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If We Taught English the Way We Teach Mathematics...

By Coryoth in Op-Ed
Tue Apr 03, 2007 at 06:58:42 PM EST
Tags: education, teching, mathematics, english, science (all tags)

Imagine that your only contact with "English" as a subject was through classes in school. Suppose that those classes, from elementary school right through to high school, amounted to nothing more than reading dictionaries, getting drilled in spelling and formal grammatical construction, and memorizing vast vocabulary lists -- you never read a novel, nor a poem; never had contact with anything beyond the pedantic complexity of English spelling and formal grammar, and precise definitions for an endless array of words. You would probably hate the subject.

You might come to wonder what the point of learning English was. In response perhaps the teachers and education system might decide that, to help make English relevant to students, they need to introduce more "Applied English". This means teaching English students with examples from "real life" (for varying degrees of "real") where English skills are important, like how to read a contract and locate the superfluous comma. Maybe (in an effort by the teachers to be "trendy") you'll get lessons on formal diary composition so you can better update your MySpace page. All of that, of course, will be taught using a formulaic cookbook approach based on templates, with no effort to consider underlying principles or the larger picture. Locating the superfluous comma will be a matter of systematically identifying subjects, objects, and verbs and grouping them into clauses until the extra comma has been caught. Your diary will be constructed from a formal template that leaves a few blanks for you to fill in. Perhaps you might also get a few tasks that are just the same old drills, just with a few mentions of "real world" things to make them "Applied": "Here is an advertisement for carpets. How many adjectives does it contain?".

In such a world it wouldn't be hard to imagine lots of people developing "English anxiety", and most people having a general underlying dislike for the subject. Many people would simply avoid reading books because of the bad associations with English class in school. With so few people taking a real interest in the subject, teachers who were truly passionate about English would become few and far between. The result, naturally, would be teachers who had little real interest in the subject simply following the drilling procedures outlined in the textbooks they were provided; the cycle would repeat again, with students even worse off this time.

And yet this is very much how mathematics tends to be taught in our schools today. There is a great focus on the minutiae of the subject, and almost no effort to help students grasp the bigger picture of why the subject might be interesting, and what it can say about us, and about the world. Mathematics has become hopelessly detail oriented. There is more to mathematics than mindlessly learning formulas and recipes for solving problems. And just like our imaginary example, the response to students lack of interest in mathematics has only served to make the problem worse. The "applications" and examples of using the mathematics in the "real world" are hopelessly contrived at best, and completely artificial at worst, and still keep a laser like focus on formulas and memorizing methods without ever understanding why they work.

Of course the opposite situation, with no focus on details, can be just as bad. Indeed, that is where English instruction finds itself today, with students never learning the spelling, formal grammar, and vocabulary needed to decently express the grand big picture ideas they are encouraged to explore. What is needed is a middle ground. Certainly being fluent in the basic skills of mathematics is necessary, just as having a solid grounding in spelling and grammar is necessary. What is lacking in mathematics instruction is any discussion of what mathematics is, and why mathematics works as well as it does.

The discovery and development of mathematics is one of the great achievements of mankind -- it provides the foundation upon which almost of all modern science and technology rests. This is because mathematics, as the art of abstraction, provides us the with ability to make simple statements that have incredibly broad application. For example, the reason that numbers and arithmetic are so unreasonably effective is that they describe a single simple property that every possible collection possesses, and a set of rules that are unchanged regardless of the specific nature of the collections involved. No matter what collection you consider, abstract or concrete, it has a number that describes its size; no matter what type of objects your collections are made up of, the results of arithmetic operations will always describe the resulting collection accurately. Thus the simple statement that 2 + 3 = 5 is a statement that describes the behaviour of every possible collection of 2 objects, and every possible collection of 3 objects. Algebra can be viewed the same way, except that instead of abstracting over collections we are abstracting over numbers: elementary algebra is the combination of objects that represent any possible number (as numbers represent any possible collection with the given quantity), and the set of arithmetic rules for which all numbers behave identically. Numbers let us speak about all possible collections, and algebra lets us speak about all possible numbers. Each layer of abstraction allows us to use an ever broader brush with which to paint our vision of the world.

If you climb up those layers of abstraction you can use that broad brush to paint beautiful pictures -- the vast scope of the language that mathematics gives you allows simple statements to draw together and connect the unruly diversity of the world. A good mathematical theorem can be like a succinct poem; but only if the reader has the context to see the rich connections that the theorem lays bare. Without the opportunity to step back and see the forest for the trees, to see the broad landscape that the abstract nature of mathematics allows us to address, it is rare for people to see the elegance of mathematical statements. By failing to address how mathematics works, how it speaks broadly about the world, and what it means, we hobble children's ability to appreciate mathematics -- how can they appreciate something when they never learn what it is? The formulas and manipulations children learn, while a necessary part of mathematics, are ultimately just the mechanics of the subject; equally important is why those mechanics are valuable, not just in terms of what they can do, but in terms of why they can do so much.

So why is it that this broader view is so rarely taught? There are, of course, many reasons, and it is not worth trying to discuss them all here. Instead I will point to one reason, for which clear remedies to exist, and immediate action could be taken. That reason is, simply, that far too many people who teach mathematics are unaware of the this broader view themselves. It is unfortunately the case that it is only at the upper levels of education, such as university, that any broader conception about mathematics becomes apparent. Since it is rare for people going into elementary school teaching to take any university level mathematics, the vast majority of elementary teachers -- the math teachers  for all our children in their early years -- have little real appreciation of mathematics. They teach the specific trees outlined in textbooks, with no real idea of forest. A simple but effective measure that could be taken is to provide stronger incentives and encouragement for prospective elementary school teachers to take extra math; whether it takes the form of courses, or math clubs,  doesn't matter, the aim is to get teachers more involved and better exposed to mathematics in general so that they can become familiar with the richer world beyond the specific formulas and algorithms. This exact approach was tried in Finland as part of their LUMA project starting in 1992. As a result the number of teachers graduating with higher level had increased dramatically by 1999. And the results are also clear: Finland finished first, showing continued improvement in mathematics and science, in the 2003 PISA survey of the reading, math, and science skills of 15-year-olds in OECD countries (Finland finished second, just behind Hong Kong, in the mathematics section). Finland has continued to do extremely well in other more recent (though less major) studies.

Whether you view mathematics as an important subject or not, it is hard to deny that, currently, it is being taught poorly in many countries around the world. With such scope for improvement, and clear examples such as Finland showing the way, isn't it time that we took at least some of the obvious steps toward improving the quality of mathematics education?


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o the art of abstraction
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If We Taught English the Way We Teach Mathematics... | 132 comments (117 topical, 15 editorial, 1 hidden)
The analogy is very real (2.25 / 4) (#5)
by boxed on Mon Apr 02, 2007 at 08:07:02 AM EST

It is interesting to note that the analogy you draw with learning English purely through dry theory is a reality for many people. I have myself witnessed people in classes parallel to mine going through this and after 10 years of studying the language still being extremely uncomfortable with even the most basic sentences. All because of horrible teachers. It also seems to be common in second language education in the US, which you notice in the abysmal French you sometimes hear in American movies and TV.

Second languages (none / 1) (#7)
by Coryoth on Mon Apr 02, 2007 at 10:18:00 AM EST

It is very true that many second languages are taught this way, and indeed, it can be rather dispiriting for those having to learn it that way.

[ Parent ]
This is how I "learned" french (3.00 / 3) (#19)
by kromagg on Mon Apr 02, 2007 at 03:38:10 PM EST

It really sucks.

[ Parent ]
That's your problem (1.00 / 3) (#60)
by Nimey on Tue Apr 03, 2007 at 11:57:37 PM EST

With French, you're not supposed to suck too hard except maybe in the throes of passion. Try sticking to just a bit of gentle fencing and nibbling.
Never mind, it was just the dog cumming -- jandev
You Sir, are an Ignorant Motherfucker. -- Crawford
I am arguably too manic to do that. -- Crawford
I already fuck my mother -- trane
Nimey is right -- Blastard
i am in complete agreement with Nimey -- i am a pretty big deal

[ Parent ]
well you have to want to do something with the (2.50 / 2) (#24)
by trane on Mon Apr 02, 2007 at 09:09:03 PM EST

language, read a book, talk to people, etc. The classroom can only give you some tools.

[ Parent ]
My thoughts (none / 1) (#59)
by ErikOsterholm on Tue Apr 03, 2007 at 10:48:40 PM EST

The biggest difference is in the "big picture" so spouted over and over.  In one's first language, one already knows what the big picture is.  To express the big picture in a second language, one must simply translate the information.  It is possible to learn a second language through immersion, but even then, one must have an idea of what one wants to say and how to say it.  

With immersion, you still know what an apple is, even if you don't know the word for it.  But when learning a first language, because you are learning about the world at the same time that you are learning about how to express it.

Mathematics is like neither a first nor a second language, and as such, it is difficult to create an analogy for it.  With mathematics, we know a little bit about how to express terms.  We know that the area below the curve can be found with the definite integral of the formula which expresses that curve.  But what the hell does that mean?  And how many real world examples can we provide that make use of that?  Not just trivial examples, but real uses for the techniques?  Integration is most useful when dealing with higher-order mathematics.  For students taking a calculus class, the real, useful examples of integration are hard to come by.

And I think that is where the argument breaks down.  As we grow up, we learn about the world around us out of necessity.  In order to communicate with people, we must learn how to express ourselves.  There is no such necessity with mathematics aside from arithmetic.

