I came, I sang . . .
. . . conquering was in short supply, but two out of three is a passing grade. And Nadia and I had a very interesting conversation about being a student and being a teacher and about learning and . . . ahem . . . getting hung up on the wrong things. I’d been thinking a lot about this anyway since last Wednesday, and especially after various comments from friends and forum members about what makes a good student (or teacher). The thing I’ve been most lately hung up on is that, at the age of eleven months and a fortnight off my sixtieth birthday, I still need to hear that it’s okay NOT to be brilliant AND IT’S OK TO MAKE MISTAKES. I still need to hear this! I am not flouncing around out here to make you go ‘there there Robin’! I really DON’T KNOW these things!! Sweet nondenominational deities, as someone on the forum recently said, I don’t know this yet? Well, I can fall back on how stupid I am, but that’s boring and overdone. But what it does make me think about, and not in a kindly, tolerant and forgiving way, is what passes for an educational system in the parts of the first world I know anything about. Public money for music in school in the UK, for example, is pretty much nonexistent, except in a few small, local, determined areas where they’ve figured out ways of doing it for themselves. There are still fabulous top-end schools for fabulous top-end students . . . but what the hell about the rest of us? 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. There isn’t much I did pick up via The Way.* I suppose this is also striking me particularly hard at the moment because of all this physics and higher maths nonsense I am unwisely poking with a stick till it bites me.**
But at the same time . . . being dumb in maths and the hard sciences is sort of half-acceptable. It’s discouraging, but it doesn’t actually break my heart that I don’t know a cosine from an algorithm***. MUSIC MATTERS TO ME. I don’t mind being a prat about calculus†. But then I’m not paying a professional calculist to teach me to do it either, you know? I appreciate that most music teachers are teaching the hoi polloi, because most people who take music lessons are and will remain amateurs. But I’m still subconsciously convinced that I am Stepping out of Line by daring to take music lessons. This was a huge amount of my trouble with the piano, that monumental solo instrument; I’m fluffing the issue a bit with the singing, by having choir singing as my goal. It’s a shock to me, having fallen back into this antique rut of being a primary-school kid who can’t carry a tune, to read Bratsche saying: I completely agree with blondviolinist…the “I’m so good I don’t need to bother” attitude is the only reason I’ve ever considered firing a student. I enjoy teaching anyone who is interested in music and in making progress (from wherever they start to wherever we get them).
One of the things that came out of my conversation with Nadia today was that while she knew I had left under a cloud last week, she had assumed it was because I was dismayed at how much worse I sounded in a small crowded room††. Feh. Not at all; I’m used to the idea that I sound like crap—it’s part of why I think I’m Stepping out of Line by taking singing lessons—I was upset because I couldn’t do the simplest mechanical things—the homework things—like pronouncing the words or hitting the dranglefabbing notes. Nadia blinked at me. I know you put your time in, she said. I can hear that you’re working. Trust me to do my job, okay?
Erm.
* * *
* This is from quite a while back but I never got round to using it. And it’s still pertinent.
Aaron wrote:
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I was in that class not because they had twigged that I was really dumb, but because of a scheduling conflict caused by being new to that school system. But I was happy with the dumb kids. |
I am interested to hear that this worked out. I got off sequence by skipping the second half of Algebra II and taking Trigonometry in the spring semester in a class consisting largely of seniors that had failed it the first time. For me at least, this was a mistake. While quietly playing blindfold chess in the back of the room with another student in the same situation was entertaining it has left my trigonometry at a “re-derive it each time you need it” level of proficiency. Conceptually complete, but too slow for real use. I took the failure to be a consequence of the different viewpoint of the other students (combined with my, admitted, lack of application). Your experience suggests that the instructor’s contribution may have been what colluded with my failings to produce an unsatisfactory result.
HAHAHAHAHAHAHAHAHAHA. Pardon me while I mop my streaming eyes and rub my aching ribs. I realise that this thread has largely been about the detrimental effects of bad teaching, but there are still a few bottom lines here including that you are good at maths and I am not. I’m willing to indulge a little friendly discussion of the possible fact that the way in to my maths brains [sic] is via a different channel than the standard—even the good standard—teaching paradigm, and that had I had a succession of Penelope Windsor Curries from my first essays in counting on my fingers I might not now turn green and queasy at first sight of any equation and, as the physics and maths books mount up, not have to give myself bracing little lectures on the subject of new horizons to conquer and that this unseemly and uncharacteristic proliferation is not because I’ve been taken over by aliens from Alpha Centauri (who, if present, are probably not having a good time).
