue of the current campaign against Ms Vorderman and these loan adverts (see the MoneySavingExpert website here - I encourage you to sign the petition, seriously), I'm here to say right, that's it, CV's place as the unofficial mathsy media mascot type person is over. Finito. I'm calling it. Maybe it was fun while it lasted, but her reign is over.

So, the next question has to be, who takes her place? Who should the public think of, when they think "maths", now that Johnny Ball is enjoying his retirement? Who can we turn to? Call on? Who will save us?

Here's where I reckon we have to think outside the box. Oh yeah, we could look around and find someone who's done a bit of maths - the Irish comedian Dara O'Briain, for example, as I read today - and try to get them to do maths work in the media, but that's what they're expecting us to do. It would be too easy. Why not come at the problem from another angle entirely - a sort of proof by contradiction, if you will?

Yes folks, the campaign starts here. My nomination for the UK's maths spokesperson is, has got to be...

... Boris Johnson.

Admit it, you're intrigued.

OK, I'll grant there may be arguments offered against this idea, so let's deal with them, one by one.

He's busy
Well, yes, to an extent, but we all know Boris is game for a laugh. Surely he'd fit us in somewhere.
He's a bit of a buffoon
Well, again, yes, but don't we say as maths teachers that we need to encourage pupils to believe that anyone can do the subject? If we can show 'em old BJ differentiating y with respect to x... well, can you imagine?
He has no idea whatsoever about maths in any way shape or form
OK, so we're getting to the meat of the argument. The crux of the matter. Or, as Boris would put it, the ummmm ahh yes well ah you see the ummm crux yes indeed the crux, crux! of the emmmmmmmmmmmmmm... matter.
But, be honest, since when has a politician ever let a lack of knowledge in a subject deter them from speaking as if they were an absolute expert? Aha! Y'see? I have absolute confidence that Boris can sound as knowledgeable about maths as he does about anything else.
He's Boris Johnson
I'll get back to you on that one.

For me, it has to be Boris. It's that rare thing... that moment of clarity when you realise you've finally arrived at a proof, and that proof is so simple, so obvious, that you wonder how you could miss it. And answer me this: would you go for a loan company on his recommendation?

About the links

2006-07-31T23:41:00.000+01:00

When it comes to IT stuff, I have to take pride in the smallest of achievements. So, regular readers of this blog (ahem) may well anticipate my elation at managing to edit the links toolbar menu thingy on the right hand side of the page. Note the use of technical terms... I've even gone so far as to claim to have coded in HTML, but that's just pure bluffery. So thank you, blogger, for making things easy.

So, a word about two new links added.

"Mathworld" is pretty much an online Bible for maths in terms of offering definitions, theorems, proof etc as well as providing breaking news (usually of the "nth prime discovered" variety) which can be entertaining if shown to a class, who will have little concept of anything new happening in maths; it also offers a few animations which may be of use. Be warned though, 'cos it's high powered stuff so you might have to rummage to find school level material.

"History of Maths" is a fabulous website run by the University of St Andrews: anytime you're looking to get the lowdown on who to blame for a piece of maths, this is the website to turn to.

I'll add a few more sometime soon, but these are my desert island maths-related websites. Which is a strange concept, I admit. Coming soon: desert island maths books...

What's minus five times minus two?

2006-07-30T22:29:00.000+01:00

OK, finally a bit of mathematics to get our webteeth into...

I caught a bit of "The Weakest Link" on Friday, or more accurately I should say it was on in the background and I wasn't paying much attention, honest. But then I heard Anne Robinson ask the above question (more or less, as far as I can recall now) and I looked up with interest. Y'see, TWL usually goes for much more basic addy/subtracty/timesy stuff, and never with negative numbers. Well, I say more basic... of course the magnitude of the numbers involved is usually much greater, so in a sense there's more of a calculation to be done mentally than with -5 times -2, but all the same, conceptually, this was harder.

So, how did the contestant do? (They were down to the last two, and the lad asked this question was clearly not the brightest of the bunch in the previous round and had only survived by the classic TWL squeeze-play where the strongest link gets voted off and does the walk of shame through gritted teeth.) Well, what fascinated me was that he looked absolutely stunned when he heard the question. Not in the sense of, "I don't know the answer", but more like "this question doesn't make any sense".

