Maths, Chaos, Darkness and Handbells

 

Susan in Melbourne posted this a few days ago:  http://www.theage.com.au/national/truth-finds-infinite-expression-in-words-and-numbers-20111209-1onmy.html

The novelist Geraldine Brooks* is attending a lecture on 'Singularities in Algebraic Plane Curves' and, perfectly reasonably I think, expecting the worst.  'I slumped into the room, armed with a doodle pad. My plan was to sit politely and let the talk sail over my head . . . perhaps, if I positioned myself wisely, a discreet little nap might be possible.'  But she began listening:  'This is like poetry, I thought, and I leaned forward to hear more. And when I set aside my firm belief that I could not comprehend her, something strange happened. It wasn't that I understood her work, but I understood her vision.'  It is a different world, but:  'I am sure though that our work, the mathematician's and mine, is essentially the same. In her exploration of the singularity in every plane curve, she seeks a way to more perfectly describe that arcing branch, or a soaring bridge, the squiggle in the iron lace of a terrace house, the quivering S-bend of a squirrel's upraised tail. She pushes her way deeper and deeper into the full truth of the world. This, also, is what I must do.'

             As it happens I've only just read this, after coming home from spending two hours helping teach a mathematician to ring the 3-4 to bob minor.  She's an excellent tower ringer but she's sweating handbells.**  She can mostly ring the trebles and slightly less mostly ring the 5-6, but the 3-4 are a ratbag.  Well, the 3-4 are a ratbag;  there are bits of the pattern you meet for the first time ringing a plain course on the 3-4, bits that if you're lucky you'll never see again anywhere else.  During the tea break the three of us were discussing ringing, learning***, and views of the one from the other.  And since this is a sample of three, it's obviously useless for statistical purposes, but Caitlin rings from an almost entirely different perspective, using different techniques and relying on different cues, than I do.  She also loves maths and the hard sciences and hated English in school.  Niall's approach to ringing is somewhere between the two of us—and while he's an engineer and thinks calculus is no big deal†, he liked writing English essays and I know he still reads novels because I see him doing it.  And I thought this was kind of interesting.  I would have expected two of Niall's handbell protégés to be picking it up recognisably and similarly based on the way he teaches it.††  Caitlin and I speak different languages about the same world.†††

            But we speak enough of some same language to talk about the weather and the excellence of the chocolate cake Penelope had left for us—and to find out that we ring bells differently, even if when we're ringing we are perforce 'speaking' the same language.  Meanwhile in another part of the forest, one of the things that yanks my chain about all this out-there physics and maths I'm (still) reading about is how similar the frelling creative process is, whatever name the drooling monster you're trying to subjugate is refusing to answer to.  These physics and maths bozos do things like go for long walks‡ and think and mutter to themselves . . . and are considered odd and anti-social by their friends and colleagues.  Of course I know the stereotype of the mad scientist like I know the stereotype of the in-her-own-little-world storyteller . . . but I hadn't realised we're very nearly the same person.

 * * *

* http://en.wikipedia.org/wiki/Geraldine_Brooks_(writer) 

** Mwa ha ha ha ha ha.  Okay, I'm a bad person, but I sweat handbells. 

*** Ajlr wrote

With this—and I think this is the barbed-wire enclosure that did me the most harm, and it doesn't seem to me it's changed that much in the last half century—goes the There Is One Way to Learn mandate, the one way being the way the Teacher teaches the Textbook, and if a student doesn't pick it up that way, well, too bad for the student, that is The Way.

I'm not saying it's perfect these days, there's still a way to go, but there is a lot (and I mean A Lot) of attention paid these days to what is called Differentiation. There're resources (this is just one site, there are an enormous number out there), it's part of Initial Teacher Training, and an ongoing focus of Continuing Professional Development schemes. Schools, colleges, adult ed, work-based learning providers, they all pay attention to it and it's checked by Ofsted. OK, maybe some teachers still don't 'get it' but they are appreciably fewer in number than they used to be. 