What is interesting about the class I was in however is that these were the screw-ups and the troublemakers—not the football hero dumbheads that had to be shoved through the educational machinery so they could go on being glossy and golden on the sports field to the greater regional glory of the school (yuck, just by the way), but the kids that were busy falling through the cracks in the system and would be either stocking grocery shelves or stealing cars in another year or two. It was also mostly boys. And they actually behaved for Mr X. I don’t know why. Nice guys usually finish last, and he was not a dominant personality or any kind of disciplinarian. But there was remarkably little misbehaviour in his class. And most of us learnt some geometry. I even got a few As.
So while I think your description missed an essential point, yes, the teacher is crucial. Which is where this conversation started. . . .
*Does being rude about calculus fail the Pollyanna requirement?
While this is footnoted from a part of your comment I have not quoted, I could not resist saying here: no. Be my guest. Please give examples.
** Niall has loaned me his favourite calculus text: Calculus Made Easy: Being A Very-Simplest Introduction To Those Beautiful Methods Of Reckoning Which Are Generally Called By The Terrifying Names Of The Differential Calculus And The Integral Calculus, by Silvanus P. Thompson. How can you possibly not want to invite this man over for a cup of tea? Since the second edition is 1914, this is probably not likely. Still. It begins with a proverb: ‘What one fool can do, another can.’ The Prologue continues: ‘. . . The fools who write the textbooks . . . seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself . . . and now beg to present to my fellow fools the parts that are not hard. . . .’ Hee hee hee hee hee hee. How far have I got? Well . . . One of the drawbacks to stuffing yourself with a large quantity of brand-new and strange information is the way it all falls back out again, like a front-loading washing machine if you don’t slam the door fast enough. And even if you do manage to get the door closed, the different bits inside get all muddled up together till you have no idea what any of it is.^ I was reading the chapter in CALCULUS about being able to ignore things that are small enough not to have a gnarly effect on your calculations, and thinking two things: one: this is one of the reasons chaos took a while to catch on. Because mathematicians and physics guys were used to making tidy calculations where they could ignore the little stuff as either unimportant or static. Sensitive dependence on initial conditions was very unpopular^^. So you have to watch out about ignoring the little stuff. That’s in the Gleick. The second thing I was thinking about is from the Hawking: that while Newton’s laws were badly screwed by Einstein, a lot of them still work well enough most of the time—and therefore people still use them. Ignoring the little stuff. Ouch. That’s my brain exploding. ^^^
^ All Wet Laundry is the Same Thing.
^^ This, however, posted by Maren in response to my reference to the time-space-gluon-sensitive-dependence-on-initial-conditions continuum made me laugh and laugh.
AKA a big ball of wibbly-wobbly timey-wimey…stuff.
^^^ In common with all the people whose brains exploded after trying to follow Aaron through the mazes of Klein thingummies:
It is actually easy to make a Klein Purse. You take two handkerchiefs and sew them together making a two by one rectangle. You give it a half twist and sew the short ends together to make a Mobius strip. Since we started with two handkerchiefs with four edges each and used up two edges in the first sewing and two edges in the second sewing the Mobius strip has a single edge four edges long. Pinch the edge together at any point and start sewing it closed. A single seam two edges long should do the trick. The Mobius strip only had one side and we didn’t cut or interrupt anything so the result also has only one side but it has no edges since we used them up with last seam. A sphere has no edges but it has two sides, an inside and an outside. How is this possible? Obviously there is something wrong with the instructions but what?
I actually do know about Klein bottles—I had a brief flirtation with topology+ many years ago, before I realised that it counted as maths and was therefore off limits—and long for a Klein bagel of my very own. But it’s the videos of Klein bottles that really do me in. There are a lot of them out there. I don’t have a favourite, they all make me go ‘ow’.
+ Which Gleick describes as ‘geometry on rubber sheets’
*** Which furthermore I keep wanting to spell ‘algorhythm’.
† And if I ever get to the point of successfully working one of the problems YOU GUYS WILL HEAR ABOUT IT. So maybe you’d better hope that I don’t.
†† It’s quite a good room to teach in, she said, because anyone then trying to sing in a proper hall with proper acoustics will blossom.
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