[ Parent ]

i'm going to go out on a limb here (2.16 / 6) (#9)
by circletimessquare on Mon Apr 02, 2007 at 10:24:12 AM EST

and say, we should probably teach less math. it's important in life to have a good vocabulary and be able to communicate your ideas well. the quadratic equation? not much use, i'm afraid

instead, they should be teaching kids the basics of credit cards and simple household finance. we're teaching them sine and cosine, but they don't know how much minimum payments is really costing them in the longterm

i'm sorry, but a lot of mathemetics is very esoteric to the real life problems and daily challenges of your average joe blow

of course mathematics is important, in every respect you say, to the advancement of mankind. well, so is the the chemical composition of steel, or the decay pathways of uranium 235, or the implications of the turing machine, or the importance of the homeobox gene family. does the average joe blow need to know these things? not so much

just because some science is massively important to mankind or history or civilization, doesn't mean everyone needs to understand. of course, the more that do the better. but those that do, usually seek it out on their own curiousity. forcing someone to try to understand something they aren't interested in understanding or don't have the capacity to, just causes resentment and backfire

you need to develop some acceptance of the essential ignorance of mankind, of us all. there isplenty i am ignorant of, and always will be. there is plenty you are ignorant of, and always will be. same for everyone. get comfortable with this unfortunate but undeniable fact

and i'm sorry, 3 variable calculus just ins't that important to daily life problems that more people need to learn it

mathematics is esoteric to most people, and always will be, and it has nothing to do with education, but simple facts of life

The tigers of wrath are wiser than the horses of instruction.

I'm not arguing that (2.80 / 5) (#10)
by Coryoth on Mon Apr 02, 2007 at 10:34:56 AM EST

Interestingly I'm not even arguing that. All I' arguing is that, if you're going to teach mathematics, at least teach it well. If you want to remove math from high school cirricula, well, personally I think that's a little silly, but that doesn't counter the point that the math that people do get taught would benefit from being taught better than it is.

As to the importance of math compared to, say, the decay pathways of uranium 235: that's a matter of the incredibly general compared to the incredibly specific. Mathematics is a way to think and speak about the world that allows you to speak incredibly generally (and yet with great precision). A way of gaining knowledge is always going to be more important than specific knowledge like the decay pathways of U235.

A better comparison would be learning mathematics and learning the scientific method (both, ultimately are very important to mankind and underlie (as opposed to "contribute to") pretty much all of science and technology today. Sure, you can quibble over the details and mechanics within those subjects. Do we need to teach U235 decay to teach the scientific method? Do we need to teach the quadratic formula to teach math?

Ultimately your complaint speaks volumes about my point: math, as it is taught, is detail obsessed. People think it is all about quadratic formulas, and sines and cosines. Those are just the details and the mechanics, just like the chemical composition of steel, or the decay pathways of uranium 235 are details from science class -- they are interchangeable specifics that don't need to be taught (they can be swapped out for something else) to communicate the core value of the subject.

[ Parent ]

you're speakiing from (2.00 / 3) (#11)
by circletimessquare on Mon Apr 02, 2007 at 10:57:43 AM EST

a highly educated point of view

you're forgetting what you were yourself before you became so educated and were able to think in such generalities

no one looks at sines and cosines and tangents and grasps two variable calculus at work. immiediately. they have to learn the rote bullshit BEFORE their minds make the jump to the abstract higher thoughts

like this: it's one thing to appreciate higher level karate moves. but just knowing they exist, and their value, means nothing if you don't have the calloused hands and highly attuned muscles and quick nervous reflexes to put them to use. and to get that, you have to punch a piece of wood for 3 years until your hand is mass of muscle and callous and tendon and sinew and your nerves fire like a laser

in other words, there is no getting around the rote work. if you want to be a karate champion, you got to put in the work. if you want to be good at math, you have to solve ax^2+bx+c=0 until you want to vomit. you need to build the muscle that is your brain

so no, you are never going to have some magic math teaching system where kids are going to magically grasp and understand the importance and implications of the higher abstract principles of math and how it can enrich their entire understand of life. not ever going to happen

you're going to have to teach them the fucking quadratic equation, and apply it rotely to 100 different examples. you are going to have to drill them in their multiplication tables up to 20x20 for a month

sorry, but that's just the way it is

what made you and your higher abstract appreciation of math? rote work. it's just that, now that you've arrived at the promised land, you threw away the map. you've fogotten your own hard work and pain, and only see the beauty that remains. for anyone else to get where you are, they need to do the same rote work you did, that you've completely forgotten, and forgotten the importance of

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

Arguing around the point (2.75 / 4) (#12)
by Coryoth on Mon Apr 02, 2007 at 11:22:50 AM EST

As is so often the case CTS, you are busy arguing all around the point. In case you hadn't noticed I never said that we should ignore the necessary rote work. Indeed, to quote the article itself

Of course the opposite situation, with no focus on details, can be just as bad...Certainly being fluent in the basic skills of mathematics is necessary, just as having a solid grounding in spelling and grammar is necessary.

You are, of course, correct that you need some fluency in the skills to be able to appreciate what's going on. That, of course, is beside the point since no-one was ever arguing otherwise. The point is that we need to communicate some of the broader perspective in conjunction with the necessary rote work. Help give students a map so they know why they're toiling down this particular road.

To use your karate example: what we do now is akin to just having kids slam their fists into boards to develop callouses and not tell them anything else. The lucky few who manage to stick with it for 3 years (or with math, 10 years or more) finally get told "and now we'll let you in on the secret, having practiced that you'll now be able to break boards, and defedn yourself in a fight". All the other kids are left believing that karate class is all pointlessly hitting a wooden board becuse no-one ever bothered to tell them that it was practice toward the larger goal of learning self defense.

There's no getting around the rote work of mathematics, but that doesn't mean you can't help motivate that by telling students the bigger picture. You don't have to have all the skills down pat to at least understand the explanations. Sure no-one does sines and cosines and immediately grasps the connection to 2 variable calculus (I would be interested to know what exactly you had in mind here btw), but that doesn't mean the teacher can't sketch, in broad terms, those connections. If students are never told that such connetions exist (and often they aren't, even between groups of topics they are all familiar with) then how are they going to ever learn to look for them?

And what of me and my math education? I was lucky, in that I had parents who did have an appreciation for mathematics. They laid out the map for me while I was learning. I didn't always understand it all because I didn't always have the skills at the time, but at least I could see the big picture and had some idea of where it all was going. Now I have an even better idea of the big picture, and I'm working to try and help communicate that to others regardless of skill level.

[ Parent ]

well look (2.00 / 2) (#13)
by circletimessquare on Mon Apr 02, 2007 at 11:34:26 AM EST

this is your passion and i'm not going to shit all over it. if you want to be a math evangelist please, be a math evangelist. god knows you are only doing good in this world, so why the fuck would i oppose you? and so i don't

all i'm saying is that my agenda would differ from yours in that teaching kids more about the simple mathematics of economics, especially simple household finances like interest rates and such, is far more important than teaching them to appreciate magical concepts of enriching their lives in some mathematically spiritual way

in other words, i'd rather see a world populated by those who don't even know fourier analysis exists, but can pay off their damn credit cards

all i'm saying is that abstract love of knowledge for the sake of enriching your life is fine and dandy, but some real world immediate applications are more wanting

so i say, rote home economics courses for all high school kids is a more important agenda than your agenda, even though i appreciate your agenda for its passion

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

Here's the thing (1.75 / 4) (#21)
by kitten on Mon Apr 02, 2007 at 05:56:22 PM EST

. Sure no-one does sines and cosines and immediately grasps the connection to 2 variable calculus (I would be interested to know what exactly you had in mind here btw), but that doesn't mean the teacher can't sketch, in broad terms, those connections.

Okay, point taken, but here's the thing -- most people won't care either. When teaching English, it doesn't take much for someone to see that if they can speak and write effectively they'll be able to use that every day, in every interaction they have with another human, whether it's small talk, personal relationships, or professional endeavours.

Math isn't quite like that. You could try to explain to students that if they learn about sines and cosines, they'll get to understand calculus later, and won't that be great? But you then want to give them an idea of why it's important and what this can be used for later, so they don't think it's just pointless drills. And the bottom line is, most people won't care about calculating orbital trajectories or figuring out the variable snowfall volume in New Jersey.

CTS' initial point was that math is fairly useless for most people, and he was correct. It is of professional use to some, of personal interest to a few others (there's obviously quite an overlap there), but, beyond basic arithmetic and perhaps a scant handful of easily memorized geometry equations about area, largely useless to the rest of the population, most of whom don't want to know how parabolas are plotted or how Fourier series work, even if they understand that the boring algebra they learn today will let them know all that stuff tomorrow. They don't care.

mirrorshades radio - darkwave, synthpop, industrial, futurepop.
[ Parent ]
wow, a 3 for kitten... and also: (2.00 / 2) (#34)
by circletimessquare on Tue Apr 03, 2007 at 09:10:34 AM EST

she, or he, or it, forgot to mention: teach them a hell of a lot more financial math than we do now. that's actually useful for the living of their lives, and some of that financial math, that they can readily appreciate the importance of learning, might be the window into a love and/ or appreciation of mathematical beauty that the author of this piece is championing

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]
So your plan... (2.33 / 3) (#42)
by Coryoth on Tue Apr 03, 2007 at 10:58:42 AM EST

...is to drop math class, ad give them accounting classes instead? I'm not complaining -- if that's what you want, that's what you want, I just want to be clear.

[ Parent ]
not so much accounting (none / 1) (#44)
by circletimessquare on Tue Apr 03, 2007 at 12:06:53 PM EST

more like home economics, where they learn to bake cookies. call it home financials, where they learn to calculate interest rates, simple concepts of investing, appreciation, depreciation, etc.

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]
Should we (2.33 / 3) (#45)
by Coryoth on Tue Apr 03, 2007 at 12:13:12 PM EST

similarly drop any higher level English (after they've learned enough reading and writing to communicate the basics that'll be fine, only very few children go on to actually be writers when they grow up) and focus on classes on reading EULAs, and contracts?