Well . . . unfortunately I think you're suffering from Making a Difference Syndrome.  The problem with being on the cutting edge of Making a Difference is that you can see the difference being made . . . in your vicinity.  It is human nature to see what's up close more clearly and in more detail than what's at a distance.  I can give you a really embarrassing example from my own life.  The obesity epidemic that so much journalistic ink and pixels have been spilt on includes not only humans but increasingly [. . . sic] our domestic fauna.^   Overweight pets happened to be topic of the week a few months ago and I read a whole raft of articles about it and I thought (my brow suitably furrowed), it can't be that bad, I rarely see a fat dog when we're out hurtling.  It took me several days for the penny to drop—DUUUUUUH, that's because the dogs I mostly see are the ones that are getting regular walks.^^  And, I guess, people clued in enough about their critters to give them proper exercise are probably also more likely not to overfeed (or overtreat) them.^^^

            The teachers I know bear with Ofsted first because they have to and second because it's better than nothing.  CPD, eh, it's only as good as the individual modules.#  A friend who is an excellent and inspirational teacher took early retirement a few months ago because she couldn't bear the paperwork caused by well-meaning but crippling initiatives to regulate teachers for their students' benefit.  She is not alone—as I'm sure you know.  But I'm questioning where the points on this continuum cluster.

            I'm willing to believe that what's wrong is different than it used to be—and I've no doubt there are resources out there that weren't available when you and I were still on the wrong side of the desk##, due to the efforts of people like you and your team.  That the teachers who still don't get it 'are appreciably fewer in number than they used to be'. . . unh.  I wonder.  I still know bright—or off the wall, or both—kids who dislike school and are failing to learn what they are absolutely capable of learning, because of bad or blinkered teaching.###  

^ And if your plant life is producing a jungle of foliage and no flowers, you may be overfeeding it. 

^^ And I think the reason the penny eventually did drop is because I'm aware of dogs that I'll see regularly for a while . . . and then never again.  Some of them no doubt moved away or their humans' schedules changed and they're taken out at different times or different places.  But some of them, I'm grimly sure, are sitting at home, because their owners forgot that a Dog Is for Life, and Not Just for Christmas. 

^^^ Supposing of course they have dogs that eat. 

# I think of all the homeopathy seminars I've taken that gave me CPD credits, if I'd been trying to stay registered.  The credits received have no relation to the quality or usefulness of the teaching or the information. 

## I mean aside from the fact that you and I grew up in the typewriter age. 

### There's also the Elizabeth Blackwell Syndrome, or, If She Can Do It, Why Can't You?   If Elizabeth Blackwell could get through medical school, then why can't you?  If Marie Curie could win a Nobel Prize (twice), then why can't you?  When I was a young oppressed science-illiterate struggling-feminist girl, these questions bothered me a lot. 

† Gleeeeeep  

†† Another thing I'm conveniently leaving out so I can make my point is that Caitlin is not merely an excellent tower ringer but another of these super-advanced models.  She can ring anything.  So she already has very well established ways she's used to ringing and learning ringing—which are not always as useful as you'd expect learning handbells for the first time.  But . . . Colin is another tediously excellent tower ringer, and did heavy computer things before he retired.  Another maths person.  And he rings a lot more like Caitlin than either Niall or me. 

††† And her eight-year-old, advanced-maths-placement son was sent home with some maths problems this week, one of which she couldn't do.   You have a series of squares, one each of which has sides [insert measurement system of choice, I think it was centimetres] of the following lengths: 1, 4, 7, 8, 9, 10, 14, 15, 18.  You want to make a rectangle of these squares—and it has to be a proper rectangle, no leftover bits and no overlaps.  What size is it?  What is/are the equation or equations for this?

            She and her son ended up cutting little bits of paper into squares and shoving them around till they made a rectangle.   And they did make a rectangle, but even working backwards she wasn't seeing how to solve it as a problem. 

            As a mathsless English major and writer of fantasy novels where lately she seems to be finding herself anthropomorphising chaos^ I still don't see why you don't add something up and then divide it by something else—I know areas are different from straight lines, but even so.  Anyone out there feel like explaining it to a level I might attain? 

^ I wonder where that idea is coming from.+ 

+ ::Gentle snoring from hellhound bed:: 

‡ I have yet to see any mention of hellhounds however.  This must be an error.