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...
Monday, July 31, 2006
Sunday, July 30, 2006
What's minus five times minus two?
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!)
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
First, choose your pen
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.
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
Maths in the movies
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?
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
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.
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
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.
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.
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