Very few kids are going to grow up to do any job that needs any science either - I mean how many people in their daily lives actually need to know the structure of the atom, or the theory of evolution? They won't help you keep your home finances straight, or be useful in any job that the majority of people will end up doing. Perhaps we should have more focus on the chemistry of cooking and laundry?

[ Parent ]

i couldn't agree with you more (none / 1) (#47)
by circletimessquare on Tue Apr 03, 2007 at 12:20:36 PM EST

yes, 100%: we teach kids too much high minded clap trap they don't appreciate and never will use or reflect upon again, and probably foster some animosity in them towards the subject matter as some stuffy crap they don't know why they need to know

there are plenty of other skillsets they need on a daily basis that we neglect. yes: the chemistry of laundry and cooking, that you say in jest, sounds like a perfect example of what i mean. dead on, i support that 100%, that's a wonderful idea

and, counter to what you say, that this is a dumbing down of education, if we educate them on the deeper points of subject matter they deal with daily, i say you will in fact fire their mind and their naturally curiosity way more than say, making them learn about subject matter utterly disconnected from anything they will ever do or need to know, like calculating trajectories or the physics of pulley systems. i didn't know it was necessary to train kids for battleship maneuvers and industrial machinery from 1890

on the other hand, computers are something kids easily grasp, and boolean logic and the basic math of computer science is something you could aggressively introduce them to

it's all about giving them something related to subject matter they can easily relate to, will need to know in thier lives, and have every day contact with

fuck the rest

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

O wither democracy (none / 0) (#65)
by The return of Lemon Juice on Wed Apr 04, 2007 at 08:20:17 AM EST

when the average citizen is an idiot.

[ Parent ]
an idiot (none / 1) (#68)
by circletimessquare on Wed Apr 04, 2007 at 08:28:59 AM EST

is someone who knows three variable calculus, but can't balance their checkbook

an idiot is someone who reads 17th century french poetry, but not a newspaper

an idiot is someone who can recount the geopolitical maps of the early medieval period, but doesn't know their neighbors

what we traditionally consider to be smart people, eggheads, are often raging retards on issues your average joe blow is quite capable at... issues that actually matter in a democracy

intelligence has nothing to do with iq score, or sat score, or your gpa in college. intelligence has far more to do with simply communicating well with your society and being engaged, and caring about your community and its fate. it's all about the here and now

a smart person is someone who cares about their country and the nuts and bolts of running it: healthcare, tax reform, planning and zoning, etc., and gets involved, and speaks out, and goes to meetings, and is concerned, and votes

and none of that, in the least, in a healthy democracy, has to anything to do with learning the fucking quadratic equation

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

OKAY (none / 0) (#86)
by clydemaxwell on Thu Apr 05, 2007 at 01:33:02 PM EST

If you know three-variable calculus, I can't even imagine how you couldn't figure out a checkbook.

The rest of your points seem to be social advocacy talking points..that's fine, although it seems a bit off from the previous conversation.

let's imagine a politician has given you some data in numbers, as they do sometimes (it confuses the average checkbook balancer). Wouldn't you rather know how to verify his statements, rather than just deciding to trust? Or will you wait for someone to call him out, and THEN who do you trust?

I mean, if you're going to go for real-life arguments, that is.

[ Parent ]

I think the point is... (none / 1) (#123)
by localman on Sat Apr 21, 2007 at 04:17:44 AM EST

If you know three-variable calculus, I can't even imagine how you couldn't figure out a checkbook.

The kids aren't learning three-variable calculus.  So they're not leaning how to balance their checkbook either.  If we only have time to teach one, I'd go with the second.

But perhaps over the course of twelve years we can teach checkbooks and the stuff CTS is suggesting and still get to a fair amount of beautiful lovely math?  Right now we're failing on both.

[ Parent ]

I used to think (none / 0) (#116)
by Another on Sat Apr 14, 2007 at 10:21:26 PM EST

you were just a clever troll.

Now I see you've got it all figured out. It actually makes sense. Please make sure you're utterly selfless, then go on to reform the world. I mean whatever, do what you do. I'll do what I do.

And if it's me and not you who gets to make the choices, I'll still follow your lead. Don't lead me astray.

[ Parent ]

One need not be a writer (2.50 / 2) (#55)
by kitten on Tue Apr 03, 2007 at 08:57:28 PM EST

to experience an immediate and direct benefit from an eloquent command of English. Anyone can "communicate the basics", as you say, but people are taken more seriously in social and professional situations when they're well-spoken, articulate, and command an impressive vocabulary. It doesn't matter who you are, what walk of life you come from, what your career is -- anyone benefits from it.

You're going to be very hard-pressed to make such a claim about mathematics, I'm afraid.
mirrorshades radio - darkwave, synthpop, industrial, futurepop.
[ Parent ]
100% dead on nt (none / 0) (#64)
by circletimessquare on Wed Apr 04, 2007 at 08:07:19 AM EST

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]
You speak like a faggot (1.50 / 2) (#66)
by The return of Lemon Juice on Wed Apr 04, 2007 at 08:21:39 AM EST


[ Parent ]
better a faggot than a retard (none / 1) (#73)
by circletimessquare on Wed Apr 04, 2007 at 08:33:49 AM EST

(that's you, darling)


The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

The difference is language (none / 0) (#87)
by clydemaxwell on Thu Apr 05, 2007 at 01:34:48 PM EST

It is more difficult to make such a claim, even with a mastery of english.

You would need a mastery of mathematics.

[ Parent ]

Language, like math, is useless when unlearned (none / 0) (#91)
by darkonc on Thu Apr 05, 2007 at 09:24:50 PM EST

If you've ever spent time in a land where the language is foreign to you, then you'll realize that you can actually get away with a surprisingly small subset of full linguistic capability, but with language (as with math) a broader understanding and capability results in a much richer experience.

I was running for the Green Party (BC, Canada) some years ago. We were at a school, and the Liberal candidate trumpeted how his party was 'promising' to up the budget for education by a whopping 15% over the next 5 years.

I told the kids that the moral of that story was that they should pay attention in math class, and then explained that 15% over 5 years came in at a bit less than 3%/year (1.15^.2), which -- even before you took into account population growth, meant a net drop in education resources after inflation.

I think that the students got the hint -- and so did the liberal candidate. I don't remember him ever mentioning that so-called promise again.

The thing is that, like with math, you can actually get away with an incredibly small ammount of language ... but as you increase your mastery of it, you also get a more complete understanding of the world around you ... and it gets a little bit harder for people to do you a snow job.

I agree, however, with one of the other posters who pointed out that the most important aspects of math lie in the logic process. Logic helps both with the math and with other situations in life.

If, for example people understood the (very) simple statistics rather than the spectacularity of the incidents, they would probably realize that terrorism isn't the kind of threat to their lives and livelihoods that bush and his cronies would like them to believe it is. It would also be a lot harder to get people sucked into pyramid schemes and other silly things that depend on people not understanding the underlying mathematics.
Killing a person is hard. Killing a dream is murder. : : : ($3.75 hosting)
[ Parent ]

Then, it's not just math that's useless (3.00 / 2) (#104)
by darkonc on Mon Apr 09, 2007 at 12:49:13 PM EST

What good does it do -- really to know who was the 7th president of the US, or who the 3rd mayor of our city was, or Cesar or Churchill?

what good does it do in real life to know who Mozart was -- or how to read a musical scale, or where Mali is?

Do you really need to know how to do proper conjunctions in English?

How does being able to catch a football make you a better business analyst?

If you're going to go down that path, then what's the value of anything you learn in school then? We got along just fine for thousands of years with less than 10% of the population able to read and write.
Killing a person is hard. Killing a dream is murder. : : : ($3.75 hosting)
[ Parent ]

Well, yeah. (none / 1) (#126)
by vectro on Wed Apr 25, 2007 at 02:59:12 PM EST

I think what you're trying to say is that a lot of useless stuff is taught in school. Well, yeah, that's true, though that's not to say that there is nothing useful for schools to teach.

It doesn't do much good to memorize a list of the past politicians of any region. It does do good to learn the stories of Caesar or Churchill, because their circumstances can inform our choices moving forward. But memorizing a list of names is completely useless.

Knowing who Mozart was is not that important; understanding his music is, because much of his work continues to affect contemporary music today; most everyone enjoys music at some level, and musicology can enhance that enjoyment.

It doesn't help to know how to read a musical scale -- unless you want to practice or study music, that is. Maybe I am optimistic in thinking that a substantial cut of the populace will practice amateur music making at some point in their adult life?

It doesn't help to know where Mali is, unless that geography is needed to inform some other lesson.

Most people don't need to study the conjugation of verbs in English, but they do need to know how to speak well -- even if they can't articulate the rules.

Playing football doesn't make you a better business analyst (unless it gets you connections or university admission, but that's a whole different ballgame [so to speak]).

“The problem with that definition is just that it's bullshit.” -- localroger
[ Parent ]

Round and round the point... (3.00 / 3) (#26)
by Corwin06 on Mon Apr 02, 2007 at 10:55:34 PM EST

Just to point out that some kids just don't need to be drilled into 100 examples just to memorize some formula; moreover, that is just the right way to have them forget it in under two months.

The right way would be to explain ax^2+bx+c=0 in different ways, and explain how every way to demonstrate or visualize it really represents the formula, that would be far more productive.

Now, imagine that from that formula, the teacher would begin to explain something else, that somehow connects to the same ideas, they could show how math  is a closed system because it recursively explains itself.

We're talking about students old enough to read Phil K. Dick, right? So, they are intelligent enough to understand that.

I had an older friend help me revise math every year, just that way. For the same subjects, because I could never remember the stuff while I had to suffer the classes. But I always passed my math exams, with under 10 hours of classes to really learn what I was supposed to have understood in 150 hrs of courses.

