Number two unveiled

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...

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...

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

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...

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

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...

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...

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...

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

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?

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

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.