I'unno... my take on things. Little poorly thought out, bit rambling, bit long, just woke up, etc., etc., etc. Wall of goddamn text warning, yo'.
You're in a room with about thirty small children, often more, each with different ways of learning and bringing different levels of understanding with them, different degrees of inclination towards the subject and school in general, different levels of baggage coming from outside of the class (some are probably tired, or ill fed, or under a great deal of stress, etc.)... some of them probably have different levels of fluency in english(/the area's native language... I'll default to english here, but that's more accurate).
You've been tasked with translating concepts into English from a language most of them probably don't speak and many have no interest in speaking, in such a way that they'll be able to identify and correctly respond to sentences using those concepts at a fairly rapidly approaching point in the future -- you've got an average of 180 days here in the states, at probably an hour a day of direct instruction at most (if it were rotating personal instruction, you'd be looking at two goddamn minutes per child per day.). So you've got 180 (bit more than a week, total.) hours broken up into 180 sessions (this in particular is a problem because you're going to lose a few minutes at the least each session getting folks ready to go, and possibly bring them back up to speed if it's been a while since the last session) to teach 30 small children (eyeball that as about a grand total of six hours per child, if you were trying to teach them individually) how to at least
look like they're somewhat fluent in another language (which they've had little to no exposure to before, and probably won't use substantially any time soon unless they're specifically going out of their way to use it. A bit like trying to learn french in an english speaking country by occasionally speaking part of your sentences in french. People are probably going to look at you funny.).
If you don't manage to do this, or if enough of the children don't manage to at least fake it, you're out of a job. Now, nonexistent gods be willing, you're there primarily to teach and not primarily to feed yourself, but this is an added issue for you. You've got a time frame and a hard limit on how things have to end up, and if you bugger up there's probably not going to be a redo or chance to fix the mistake.
So, time investment. You're dealing with a rather incredibly small amount of time: LB mentioned taking two hours of one-on-one instruction with a fairly capable individual to teach something fairly basic, presumably in a pretty decent situation -- outside of a classroom and away from 29 other kids and uncomfortable chairs -- and with a kid that was probably in a pretty alright state in relation to other things (food sleep, stress, etc. -- and apologizes if I overestimate the situation, LB). You've got about six per kid -- less, really, and shattered into a crapload of smaller pieces -- to teach fairly basic concepts (and, let's be honest, nothing before college and maybe late high school gets into anything really complicated) to children who all probably aren't that capable (some are, some aren't), are in a pretty poor situation (uncomfortable chairs, 29 other wriggly distractions, etc.), and at least some of whom are hungry, tired, or badly stressed.
At this point, it's kind of a good goddamn luck thing. You've got some problems. You've also got some solutions. Some are bad, some are good. Some have been working, if not well, and is essentially the "party line". You can try to teach these kids enough fluency in this other language so they can do the translation work themselves or just speak the language -- this is basically the ideal. This is what you want, and you've got about six hours to do it. You're damned good. Are you
that good? You willing to risk it? If it turns out you're not that good, you're out of a job and these kids are possible held back a year, which can pretty royally fuck them up. Hell of a risk, you're gambling on a lot, and if you're wrong it's not just you that pays.
There's another option. It's faster, it's probably more likely to work (or at least
look like it's working) given the situation you're in, since it's by and large a lot easier from a functional standpoint to deal with for the kids. It's less ideal. You can pull out the phrase book and have them memorize phrases. Lot of (fairly shitty) rapid language courses have done this in the past, and if you're not going to be interacting with the language for very long (which, in the short term and for many the long term, they're either not or going to be able to get by without it) it's fairly workable. Worst of worst things, this is basically the party line, and you've got good odds whoever these kids go to next (assuming it's not you again -- if it is, you might be more willing to mix things up and try to get a little fluency in there!) is going to be doing that, so if you teach them via a different method there's probably going to be some compatibility issues and then interoffice politics 'cause the buck-passed person is complaining to the boss and yadda yadda yadda. And this way... hell, you can mix it up. You can do what you can to teach fluency here and there and hope whoever takes over is doing the same thing.
So... what do you do? And, perhaps more importantly, how much blame are you willing to apportion to people that choose the latter?
It is kind of a tragedy how badly the states, at least, teach the only other language most of their schools teach. Being bilingual in mathematics is pretty damn helpful, after all, even if you're only limitedly fluent (such as folks like myself -- but I was damn lucky and gifted classes did fairly advanced math, which meant much more personalized instruction in a much better situation for the first three or so years of grade school. I basically stopped learning math in fourth grade, and passed highschool on that.). But there's only so much I'm personally willing to harsh on the teachers in this situation. Many of them are choosing the less ideal path, but they've got a
really shitty situation and many are coming into it with very limited training or, as LB and others have noted, limited fluency themselves. The ones that manage more are basically bloody saints, and I can't really fault others for not being a saint, heh.
Solutions would be a pretty interesting topic. I'd personally wager if we divorced our mathematics system away from standardized testing a bit we might be able to hack together a more functional language course spread over several years, as many language courses are, and actually teach math with a goal of
fluency instead of a goal of test passing. There's other things you could do as well -- just reducing the number of sessions while keeping the time about the same would likely work some degree of wonder, providing the distance between the sessions were managed well. Better access to personalized instruction, smaller classrooms, better equipped teachers... there's a lot that could probably be done.
On a side note, the most annoying thing to me in math classes are people who raise their hands to disrupt class with a question of
'yeah, but when are we actually going to use this? (implying this is stupid and there is no reason to learn it)' <_>
It's not very different from someone being taught how to speak esperanto or something. When you never see the language spoken around you, you want to know why you're learning it. It doesn't necessarily imply that there's
no reason to learn it, or that it's stupid, but rather it asks "Why should
I learn this? When am I going to speak this language?" If that question can't be answered, why in the blue hell are you learning the language? Some folks are interested in that sort of superfluous (to them, and to a degree in truth) learning, but many aren't, and you unfortunately can't separate them very easily in a classroom setting.
My mother's actually pretty decent at most basic mathematics nowadays -- she teaches them, after all, and fairly well (the situation she teaches them is a metric fuckton better than most public school classes) -- but one of the things that kept her from basic fluency (as opposed to rote memorization) until her thirties was because no one would answer that damn question for her when she was younger and so instead of being motivated to learn, she was constantly being assailed by the question "Why the fuck am I doing this?"
Some folks probably are asking the question implying that it's stupid and there's no reason to learn it, but... if that's what they're asking, shouldn't there be an answer for them? If it's
not stupid and there
is a reason to learn it? There were some things we learned in high school that the teacher literally said we would never use again -- and so did college teachers when they ran into the same thing there. It was on the test, but completely useless even to higher mathematics (which had other tools they used for that sort of situation) or practical use beyond that.
Author
Topic: "People Who Understand Math" and "How Math is Taught" (Read 8516 times)