Draw your own conclusions...
"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
mostly agreed except... (none / 1) (#33)
by circletimessquare on Tue Apr 03, 2007 at 09:06:50 AM EST

reading philip k dick does not in any way suggest a propensity for understanding math, or anything else for that matter. if i read "star wars" does that mean i have some sort of understanding of the physics of warp drives or construction of large spaceships?

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]
Abstraction (none / 1) (#43)
by Coryoth on Tue Apr 03, 2007 at 11:01:24 AM EST

I suspect he was getting at Dick's propeneity to have multi-layered realities, and to question the whole idea of reality, and how you know anything is "real". Reading that sort of thing, and the twisted maze of abstract thought it leads you through is some indication that you can understand abstract ideas.

[ Parent ]
what bullshit (2.00 / 2) (#46)
by circletimessquare on Tue Apr 03, 2007 at 12:13:40 PM EST

utterly and completely different mental skills involved

however, if you want to talk about a seemingly unrelated skillset that DOES feed into math, it's music. not so much listening to it, but learning to play a musical instrument. it has been proven to sharpen kid's math skills

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

Music and math (3.00 / 3) (#81)
by Corwin06 on Wed Apr 04, 2007 at 10:49:45 PM EST

If you have the slightest clue about musical notation, what follows should be clear (or become clear after you read it several times) :

(From Wikipedia)

"In a typical Meshuggah song, drummer Tomas Haake plays two separate rhythms: a standard 4/4 beat with his hands, and a completely different metrical subdivision with his feet. The guitar riffs drive the bass drums, creating an awkward but pulsating rhythmic pattern to work as the basis of the song.

To give an example, the main riff of the song "New Millennium Cyanide Christ" from their 1998 album Chaosphere follows the aforementioned blueprint. Haake beats a rather slow 4/4 rhythm with his hands, while the bass drums and guitars play a repetitive 23/16 rhythm pattern on top of it. As the subdivided pattern is repeated, the pattern's accents shift to different beats on each repetition.
After repeating the 23/16 pattern five times, a shorter 13/16 pattern is played once. These patterns sum up to 128 16th notes, which equals exactly 8 measures in 4/4 meter."

This is arithmetics. (23/16)*5+13/16=(4/4)*8.

If you double the frequency of a sound, either by shortening a string by half or playing the sound in half its length, it will go up one octave. Cut the length in half again, one more octave. (Any 24-fret guitar has thus 2 octaves on each string. Ever noticed that the 12th is at half the string's length and the 24th at one fourth?)
That ties into physics and trig. More math.

But it's quite far from college-level math, really. Music is not an intro to math. It may serve to illustrate things, or math can be used to explain things in music.

Understanding a novel which includes several layers of reality, and intricate paradoxes, can and will do much toward teaching abstract thought.

"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
bullshit (none / 1) (#109)
by cronian on Wed Apr 11, 2007 at 10:06:37 PM EST

When I was about a Freshman in High School, I got sick of all the rote nonsense, and I went and picked up a Calculus. About a day later, I understood most of the basic concepts of calculus. It wasn't that hard.

Maybe, it'd take others longer, but even so.

We perfect it; Congress kills it; They make it; We Import it; It must be anti-Americanism
[ Parent ]
Thank you (none / 1) (#111)
by Corwin06 on Fri Apr 13, 2007 at 08:51:47 AM EST

SO much.
"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
This is a fantastic point. (none / 1) (#58)
by nepenthes on Tue Apr 03, 2007 at 10:46:12 PM EST

And a fantastic article.

I agree with both the op and the reply that I'm replying to, in that:

A) I tend to agree that higher-level maths is functionally useless for the vast majority of 'average' workaday folks, and there is no point in them learning such things as the quadratic equation if they're not interested in them. I certainly wasn't as a student of elementary or even secondary school.

B) Regardless, mathematics is an insanely significant portion of society. And rather than teaching it from a purely formalistic perspective, we need to be teaching it from a holistic perspective, so that students are introduced to the philosophy of mathematics simultaneous with mathematics itself. Because even if we aren't interested in a field, we tend to know roughly what it does, and where it fits as a discipline within the general spectrum of human endeavour. Physics studies molecules, chemistry studies chemical interactions, biology organisms, etc. etc. In the human sciences, sociology studies social organization, anthropology humans, and so on. And yet people in general have absolutely no idea what the function or rationale behind mathematics actually is. It's just playing with numbers. This is therefore directly implicated in why people have such a lack of interest. And although it may seem from the perspective of a young student, or someone who has little familiarity with the subject, that complex mathematics have no relevance to 'real life,' this is not to say that it will never become of relevance. I couldn't have cared less about math, like I said, but now I wish I had, as I see the parallels between my own field (philosophy, social theory) and mathematics.


[ Parent ]

no, you can't teach math holistically (none / 0) (#72)
by circletimessquare on Wed Apr 04, 2007 at 08:32:05 AM EST

without the rote effort, there is no underpinning for the higher concepts, and they float from the mind, unappreciated and quickly forgotten

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]
I still insist (none / 1) (#82)
by Corwin06 on Wed Apr 04, 2007 at 10:58:58 PM EST

that the rote effort is wasteful, because it made me, and each other student, needlessly hate the stuff.

Oh, I love math, really, I do. It's fascinating! But the rote effort is useless, because if you use what you just learned, not to solve one hundred mindless problems, but to learn one more thing that makes direct use of it, you will cover much more subject matter, much faster and much more thoroughly (provided you explain every possible type of answer for each class of problems).

"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
ever watch the karate kid? (none / 1) (#83)
by circletimessquare on Thu Apr 05, 2007 at 12:11:05 AM EST

wax on wax off danielsan

without the rote, there is nothing greater to achieve

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

karate kid (none / 1) (#88)
by clydemaxwell on Thu Apr 05, 2007 at 01:40:05 PM EST

wax on, wax off: muscle memory
rote repetition: ??

If you learn to do math by rote, you don't learn to think about what you're doing; only 'which formula goes here'. Muscle memory of the brain, so to speak. Habit. Learning to think about it is the method to being able to grasp the higher levels that aren't  learnable by rote..

[ Parent ]

the brain is a muscle (none / 1) (#93)
by circletimessquare on Thu Apr 05, 2007 at 10:03:26 PM EST

and thoughts are emanations of a well-oiled machine. each thought, each firing of a synapse, is an expression of an effort held up by thousands of other well-exercised, or flabby, parts of your mind

thoughts are not feeble empty farts in a room of still air that ust jump into being fully formed

what you are calling free thought is enfeebled grappling in the dark

the guy who goes through the rote effort of the mindnumbing machinations of macroeconomics, for example, puts his mind in a place to make smart, observant, prescient ruminations on the economy

by your model, some asshole in a coffee shop who knows shit about economics is suddenly able to have the same thought, and appreciate its value the same way

in other words what you just said is ignorant bullshit

habit doesn't create originality, but habit puts the original mind in a place to make a truly important and useful thought, rather than random feeble mindfarts, underpinned by no context or value, completely useful to no one, and appreciated by no one, not least of which, the one who thought it

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

You don't get my point (none / 1) (#94)
by Corwin06 on Fri Apr 06, 2007 at 10:48:47 AM EST

My point is, instead of getting the brain to hard-wire itself to solve the problem by solving it one thousand times over, you can use its ability to understand abstract concepts by describing how they interact with each other, in a closed, recursively self-explaining system.

How hard is that to understand or implement?

"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
i get your point, and it is wrong (none / 1) (#103)
by circletimessquare on Mon Apr 09, 2007 at 01:58:26 AM EST

the mind is not in a position to understand anything, until it has grown an appreciation for why it should understand something

and it only does that through hard work

you can't get what you are seeking: deeper meaning, without digging through the surface layers with a pickaxe. You cannot simply will yourself or a child into a deeper understanding, they must WORK hard to get there

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

No need. (none / 1) (#112)
by Corwin06 on Fri Apr 13, 2007 at 09:16:11 AM EST

Why do you insist that you HAVE to bore the kids to death before they can hope to undertstand that they really didn't need to?

I'm all for teaching how math can be used in Real Life, but could that not be done JUST by doing away with all that useless rote crap, and using the other class hours for teaching the kids how to apply what they just learned?
Not by constraining the problems they already know, just replacing the variable names. That is a game of matching cards, not math. Better to give them numerous math tools, present them a complex real-life problem, and tell them "Solve this". They'll have to break it down, find the variables, apply formulas, finding their own way to the solution(s), maybe develop some that no one else had thought of. Then, don't rate it, just analyze how the kid thinks, and if there is something he's not understood, you can correct it by explaining how it really works, in a way he WILL understand; because you already know HOW he misunderstood it. THAT's how to teach math.

"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
Rote practice is (none / 0) (#131)
by zagloba on Thu Aug 09, 2007 at 02:56:38 AM EST

boring as fuck. But being able to do the algorithmic computation without having to think about it means that you can actually get to the interesting math! That is, the problems, the patterns, the way math is actually used to describe the world. "Math is a language" is a meaningless phrase until someone has actually used math to describe something.

|He is a fool who only looks for truth where he knows he can find it.|
[ Parent ]
Everything is esoteric to most people (3.00 / 2) (#22)
by debacle on Mon Apr 02, 2007 at 08:43:43 PM EST

Mathematics is a state of mind that puts people in the position to make better decisions. Most people don't learn multivariable calculus, so I don't get your point there, and problem solving (like choosing the best interest rate given the sitation) is the hardest part of mathematics for most people because it involves thinking on more than one level.

Ignorance and a lack of knowledge are two utterly different things.