It really was quite a look, and I thought to myself, OK, this guy has never, ever encountered multiplication within the integers. (I would think that, being a maths teacher and all.) In a way he had the common sense to think that this is nonsensical, in as far as it met his experience of mathematics.

So here's the thing: how best to get across the concept? Classically, (assuming we're OK with addition and subtraction in the integers), we move from 5 times 2 (OK, got that) to 5 times -2 (OK, still with you, sort of), then we have to dance a little (who wants to mention commutativity?) to get -2 times 5 being the same thing (well, OK, I suppose so) ... and then comes the final piece of the puzzle. Again, classically I suppose we have to say that we get -5 times -2 being negative negative ten, which has to be ten (cue some hand-waving). But though I think I can get a class through this with no apparent trouble, I'm now wondering how many are like this contestant, and saying "eh????" to themselves. And I'm open to better offers... concrete, real-life applications?

OK, OK, you want to know what answer he gave. He said, after much thought, "zero". And in a way I admired him for it. I think he was reasoning, "this doesn't make any sense, so I can't give any answer other than zero". Or maybe he thought it was a trick question.

"No, -5 times -2 is 10" said our Anne, correcting him. And he still looked astonished. The sum is so easy to those of use who know the rules, I suppose, but what about those who don't know they're playing a game?

Please don't think I was laughing at this lad, by the way. This is what teaching is all about.

(Saved for another time: correct usage (minus versus negative; times versus multiply). Things could get nasty!)

First, choose your pen

2006-07-29T21:49:00.000+01:00

The new session looms ahead. An expectant teacher gets ready. Things to do: lessons to plan, classrooms to tidy, textbooks to find, mugs to give their annual washing... but most important of all: get the new pens in.

Oh yes, it's a real beginner's mistake to think you can just get away with your basic red Bic - what do you think you are, a PE teacher? Oh no, no sir. Pupils note everything. And the pens we use say so much about us. Are you cheap? Colourful? Smooth? Retractable?

After careful scientific testing I've come down in favour of the classic Pilot series of pens (.03 in particular) as being ideal for diagrams etc on worksheets, but damn and blast, they don't make 'em in any other colour but black. The search for a decent red pen continues... "I will find you!", as Daniel Day-Lewis emotes in The Last of the Mohicans, though I don't think he was talking about Staedtler and Rotring.

You'll note I say "red" specifically... well, yeah, call me a traditionalist, but for good old ticks and crosses, you can't beat a bit of the old scarlet. It's like an unspoken rule. I mean, yes, green ink's OK at a stretch, but venture beyond those two colours and you run the risk of being called a rebel. And as for purple, scented jobs - och no, that'll never do.

Come to think of it, you'd think stationery shops would make special teacher packs of pens, wouldn't you? They could call them something cool, like, er... the Pilot Chartered Teacher 2000 (with interchangeable CPD nibs). They could have pen reviews in the Times Educational Supplement - and adverts too, with teacher testimonials: "I stayed up all night to finish marking and the Uniball Steady-tick didn't let me down once", says Senga McHaggis of St Jonquil's School for Young Conservatives. Or: "When I mark a sum wrong with the Pentel Punisher, it stays wrong!" says Bob McBob of the Bob Robert School for Bobs.

I'll stop now and lie down. Or go and watch Julie Walters, who's busy doing a "don-key!!!" Shrek accent on ITV in a teacher drama. It really could go either way.

Maths in the movies

2006-07-28T12:39:00.000+01:00

On a train today and saw an advert off in the distance (Scotrail must have cheap rates for posters): "Teach Dieticians About Pi". As far as I could make out, this was an advert encouraging people to consider teaching - specifically mathematics - as a career. Well, why not, cos jings we need them, and none of us is getting any younger. There is a real problem in getting new recruits in the subject. Why? Well, I could mention pay and conditions, I could mention the heavy workload of maths (and English) compared to other subjects, I could mention... Well, you get the idea. But maybe it's a more fundamental problem: we just don't get enough positive role models for mathematics generally in the media. Consider the evidence:

Movies with mathematicians in them:

1. Jurassic Park
Jeff Golblum wears ridiculous glasses, acts kooky and calls himself a "chaos mathematician". A nation looks on incredulously.
Basic message: mathematicians are weirdos who get eaten by cloned dinosaurs.

