Saturday, December 16, 2006
Saturday, December 09, 2006
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.
Sunday, November 19, 2006
Some more thoughts, then, on the whole "I don't know, kids nowadays, they can't even add up" business.
I'm not entirely disagreeing with these sentiments, but what frustrates me is that I know - know, dammit! - that the kids in front of me nowadays can actually do more in the way of mental arithmetic, or simply without a calculator, than they could when first I started teaching.
Y'see, when first I hit the chalkface, the exams in maths at school could all be done without a calculator. Now of course we did still teach pupils the basics of arithmetic, but they quickly worked out that if they were allowed to ue a calculator come the actual exam, they were going to darned well use the calculator in class too. We did what we could to stop them but, being mathematicians, we had to admire a grasp of simple logic. Naturally enough, quite a few pupils then started using the calculator for everything: why work out 6 times 9 yourself when the calculator will guarantee the right answer? (And - still the case today - why bother even considering if the answer seems reasonable? Would the calculator ever lie?) So it came as no small wonder that we were turning out a nation of somewhat less than numerate children back in the nineties.
Ah, but then. Then someone somewhere decided the Thing To Do was to give pupils exams which had to be done in two parts: one with our electronic chum, one without. Hurrah! we cried, and set about teaching percentages, fractions etc etc with renewed vim and vigour. All seemed well. All was well. I remember teaching a lower ability class in S3 with an S6 prefect helping out, and I well remember the prefect telling me that she didn't really know how to do half of the stuff these less able pupils were managing. Result!
So, dear general public, rest assured that we do teach tables; that the kids in class do know how to do a fair bit of what "we" used to be able to do standing on our heads.
Nevertheless, I have to agree, pupils emerging out into the world of work nowadays simply are less numerate. And I'm really not sure there's much we can do about it.
Well, as I've mentioned before, in this electronic age, there's simply little or no opportunity for pupils to use or practise these skills out in The Real World. I mean, when last did you seriously - seriously - have to add up some numbers, or do a long multiplication, or add (multiply??) fractions? These kids can do the arithmetic well enough to pass exams, but the skills then atrophy through misuse.
Like it or not most of us rely on electronic aids more than we'd care to admit. Those of us Of A Certain Age do still have reasonably high levels of numeracy, but only because (a) it was about all we ever did in school for the first seven years and (b) we did have to use these skills to a certain extent in everyday life.
Those days are gone.
It would be nice to think that this then frees us up more to concentrate on less mundane skills in maths - on more reasoning, for example - but it may well be that the ability to reason follows the ability to execute the basics with confidence.
To put it another way, we're screwed.
Or maybe not. Does all this matter in the larger scheme of things? And were we really so good at arithemtic back in the day? (Take written English for comparison: OK, so a lot of kids nowadays can't spell or use basic grammar, but reading other teachers' reports I do wonder if 'twas ever thus.)
Tuesday, November 14, 2006
(If anyone knows how I can get recent comments to appear summarised in the sidebar, do let me know.)
Friday, November 10, 2006
Regular readers may recall a considered piece/rant from a wee while back, wherein I vented some spleen at the whole new thrust in Scottish education currently striding forth under the banner "Assessment is for Learning" (hey, I'm a maths teacher, so I can mix metaphors all I want).
Since then I've been in-serviced with current thinking in AIFL (I'd argue for AifL, but what do I know) - quite a good in-service, actually. And, secure in the knowledge that HMI have a gun to our heads on this matter, you can bet your life that the learning outcomes for my lessons are now regularly being shared. As in, I write them up on the board.
Hoorah! my class cry as they realise the overall quality of their education has just improved all but immeasurably.
Now in fact, I'm quite happy to admit that this AIFL stuff may well be more or less A Good Thing (though I reckon a little may also go a long way). I do wonder, mind you, quite how the pupils are going to take it all in once they encounter the same approach in all their classes, but who knows, maybe it's just what they want.