It tastes sweet.
[ Parent ]

so what are you saying? (2.00 / 2) (#32)
by circletimessquare on Tue Apr 03, 2007 at 08:40:00 AM EST

how does calculus help joe blow?

i think he should learn household finance, investing, loan calculation, etc., and leave it at that

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

You think he can learn household finance (2.66 / 3) (#39)
by debacle on Tue Apr 03, 2007 at 10:26:55 AM EST

But not calculus?

There is a thing called theoretical learning and it aids people in every other aspect of gaining knowledge.

Household finance is a complex subject, and investing is even more complex. You're talking about people who can't handle more than one variable in an equation or understand basic matrix algebra.

It tastes sweet.
[ Parent ]

zzz (2.00 / 2) (#40)
by circletimessquare on Tue Apr 03, 2007 at 10:49:08 AM EST

#1: joe blow needs to appreciate why he should try to learn it. if he can't appreciate it's value to him directly, why should he try to learn it? i'm not asking you to answer this question with your philosophical bullshit about "theoretical learning"... shut the fuck up. how can JOE BLOW HIMSELF appreciate DIRECTLY and IMMEDIATELY why he should learn something

#2: calculating something like an interest rate and projecting how long it will take to pay it off is NOT fancy math. yes, there is fancier math in finance, but the point is, you don't have to go off the deep end to matrices to impart quick and easy educational value with financial math for joe blow

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]

In other words: (none / 1) (#30)
by shm on Tue Apr 03, 2007 at 07:19:39 AM EST

the right math, not less math.

Probably the right math at the right time, but definitely not less math.

[ Parent ]

household finance, investing nt (2.00 / 2) (#31)
by circletimessquare on Tue Apr 03, 2007 at 08:39:00 AM EST

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]
heh: shm's two line lesson enclosed. (2.50 / 2) (#38)
by shm on Tue Apr 03, 2007 at 10:05:19 AM EST

Those credit cards you have there?
Burn 'em.

[ Parent ]
best. math. lesson. evar. nt (none / 0) (#41)
by circletimessquare on Tue Apr 03, 2007 at 10:49:32 AM EST

The tigers of wrath are wiser than the horses of instruction.

[ Parent ]
So your math classes (none / 1) (#67)
by The return of Lemon Juice on Wed Apr 04, 2007 at 08:24:03 AM EST

would consist of children burning peices of plastic?  I don't want to live in your world, you are an idiot.

[ Parent ]
He might be an idiot (2.50 / 2) (#75)
by Cro Magnon on Wed Apr 04, 2007 at 11:04:59 AM EST

but in this case, he's right.
Information wants to be beer.
[ Parent ]
It was my math lesson. (none / 0) (#85)
by shm on Thu Apr 05, 2007 at 09:58:34 AM EST

And it was a figure of speech. I believe an article arguing about teaching English as if it was English is in order.

[ Parent ]
I disagree (3.00 / 2) (#57)
by The Rizz on Tue Apr 03, 2007 at 09:58:49 PM EST

Credit cards are excellent things if you pay them off every month. Most credit cards nowadays give 1%-5% cash back on various purchases. Almost everywhere takes credit cards nowadays. So, if you get a decent cash back card and never pay any interest on them (pay off entirely every month!), you will be gaining at least 1% extra back on all your purchases. Combine that with the fact that it's non-taxable (it's a rebate, not a paycheck), and the fact that you can have that money in an interest bearing account until you pay of the bill, and you end up getting a small, but significant, extra cash flow each year.

The primary steps to take to do this effectively:

  1. Shop around for cash back cards: Rewards cards (i.e. rewarding merchandise instead of $$) are almost never as good if you compare the points needed for items vs. what you'd be able to buy them for. Different cards give different % back for different things - you will probably end up with multiple cards in order to maximize your returns.
  2. KEEP TRACK OF HOW MUCH YOU CHARGE: This is the vital step, and the one most people don't do. If you can't do this, take the parent post's advice and get rid of your cards - they will do you more harm than good. Treat your cards like checks - carry a spare checking register around with you and keep track of every charge and balance. Alternatively, use Quicken, MS Money, or some other similar option that can give you daily reports on what you have spent.
  3. Always be able to pay off your cards: Grab a savings account with a good interest rate (online usually have better rates), and as you spend money on your cards transfer an equal amount into the savings account. At the end of the month you do a direct payment online from the savings account to pay off the bill. If you have trouble remembering to pay bills on time (like I do) talk to your credit card company; most cards have auto-pay options where they will automatically deduct the balance from your checking or savings account on the due date.

Doing the above steps gains me an average of $60 per month spread across 4 cards (1 general use, 3 because they give extra for specific types of purchases).

[ Parent ]
That's what I do as well. (none / 1) (#63)
by shm on Wed Apr 04, 2007 at 05:53:21 AM EST

But the Joe Blow audience that CTS wants to cater for probably can't figure out or track all of this for themselves.

[ Parent ]
Not everyone teaches them self this lesson (2.50 / 2) (#76)
by hatshepsut on Wed Apr 04, 2007 at 11:52:44 AM EST

but that doesn't mean they can't learn the lesson if it is pointed out.

The number of otherwise intelligent people who forget that credit cards represent a debt (unless they are payed off each month), who don't understand basic personal finance (what comes in and goes out each month, etc.) is staggering. But, just because so many don't understand these concepts doesn't mean they can't...some of them don't learn the lesson until they are buried so deep they may never get out.

I think CTS's concept of "basic" useful, every-day math isn't a bad one. Start that one early (kids who get a set allowance, for example, learn early that if they blow it all before their next allowance "paycheck", then they have to do without). The type of stuff CTS is talking about is stuff that can be started with grade schoolers. Then you can move on to more and more complicated ideas, including the article's interconnected concepts of the universality of mathematics by the time kids are teens.

I am a firm believer that knowledge for the sake of knowledge is a good thing (for the person, for society, etc.), but trying to teach something that no one learns (for example, 90% of the stuff that passes for high school math, which is forgotten by August 1st) isn't good or useful for anyone.

[ Parent ]

how ready and willing you are to (1.33 / 3) (#78)
by balsamic vinigga on Wed Apr 04, 2007 at 01:04:57 PM EST

spread your anus for big brother for chump change...

Any idea why credit/debit/cash cards encourage you to spend with them? Because there's a wealth of information for them to datamine and collect amng populations and you as an individual that's worth far more to them than the measly 1%.

hell, they can sell that information again and again for far more than they paid for it.

Please help fund a Filipino Horror Movie. It's been in limbo since 2007 due to lack of funding. Please donate today!
[ Parent ]

perhaps (none / 0) (#79)
by The Rizz on Wed Apr 04, 2007 at 08:15:06 PM EST

Maybe they are doing that. However, what does it really matter? So they know which grocery store I go to - big deal. They know how often I travel? Whatever. They know how much I buy over the internet? So what? If I really cared about that, I'd get a credit card that specifically says they aren't (there are ones that do).

Really, though, I have my doubts about just how much that data is worth; I get back $700+ per year. I seriously doubt that they're counting on data mining for any real effect on their bottom line (they have millions of customers - who exactly is supposed to by paying them several $billion for this information?), and in many cases, your card agreement excludes them from selling your data like that.

The real reason companies are giving you cash back is so you will use their card, rather than a competitor's. There are 2 main reasons for this:

  1. Credit cards make the bulk of their money not from selling information, but from merchant fees. Every time you buy something with a credit card, a % of that sale goes to the credit card company - that $700 cash back I get a year? Odds are they're making somewhere around $2000-3000 per year in merchant fees off me.
  2. Credit card companies' second main source of income is from people who carry a balance. Even at the "good" rates around 10% that's a lot more return on investment than you make on almost any other investment type. A large portion of the cards have rates in the 17-27% range - this turns into a massive amount of money very, very fast -- an increasing % rate leads to exponential growth rather than constant growth (check amortization tables for a good example of how this works).

[ Parent ]
Er, no. (none / 0) (#124)
by vectro on Wed Apr 25, 2007 at 02:46:17 PM EST

The reason card companies can afford to make these bonus payouts is that they get a steep commission from retailers of 2-5%. They can then pass some of that on to you, the consumer, and pocket the difference.

You can, in fact, direct them not to sell any of your purchase information (though infuriatingly, you must opt out), and you'll still get every bonus.

“The problem with that definition is just that it's bullshit.” -- localroger
[ Parent ]

More than that. (none / 1) (#125)
by vectro on Wed Apr 25, 2007 at 02:49:12 PM EST

Card companies routinely offer purchase or balance transfer offers at promotional rates substantially lower than prevailing interest rates. At the moment I have about $27,000 of outstanding credit card debt, at an average interest rate of about 1%. That money sits in bank accounts, safely earning 5% or more risk-free.

“The problem with that definition is just that it's bullshit.” -- localroger
[ Parent ]
Well rounded (none / 1) (#96)
by kreyg on Sat Apr 07, 2007 at 06:47:46 AM EST

the quadratic equation? not much use

Well, I don't know... in my work as a programmer developing games, I've used it more than once. On the other hand, the majority of stuff I learned about poetry, Shakespeare and the French Revolution has been of vastly less use. If I had become a writer or politician, I would fully expect that to be reversed.

I don't really resent having learned any of it though, and I can't ever imagine a complete consensus on what information is valuable and what is trivia. Specializing too early makes it much harder to switch fields or interests later, as you have no basis to build on. Understanding a wide variety of subjects helps us understand each other better.

There was a point to this story, but it has temporarily escaped the chronicler's mind. - Douglas Adams
[ Parent ]
Bravo! (none / 1) (#102)
by grahamsz on Mon Apr 09, 2007 at 01:21:13 AM EST

I have also used the quadratic equation. I've used matrix convolution, number theory, statistics, probability and more in my day to day work.

I routinely do financial calculations while make purcahsing/banking choices. I use geometry in home construction projects.

But i'm reaching the conclusion that other things from school are still useful, although by no means as much.