2. A Beautiful Mind
Russell Crowe wears glasses , acts well barmy and wins a Nobel Prize - though he's still nutso. A nation weeps.
Basic message: mathematicians are weirdos who get weirder.

3. 21 Grams
Sean Penn (no, seriously) plays a Mathematics professor who has an adulterous relationship and, for reasons I can't recall, kills someone. A nation wonders how far Mr Penn can count unaided.
Basic message: mathematicians are murderers. And weirdos.

4. Pi
Darren Aronofsy directs a movie about a young mathematician going mad, who eventually cures himself by taking a Black and Decker to his head. A nation winces.
Basic message: yup, back to the weirdos again.

I could go on. What about TV, you ask? Well, there's a strange US cop-type show with that bloke from Northern Exposure and his wacky, weirdo maths genius brother, called "Numb3rs", and there's Carol Vorderman. Oh, and in a recent Doctor Who episode, the entire maths department of a school turned out to be evil monsters trying to take over the universe.

Now OK I could be missing stuff, but all the same it's a reasonably compelling set of evidence as to why people get the wrong message about the subject. Unless, of course, we are weirdos after all.

Evidence to the contrary, anyone?

About a blog

2006-07-28T12:15:00.000+01:00

Why a blog?
Heck, why not? It's not as if many maths teachers can write, so I suppose every little helps - as they say. I doubt any publishers would be interested in a book on teaching maths in the Scottish system... But hey guys, if you're out there, bring it on! I'll have this blog snuffed out in seconds for the right price, and a shiny enough cover on the book.

But isn't a blog meant to be like a diary or something?
Indeed. And I plan to write stuff as it comes to me, which may or may not happen as a result of events of the day. It may at least follow the pattern of a school year, which can't be a bad thing, surely?

OK, so who the hell are you to comment on maths teaching?
Shh... No names, no places, no employers will be mentioned. Let's keep this on the right side of the law. If you want a blog where someone mouths off about their work, go look elsewhere. Which isn't to say that I won't be grumpy every once in a while. Or more often. But I'd rather not get Alan Sugared, thank you very much. Suffice it to say, I've been teaching Mathematics (ooh, capital M, he must be serious) for well over ten years now, in the Scottish system, and I've been around a few schools, so it might be that I know what I'm talking about. Besides, this is the internet, for goodness' sake! Who are you to question my right to prattle on about something I may know nothing at all about? Have you heard radio phone ins lately?

The big idea...
... is of course to get a bit of discussion going about maths teaching, so please do join in.

Summer

2006-07-28T11:53:00.000+01:00

Ah, the summer holidays.

Six weeks - count 'em, six weeks - of uninterrupted joy and bliss. No jotters to mark, no kids to shout at, no staff meetings to attend. What could be better?

Do we really need six weeks to recharge our respective batteries in the teaching profession? In all probability, no - but we'd kill anyone that was to come out and say that outright (oops). I'm now four weeks into my break and I hate to admit it but I have done a little bit of school work and even had a wee browse on the net for maths related stuff last night. If you like, that's a sign that I've now moved from recharging batteries to actually enjoying a rest, cos it really does take a while for teachers to basically stop feeling tired all the time when their holidays start. Weird.

But I'm not complaining. The holidays are a really good perk of the job; a necessary one. Don't believe me? Try doing the job, just for a week. Student teachers and probationers know what I'm on about. It's hard to get across just how tiring the job is. Most new teachers collapse in a heap when the first proper holiday comes along (October round these parts), from sheer mental and physical exhaustion. Knackered.

So it's reassuring that after a while, during the mammoth summer break, you maybe almost not quite but maybe yes do miss the job a bit.

Or, maybe I just need to shout at someone to get it out of my system.