- I read a fascinating blog here recently, which looked at the notion of Accepted Solution Time in mathematics: the idea being that AST is the amount of time (and effort) a student is willing to invest in a problem before either getting the solution or giving up. The problem is, as the blogger points out, that AST seems to be decreasing, even for students supposedly "able" in mathematics. Well, if all this AIFL stuff is going to be breaking down the content of the subject into ever smaller pieces, isn't there a real danger that this is precisely the sort of approach which all but guarantees that students will become greatly distressed if ever they are asked to do something a little out of the ordinary or off-beam? "What's the learning outcome here?" I can hear them complaining already.
- This leads neatly into my second point, which is basically that behind all this I think lies a philosophy that wants to reduce education to training; that believes that something as massive and amorphous as mathematics - even at school level - can be reduced to a checklist of "be able to". Oh jings, it's that Thatcher woman again isn't it?
Let me put it another way:
There are more things in mathematics than can ever be dreamt of in your learning outcomes.
Wednesday, November 08, 2006
Sunday, November 05, 2006
Bit of a problem here, actually.
You'd think I would have known all along what I had in mind for the number one all-time bestist ever Scottish mathematics textbook, wouldn't you?
I mean, let's face it, leaving it 'til the end and hoping for inspiration - that would be pretty stupid, wouldn't it?
And, as I've said before, it has been a bit surprising to go for a wander down memory lane and find that so many textbooks let you down one way or another. Yes, even good old Blackie Chambers could get a bit weird on you every now and then.
So, maybe it's a copout, but I'll give you two options to choose from, in the hope that maybe one of them will feel a bit less like a let-down:
Option (a): there is no best ever textbook. How could there be? Isn't there always going to be a need for teacher input specific to the class in hand, which means that any textbook will only be of some use, to some pupils, some of the time? When will we learn that we need to focus more on what we need to teach in a lesson, instead of just turning to the next page of the textbook?
(Yes folks, this is the "educational high-ground" copout!)
Option (b): whilst not a textbook per se, any worksheet made with Banda fluid was always a huge hit with maths classes. Especially if they were fresh from the machine...
Accepting the award tonight on behalf of the Banda corporation is Malkie McAsbo, whose memories of maths at school are hazy to say the least, though he does remember colouring in some SMP booklets on "Rules and Formulas" in S2, which always baffled him on account of his grasp of plurals. Oan yersel', big man!
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.
Tuesday, October 31, 2006
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.
Sunday, October 29, 2006
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.
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...
Wednesday, October 25, 2006
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...
Sunday, October 22, 2006
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.
Friday, October 20, 2006
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.
Wednesday, October 18, 2006
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!
Tuesday, October 17, 2006
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.
Monday, October 16, 2006
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.
Friday, October 13, 2006
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.)
Tuesday, October 10, 2006
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!
Monday, October 02, 2006
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.
Wednesday, September 27, 2006
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".
Tuesday, September 26, 2006
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?
Monday, September 18, 2006
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.
Saturday, September 16, 2006
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.
Monday, September 11, 2006
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.
Friday, September 08, 2006
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...
Monday, September 04, 2006
Sunday, September 03, 2006
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?
Thursday, August 31, 2006
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.
Monday, August 28, 2006
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.
Sunday, August 27, 2006
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.
Thursday, August 24, 2006
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...
Wednesday, August 23, 2006
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?
Sunday, August 20, 2006
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.
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.
Wednesday, August 16, 2006
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.
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...
Sunday, August 13, 2006
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...)
Thursday, August 10, 2006
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...!)
Tuesday, August 08, 2006
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".
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.
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.
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.
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?
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.
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.
Sunday, August 06, 2006
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.
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?
Saturday, August 05, 2006
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?
Thursday, August 03, 2006
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.
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.]
Tuesday, August 01, 2006
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.
Monday, July 31, 2006
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...
Sunday, July 30, 2006
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!)
Saturday, July 29, 2006
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.
Friday, July 28, 2006
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.
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?