I recently ran into a situation where I was trying to solve a particular software issue for work and there was a discussion post about it in french. I was able to recall enough high school french that combined with an online dictionary I was able to solve the problem.

A cursory recollection of color wheels from a graphic design course 12 years ago helped me come up with an reasoned approach to finding 10 colors that looked as differently as possible.

Being able to articulate myself sucessfully has proved very helpful in my career (Though my drunken ramblings on k5 don't demonstrate this).

It's evident in the tech field that many choose to disregard the advantages of being well rounded, so should it be surprising that math is abandoned by those who choose other fields.
Sell your digital photos - I've made enough to buy a taco today
[ Parent ]

But Recurrence Relations are Useful. (none / 0) (#127)
by jbs36 on Sat May 12, 2007 at 07:05:44 PM EST

minimum payments is really costing them in the longterm

Actually, to know how much you should be paying as per-month to pay-off a debt in a fixed time period requires solving the following recurrence relation:

c(n) = c(n-1)*(1+(r/12)) - d

Where c(n) is the amount of debt after month n, r is the annual interest rate, d is the monthly payment.
Solving this,

c(n) = c(0)*(1+(r/12)^n - 12*(d*(1+(r/12)^n))/(r) + (12/d)

This expression tells account status at month n, where c(0) is the initial debt.

We want to know the payment that will exactly zero out the account with in n months. Solve the following expression for d:

0 = c(0)*(1+(r/12)^n - 12*(d*(1+(r/12))^n)/(r) + (12/d)

d = (1/12) * (c(0)*r*(1+(r/12))^n)/((1+r/12)^n)-1)

This is a closed form expression that tells you how much the monthly payment should be to pay-off the loan for c(0) Euros after n months with a fixed interest rate of r.

The only thing shameful, about this, is that I had to go to university to even think like this.

[ Parent ]
Well, y'know (2.37 / 8) (#20)
by kitten on Mon Apr 02, 2007 at 05:44:43 PM EST

In many ways that is how English is taught. We diagramed approximately forty thousand sentences throughout middle school, something for which even the most die-hard English majors have no use.

When reading a poem, we were rarely asked to discuss it, but instead subjected it to a series of rigorous analysis about meter and rhymescheme, and memorize some useless trivia about the poet's life, like when he died or when she married.

If we read a short story, we usually had to answer a few cursory, superficial questions about the story's content ("Why did John want revenge against Bob?" or "Which character did you most identify with? If not, why not?" Seriously.), and then analyze the story for examples of alliteration or allusion. Nary a word was spoken of how allusion can enhance a story, or why alliteration is useful even in stories not read aloud. Just circle the examples and shut up.

When writing an essay we were told to adhere to the standard five-paragraph, intro-body-conclusion model, and deviations were punished. Content and clever prose were rarely rewarded, or even noticed. Spelling, and to a lesser extent grammar, were the focus of the teacher's mighty red pen, but as long as everything was spelled correctly you could have written a treatise on elephant feces without comment.

When writing reports, ten times more emphasis was placed on arbitrary rules about proper MLA citation, whether or not our bibliography was organized the way the teacher or professor wanted it, or the layout of the title page, than was ever placed on the subject matter and execution. Most instructors were damn near fanatic about insisting you had notecards, an outline, a revised outline, a rough draft, a revised draft, and then a final draft. In that order. No thought was given to how some people don't write according to formula. I often felt as though I may as well be filling out Mad Libs than writing anythings.

I can't imagine that the two high schools I attended were special in any way, and in discussing this with others from around the country it seems everyone had more or less the same experience. And don't even get me started on the unbelievably wretched books we had to read; god forbid they find something even remotely interesting.

The state of English instruction in American public schools is every bit as abysmal as math instruction. I am reminded of this fact every time I get email from one of our users.
mirrorshades radio - darkwave, synthpop, industrial, futurepop.
and yet (2.50 / 2) (#25)
by trane on Mon Apr 02, 2007 at 09:11:42 PM EST

we manage to use English all the time to communicate, online for example.

[ Parent ]
Perhaps (3.00 / 2) (#27)
by kitten on Tue Apr 03, 2007 at 01:22:37 AM EST

But don't be so sure.
mirrorshades radio - darkwave, synthpop, industrial, futurepop.
[ Parent ]
Similar, yet different (none / 0) (#28)
by boxed on Tue Apr 03, 2007 at 03:46:56 AM EST

The best teacher I've ever had was in Swedish in grades 6 to 9. She had the class disciplined and not only did you need to earn her respect but you felt you wanted to. She insisted on everyone actually handing in a draft and then the final copy in writing assignments. I could never stomach that kind of writing, for me the words always flowed from the first sentence to the last without interruption. I got in the habit of writing a draft after I wrote the final copy. After a while she gave up and accepted that I did not benefit like the other children from the drafting phase :P

[ Parent ]
Heh, me too. (none / 1) (#37)
by kitten on Tue Apr 03, 2007 at 09:59:22 AM EST

My paper-writing technique in school was similar. I'd sit at the computer and hammer out what was more or less the final product, maybe going back the next day for minor, minor revisions but usually not.

Then I'd go write the "rough draft" by taking the finished copy and inserting some gibberish, misspelling some things, or adding an incoherent paragraph that I'd "later" remove, to show how I was trimming the paper to keep it focussed.

Then I'd make an outline based on what I'd just done.

Finally, if the teacher was retarded enough to require fucking notecards I'd go make those. Those always ticked me off the most. Outlines, I can see how that could help organize the flow of a paper before writing it. Rough drafts -- fine, I guess I can see the point, though in this day of computers it's not like we really need them anymore.

But notecards. Dear god, that is so far removed from my style, I cannot even fathom how anyone could honestly sit with a stack of periodicals on the left and index cards on the right and jot down little notes on each card, then reference them later. If some poor soul out there is helped by doing that, then great, let 'em, but for crissake, teachers of America: Let it go. Not everyone works that way. And when you require us to do silly things that don't work, we just game the system.
mirrorshades radio - darkwave, synthpop, industrial, futurepop.
[ Parent ]
heh my favorite part of kitten's edumacation (1.50 / 2) (#49)
by balsamic vinigga on Tue Apr 03, 2007 at 02:21:27 PM EST

trolls is the part where he's like "people shouldn't be required to learn math beyond basic 'rithmatic but for god's sake if they don't scrutinize every line they tap out for lazy mistakes like its/it's mixups they're uneducated mouth breathing cretin that don't know any better"

Or like, "the quadratic equation is a waste of time to memorize or be able derive from its underlying theory..  but omg if you can't correctly memorize the spelling of every english word you wish to type and/or poperly derive that spelling from its underlying etymology then you're a worthless sack of shit that needs to go back to 6th grade."

Please help fund a Filipino Horror Movie. It's been in limbo since 2007 due to lack of funding. Please donate today!
[ Parent ]

Very well put (nt) (none / 0) (#50)
by Coryoth on Tue Apr 03, 2007 at 02:56:36 PM EST

[ Parent ]
Nice try, Ace! (none / 1) (#53)
by kitten on Tue Apr 03, 2007 at 08:51:55 PM EST

But math is easy to forget, because you have so little call to ever use it outside of a classroom. Like anything else, if you don't use it, you will forget it.

Do you really want to compare that situation with English? You see, speak, read, and write English every single day of your life. Yes, I mock the people who can't remember the distinction between "your" and "you're" because it is something they see and do every single day. Unlike math, where one could easily forgive someone for saying "Gee, I haven't even seen a quadratic formula in thirteen years, I don't remember how to do this," there is no such excuse for English.

Insert another quarter, pal.
mirrorshades radio - darkwave, synthpop, industrial, futurepop.
[ Parent ]
They should teach sex technique in school (1.50 / 4) (#71)
by The return of Lemon Juice on Wed Apr 04, 2007 at 08:31:51 AM EST

Cause I'd like to use that everyday.

[ Parent ]
I wish (none / 1) (#74)
by Cro Magnon on Wed Apr 04, 2007 at 11:01:12 AM EST

that I could have learned sex techniques from my Spanish teacher. She was hawt!
Information wants to be beer.
[ Parent ]
While you'd like to use it daily (3.00 / 2) (#80)
by godix on Wed Apr 04, 2007 at 10:02:52 PM EST

Why should school bother to teach you something that YOU will actually use once or twice in your life?

- An egotist is someone who thinks they're almost as good as I am.
[ Parent ]
Frankly? (none / 1) (#113)
by Corwin06 on Fri Apr 13, 2007 at 11:02:25 AM EST

If some random loser like me could learn English in under two months and never make a spelling mistake in it, then you'd have to be a total cretin to mix up its and it's, use "greater then" and so forth.
"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
... if you are a native speaker, that is. (n/t) (none / 1) (#114)
by Corwin06 on Fri Apr 13, 2007 at 11:03:03 AM EST

"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
So shut up stupid. (1.00 / 3) (#69)
by The return of Lemon Juice on Wed Apr 04, 2007 at 08:29:18 AM EST

You're like this cat that was meowing outside all the time. Then a car ran over it.

[ Parent ]
Ha (none / 0) (#108)
by unknownlamer on Wed Apr 11, 2007 at 01:31:01 PM EST

I loved all of the concern that was put into style and formatted because I learned about LaTeX and BibTeX when I was fourteen.

\usepackage{mla} now I'm done!

<vladl> I am reading the making of the atomic bong - modern science
[ Parent ]
The problem with your analogy (none / 1) (#23)
by trane on Mon Apr 02, 2007 at 08:53:40 PM EST

is that English is taught using English, and math is taught using English. You have a concrete example of how to apply English because you're using it while learning about it. It's like a computer language that can compile itself, sort of.

Interesting, (none / 0) (#62)
by Joe Sixpack on Wed Apr 04, 2007 at 05:34:34 AM EST

I was taught English using Hebrew.

[ Parent ]

This is how Latin is taught (none / 0) (#35)
by Stereo on Tue Apr 03, 2007 at 09:26:37 AM EST

Grammar drills, pointless exercises and no emphasis on actually using the language for "normal" reading - it isn't surprising that, when they do take them, most people forget their Latin classes quite quickly. How different things would be if Latin students read Martial and watched Rome dubbed in Latin.

kuro5hin - Artes technicae et humaniores, a fossis

Another way to teach math.... and math history (none / 1) (#52)
by urdine on Tue Apr 03, 2007 at 08:14:05 PM EST

The English analogy is OK, and I agree with your general point.  I always thought math should be taught from a more historic standpoint - go through the history and important figures of mathematics to discover the expectations and understanding people had about the world, and how math changed and opened things up with each new discovery.  That would give people something to hold on to and something to fall back on - and a sense of journey as they learn deeper mathematics.  Rather than these odd "schools of thought" that jump from algebra to geometry to calculus with only a cursory amount of overlap.  People retain information best when it's in context.

As for the stupid word problems, those might be fine in 3rd grade, but a much better way for later high school math would be to combine computer programming and math.  Suddenly, homework and class project become a lot more interactive and interesting.  You might be solving the same problem for the millionth time, but working with variables and functions (ie. proofs, in a way) you have to really understand WHY things work to get the pretty graph to draw right.

It doesn't help that the current age range for (none / 0) (#54)
by Mystery on Tue Apr 03, 2007 at 08:53:31 PM EST

...teachers in elementary schools through college are aged directly improportionately to the age of the students. In gradeschool, I had a long procession of teachers aged 45 through 65 and pushing retirement. In highschool I had teachers in their mid-30s through mid-50s. In college, every professor I've met has either been a barely post-masters student, or one of the lifers that has spent every moment since their own graduation teaching college or university because children make them crazy.

It might not be a bad thing if teaching actually became encouraged again... Especially innovative teaching. Oh, and allowing teachers to use revised curriculums of their own choices each year. That might help a little too.

Our schoolboards are run like corporations, monitored by tax payers like investors, while being driven forward by local government to become better without any direction toward what that might be.

The whole system needs revision, and updating. All of it. The classes, the schools, the leaders, their methods, and what they all talk about. I always thought it would be smart as hell to introduce an entire year long course that only discussed current events to force students to pay attention to their own world. Would such an idea fly? No, you can't quantify it for testing on the SAT.
Failure is not an option -- It comes bundled with the software.

by Loltrand Lollell on Tue Apr 03, 2007 at 09:42:55 PM EST

I think that what you are getting at (none / 0) (#61)
by the77x42 on Wed Apr 04, 2007 at 01:24:16 AM EST

is some sort of axiomatic logic and set theory instead of applications of those theories or systems. The problem has always been what I believe the 'backwards' approach to education.

It's not until the university level do you understand the proof of 1 + 1 = 2 is so vastly long -- it wasn't the result of flash cards and apple-drawings. It's not until that higher level do you learn about syntax and semantics and the nuances of linguistics. It's not until then that you actually contemplate the basis for all empirical knowledge through some philosophical study.

What is taught at grades 1 - 12 are applications of theories that constitute pure reason or pure math. It's almost the cart before the horse.

"We're not here to educate. We're here to point and laugh." - creature
"You have some pretty stupid ideas." - indubitable ‮

Vastly long? Depends on your font. (none / 1) (#95)
by basj on Fri Apr 06, 2007 at 06:10:58 PM EST


0 = 0
1 = S(0)
2 = S(S(0))

Rule 1: n + S(m) := S(n) + m
Rule 2: n + 0    := n


S(0) + S(0)
            = S(S(0)) + 0     by rule 1
            = S(S(0))         by rule 2

Complete the Three Year Plan in five years!
[ Parent ]

okay (none / 0) (#97)
by the77x42 on Sun Apr 08, 2007 at 12:53:15 AM EST

Now try explaining that proof to someone in grade 1. My comment about length may be better replaced by complexity. And if you think that the proof is not complicated, remind me how many texts I have on set theory.

"We're not here to educate. We're here to point and laugh." - creature
"You have some pretty stupid ideas." - indubitable ‮

[ Parent ]
Build It (none / 1) (#98)
by cronian on Sun Apr 08, 2007 at 04:03:04 AM EST

While the theory may be a bit tricky, its physical manifestations are quite simple. The simplest manifestations of such things would be something like a computer.

Complex computers hide the intricacies. However, simple computers, like an abacus can be easily understand. It is easy to that if you move one bead up, and then move another bead up, you will have two beads up. If you can realize the same principal applies to other things, you are beginning to understand mathematics.

Multiplications may be trickier. However, it becomes intuitive geometrically, if you draw lots of rectangles. Mathematics becomes meaningful, when you realize the simplest physical instance of a mathematical concept is the same as any other instance of it.

One realizes the beauty of mathematics, when one realizes the simplest instances of concepts are symbolic. The brain itself creates the physical instantiation of the mathematical concept. The mathematical language can communicate it. However, can be many physical manifestations of the symbolic things, which are all really the same.

We perfect it; Congress kills it; They make it; We Import it; It must be anti-Americanism
[ Parent ]
whut u need set theory 4? [nt] (none / 0) (#106)
by basj on Mon Apr 09, 2007 at 04:26:55 PM EST

Complete the Three Year Plan in five years!
[ Parent ]
how'd you get rule 1? (none / 1) (#99)
by damiam on Sun Apr 08, 2007 at 12:14:22 PM EST

I've never seen anything like that as an axiom. If we accept arbitrary rules, I can do a short proof too:

Rule 1: 1+1=2

[ Parent ]

How else would you define + ? (none / 0) (#100)
by joto on Mon Apr 09, 2007 at 01:00:34 AM EST

Ok, maybe I would choose...

Rule 1: S(n)+m = S(n+m)

...myself, which gives the proof:


but it doesn't really matter. Either way is a perfectly valid way of defining what + means. The choice of definitions is equivalent, and can be used to get the other as a theorem.

[ Parent ]

Oops (none / 0) (#101)
by joto on Mon Apr 09, 2007 at 01:05:12 AM EST

Not that it really matters, but since rule 2 had 0 on the right side of the plus sign, I would probably put S(something) on the right side of the plus-sign too. This makes proving theorems easier. Not that it really matters much. Sooner or later, you will have to prove that + is commutative.

[ Parent ]
Wonderful, (none / 0) (#132)
by zagloba on Thu Aug 09, 2007 at 03:05:51 AM EST

wonderful... except that those aren't the axioms that the "proof that 1 + 1 = 2" uses.

At least not in the Russell/Whitehead form. (Principia Mathematica is the  archetypical masterpiece unreadable by any human, no matter how devoted.)

|He is a fool who only looks for truth where he knows he can find it.|
[ Parent ]

Everyone has an angle... (3.00 / 2) (#77)
by TDS on Wed Apr 04, 2007 at 12:07:30 PM EST

and the teachers are stuck in the middle. You think primary teachers should take extra "math" now? Well fair enough, should they drop the extra French/German/Mandarin (look how well they do at languages in European countries where they start aged 4) they are being made to learn and also cut back on the extra PE (obesity is killing people you know). Or maybe they should remove the extra "literacy hour" because kids cant reed wurds. And of course, this going to take time out of having a clear position on synthetic phonics that can be defended in the face irate parents. Meanwhile, the Johnson kid has pissed his pants again and Jones twins are fighting but there isn't time to help with either is there. Its all so obvious isn't it? Thats what everyone else thinks as well.

I don't as such disagree with you but you are just another person yelling from the sidelines. No wonder its hard/impossible to attract the best candidates into teaching. Shit pay and everyone spends their time telling you how to do your job and screaming at you for everything that is wrong in society.

Are you going to give up your academic career to be a school teacher? I don't think so and nobody else is going to do it either. Until you do you're a guy with an opinion, just like everyone else.

And when we die, we will die with our hands unbound. This is why we fight.

This "abstract" way... (none / 0) (#84)
by pruneau on Thu Apr 05, 2007 at 08:16:41 AM EST

...of teaching is exactly how foreign languages (including english, of course) are taught in France.
With the same results: your run-of-the-mill french tends to have some command of the written lingua, but are mostly horrible at speaking.
Usually, when a french has a better command of the spoken language, it's because he/she traveled to learn, or has parents that have a multi-lingual background.
(I was born in France and lived there for 30 years, so no, it's not a cultural bias, it's from experience.)

Not the point (3.00 / 2) (#89)
by Corwin06 on Thu Apr 05, 2007 at 02:12:04 PM EST

You know, I've taught myself English in 6 weeks because I found that the classes would be useless (no one in school who could actually speak English had learned it there) and I was curious.

But I learned it in the most abstract way possible! Just like I described math above: learn one rule, apply it once in every way it can be applied, so you get one example for every use, then go learn the next rule.
How difficult is that?

I described every "line" of rules as defining a  nuance of meaning, too, so that as soon as you're done with my course, you can think in English instead of having to translate from your primary language, losing lots of meaning in the process.
I know it sucks because that's how I speak Dutch : I have to first think the sentence in German, then translate it. It's a slow, error-prone and boring process.
I learned German by living 8 months in Germany and going to some language courses; I can tell it was nowhere near as fast or efficient as the method I used to learn English...

"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
Music and Math education BOTH! (3.00 / 2) (#90)
by chocolatetrumpet on Thu Apr 05, 2007 at 06:51:12 PM EST

Using language learning as a model for "how things should be done" is very common in the field of music education.

How people learn language...

  1. You listen to a lot of language being spoken.
  2. You babble.
  3. You start to speak some words and eventually sentences, with meaning.
  4. You learn to improvise a conversation.
  5. You learn to read by matching symbols with words you already know.
  6. You learn to write by transcribing symbols for words you already know.

You go on to be able to improvise writing, etc. Notice how notational symbols aren't even involved until 5., as they have no inherent meaning - they are given meaning by the reader.

If language was taught like music is taught...

  1. You look at some simple words and sentences.
  2. You learn to decode the symbols for words and sentences.
  3. You learn to pronounce the words and sentences while looking at them ("reading music!").

Most music programs in the states stop there. Notice how meaning is no where in the picture. Imagine how someone who learned language like this would sound when "reading aloud" - probably dull, lifeless, and mechanical, as they wouldn't know what the words meant, so they wouldn't know where to put emphasis or how to phrase to convey meaning. They would probably not be able to improvise a conversation. They might be able to write some words, but they probably wouldn't know such basics as "sentences start with capital letters and end with periods."

While music is not a language - it does not have a grammar, it DOES have syntax; the order of "words" (chords) and rhythms in the context of meter and tonality is what gives music meaning.

Math education in the states is a lot like music education in that children spend all their time learning to manipulate and decode symbolic notation without actually gaining any insight or meaning into the mental process of math (or music). Math students rarely learn to mathematically "visualize," and music students rarely learn to audiate (the mental process by which people give meaning to music).

Both fields need a serious overhaul! This can take place at the teacher education level. I know of some music educators (Dr. Edwin Gordon, Dr. Christopher Azzara to name two) who are committed to reforming music education. Shameless plug - I write about music education on my blog.

There must be some major math researchers out there who are studying how people learn math and are committed to reforming our education practices. Does anyone know who they are?

The truth is in the ice cream.

Tell them, tell them, brother! n/t (none / 1) (#92)
by Corwin06 on Thu Apr 05, 2007 at 09:29:30 PM EST

"and you sir, in an argument in a thread with a troll in a story no one is reading in a backwater website, you're a fucking genius
[ Parent ]
Speaking as a math teacher (2.50 / 2) (#107)
by romanZeta on Tue Apr 10, 2007 at 10:12:47 PM EST

There are many things in this article that I agree with. Specifically,

  1. The subject is too detail-oriented
  2. The "real world applications" are convoluted
  3. The broad view isn't really taught.

The thing I didn't see, though, is a suggestion of a way to do it better. So, help me out boys and girls. What are some of the ways this can be adressed while still teaching people

a) how to think abstractly
b) how to balance their checkbooks.

Best answer gets a gold star

Teach the abstraction (3.00 / 3) (#110)
by Coryoth on Wed Apr 11, 2007 at 11:03:24 PM EST

It's far from a complete solution, but it does provide some benefits: actually teach the process of abstraction that leads to the mathematical rules we use. By that, I mean actually describe to kids the process by which we generalise over a range of cases and arrive at methods that are applicable to all cases. This is, of course, fundamental to science as well as mathematics, but it is what mathematics is, at heart, in many ways. This teaches abstract thinking, and leads to discussions of the broader view, and by showing how the ideas and techniques developed in this manner are universally applicable, shows how they can be applied to specific cases like balancing your checkbook. For an example of what I mean, try my discussion of numbers or my explanation of fractions and algebra.

Such an explanation is, of course, only ever going to be a supplement to the necessary rote work to hone the skills and techniques of manipulation that the process of abstraction develops, but it can help provide some understanding for why the rules are the way they are, and why they are important (they are universal generalisations).

Such a technique is also not going to be ideal for early elementary students, who won't have quite the required grasp of abstract thought yet. In that case I expect that demonstrating the universal applicability by demonstrating that the particularities don't matter is going to be your best bet.

[ Parent ]

I only read the first paragraph. (none / 1) (#115)
by Vesperto on Fri Apr 13, 2007 at 01:33:18 PM EST

Didn't even bother reading the rest of the comments. Why are you comparing a language with an exact science?

Geez, this sooo looks like a troll. But it ain't, really. Is K5 still troll-infested? It's been a while.
If you disagree post, don't moderate.
Not a Premium User.

your plagiarism amuses me. (none / 1) (#117)
by la princesa on Mon Apr 16, 2007 at 01:51:31 AM EST

it also amuses me that this site has been so tolerant of it.

<qpt> Disprove people? <qpt> What happens when you disprove them? Do they disappear in a flash of logic?
Interesting. (none / 1) (#118)
by Coryoth on Mon Apr 16, 2007 at 10:55:29 AM EST

Who or what do you feel I have plagiarised? Details would help.

[ Parent ]
I believe the article in question is . . . (none / 0) (#119)
by Mystery Girl on Thu Apr 19, 2007 at 06:30:13 PM EST

Leland McInnes's blog post of the same title.

I don't accuse you of plagiarism only because you may well be Leland McInnes. How would I know?

Though, if you are, you might want to make some comment regarding the article's cross-posting. It would spare you the baseless accusations (if, indeed, they are baseless).

[ Parent ]

Or you could glance at my userpage on K5... (none / 0) (#121)
by Coryoth on Fri Apr 20, 2007 at 10:57:14 AM EST

[ Parent ]
Your k5 user page . . . (none / 0) (#122)
by Mystery Girl on Fri Apr 20, 2007 at 12:17:21 PM EST

Could say you're Jesus H. Christ for all it matters. (Though, admittedly, I couldn't say why anybody would fake up the ID of a Canadian larval-stage doctorate-grade mathematician.) I did read your page, which is why I suggested the cross-post note rather than accusing you of stealing from yourself. I was just leaving the possibility open that some sort of wacky high-jinks were up, as I'm not about to go and try to confirm the meat IDs of anybody on this site.

[ Parent ]
good article (none / 0) (#120)
by ljj on Fri Apr 20, 2007 at 07:32:39 AM EST

K5 rocks.


Engineering (none / 0) (#128)
by red eye on Tue May 22, 2007 at 08:22:40 PM EST

It is interesting that there is no mention of engineering anywhere. There is a huge disconnect between mathematics and engineering in this country. This is more obvious to people educated in either field outside USA. While your allusion to "applied math" is  for the intents and purposes of the piece acceptable in accuracy, I think comparing "engineering math" to "pure math" will give you more insights into this matter. Most countries in the world with an advanced education system "get this" about math, i.e. applied math=enginnering. So applied-math curriculum is designed with engineering school in mind. This gives direction and continuity to teaching and learning math in school.

Having said that, I also have to say that there is an inherent contradiction in your piece. As you point out you can't appreciate math unless you appreciate its abstract nature. And you can't appreciate its abstract nature unless you, well... abstract it from the underlying applications. But I agree with you in that we have to hit a balance here and we are far from it.

All the poems we read (none / 0) (#129)
by quetzalcokebottle on Sat Jun 02, 2007 at 02:24:27 AM EST

You imply that English is taught much more successfully than mathematics, but is that actually the case?  Does the person who is average product of the school system you refer to actively read or passively comprehend poetry, for example?  (and actually, what school system are you referring to, anyways?  Comments above seem to indicate that you are Canadian.)

I agree with you that the lack of a greater affection for mathematics is by changing the way it's taught, but like some of the others commenting I don't think that modeling it on the way English is taught or increasing the amount of secondary education for the teachers will achieve this.

Do people with doctorates in English make the best English teachers, for example?  I would be surprised if that is the case.  Similarly, despite your reference to that Finnish project, from my own reading on the matter I do not recall that a more extensive education program for teachers results in greater success of an education system, in fact I think I recall that the opposite was the case, that teacher education level and the available measures for student success are not correlated.

From your description, you're at least speaking of an education system similar to the U.S. one that I grew up in.  I agree that there should be higher-quality and more innovative teaching of mathematics at younger ages but this innovation needs to be systemic, not dependent on the teacher's individual grasp of math.  The improvement needs to be in the curricula, teaching tools and resources, time devoted to mathematics (both for the student and for teacher lesson prep), and smaller class sizes / better student-to-teacher ratios during mathematics lessons, rather than pushing teachers into situations where they'll purportedly achieve an appreciation of the finer things in math.  I'm not saying that wouldn't be important (although... math clubs? For real? Are you a member of any English clubs?), particularly some sort of class for elementary-school teachers that indoctrinates them into believing that math is endless fun, a complete barrel of monkeys, but that  alone would be an ineffective measure.

The simple fact of the matter is that computational skills are a very important part of learning mathematics that you're not going to get away from.  I think that more big-picture stuff is important to spice things up and that the teaching of computational skills should be more conceptual and less procedure-oriented, but mathematics is a tower of complexity next to the self-taught-carpenter-built hovel of English.  There's a reason why there are divisions between the hard sciences, the soft sciences, and the fluff-filled "humanities" in academics; mathematics simply takes a great deal more intellectual rigor and discipline to pursue than reading novels and writing essays.  Notice how you don't see too many lat-de-dah "liberal studies" types digging into a good Chomsky linguistics treatise, no matter how much linguistic communication their particular discipline involves?  That's right.  Because that's the hard stuff and they're going to stay away from it even on their own turf.  Sheesh, whadda bunch of softies.

I hereby excuse myself from any and all errors of grammar I've committed in this article, since I'm an engineer and all of that stuff is beneath me.

Disagree. (none / 0) (#130)
by vectro on Mon Jun 04, 2007 at 03:45:40 PM EST

The simple fact of the matter is that computational skills are a very important part of learning mathematics that you're not going to get away from.
I had a terrible time with computation in high school, and continue to have trouble with it as an adult, but I love math and have no problem working with symbols, equations, theorems, and proofs. And I know I'm not alone in this, either.

“The problem with that definition is just that it's bullshit.” -- localroger
[ Parent ]
If We Taught English the Way We Teach Mathematics... | 132 comments (117 topical, 15 editorial, 1 hidden)
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