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Charlie Kondek
10th July 2003, 16:48
Hi, yaw. You're all a bunch of smart mofos and I was wondering: Why does the American educational system (or any, for that matter) push mathematics so much in the curriculum. When I was a kid, if you were one of the "smart" kids or on the AP (Advanced Placement; college prep) track, you were pushed into higher levels of mathematics.

Yay, I love math (I'm no good at it) but I can't help feeling that some of these kids would have benefitted more from business courses, computer courses, and other courses. Who ends up using Advanced Calculus in life besides mathemeticians and some scientists? Seems to me most of the math-heads go into engineering and should be concentrating more on business, CAD and such, or biology and should have been concentrating more on - well, biology.

What gives? Do I just not understand the function of math in the world? I thought most mathematics was the realm of the academician.

elder999
10th July 2003, 17:23
Space race.

or

New Math.....

Do a search; it makes for some interesting history, though opinions will-as usual-differ....as an engineer, I have to use math regularly...though I haven't liked it much since sometime between 3rd and 5th grades....let alone loved it.....:rolleyes:

Shitoryu Dude
10th July 2003, 17:24
Math is everywhere - knowledge of higher mathematics is very enlightening in that it demystifies the world. Even if you don't remember how to do differential equations worth a damn, the concepts and applications are still there in your head. You understand things far better just because of that. The universe runs off of math.

Most people use math far more than they think they do. They have just become so used to doing it that it no longer registers.

:beer:

Charlie Kondek
10th July 2003, 17:45
Just the two guys I hoped would chime in. So, Harv, your point is that Math enriches the soul as much as the Humanities? In fact, at one time, one could have glossed them together.

But I must ask: I am ignorant of the higher functions of math. After algebra and geometry, doesn't it start to become so abstract as to be unpragmatic?

Help me out here, I got my degree in Literature and History. I took art classes in high school. :D

seskoad
10th July 2003, 18:02
Math is the way to train your brain to solve problem. Most educator told me that math will train your brain to deal with difficult problem so perhaps in the future we will be able to find easiest way. It's similar to education in university that also train the way your thinking. Often I heard people change their proffesion other than the degree they learnt in uni before. Or people said "well, in work so many things that I didn't get from uni or much different from I learnt than uni".

wimp_lo
10th July 2003, 18:09
You need the abstractions to connect underlying principles. Then you can apply the principles to problems which before may have seemed unrelated. The abstractions are mainly for mathematicians, but the applications are for anyone who can make use of them.

As was mentioned before, mathematics is an excellent tool to promote overall critical thinking skills.

Shitoryu Dude
10th July 2003, 18:19
After algebra and geometry you get into analytical trig (advanced geometry) in which you learn the in-between steps into calculus (a big-ass number of trig identities). Calculus lets you solve simultaneous equations that would take forever and a day to do with algebra, if at all. It isn't all that hard as long as you can remember a few dozen trig identities.

I took statistics, which starts off with simple stuff like flipping coins and rolling dice and ends up being able to alter numerous variables at once and tracking them on 3-D geometries to determine where variables overlap to get the desired result (Design of Experiments).

There are esoteric fields of math study that hurt the head. Aaron most likely needs them to explain things like 17 dimensional geometries and quantum mechanics and what time to feed Schroedinger's cat. My brother used it to design orbital optics and laser cavities.

A truism of mathematics is that you don't really understand one area of it until you have advanced past it. Once you understand advanced trig and calculus, algebra seems like the most simple of methods of doing stuff. It is slow, awkward, and limited. What takes 3 sheets of paper and two refills of your mechanical pencil is reduced to two lines of elegant number crunching which typically gives you a more accurate answer. Once you know advanced stats, things like determining the odds of some event happening (like winning the lottery) become afterthoughts.

:beer:

elder999
10th July 2003, 18:42
I wouldn't exactly say that "the universe runs on math."

More like, mathematics explains the way the universe runs.
(And it's only one way, not the only way, IMHO...)

The higher it gets, the more pragmatic it gets for the person using it, whether it's to do something as simple as calculate the efficiency of an engine something I did all the time when I was in the power industry, and it only takes algebra to do so.., or to calculate the expected geometry and yields of variable quantities and shapes of high explosive, or to predict the dispersals of materials over a given area given an event and the weather conditions at the time of the event....though I'm allergic to cats Harvey, most probably Shroedinger's as well....when it's there.:p

Or just for playing poker and betting on sports......

As for "enriching the soul," well, there are those that believe that-they've been around as long as mathematics has, and if you don't believe that do a search on "sacred geometry." Interesting stuff.

I don't really believe it's enriched my soul, though I could be wrong, but I am something of a special case in that regard, in that while I have a facility for a number of tasks associated with math and math itself, I don't really like it, and my occupation is not necessarily my true vocation-so take what I say in that regard with a grain of salt.

Math did make me a better musician,chess player and pool player, though, and more money than I'll ever make teaching school.:p

Mitch Saret
10th July 2003, 19:22
I need to tell you a bit about my wife, Jayne. In college she was a theater major. She has even been on stage with some famous people, we have a picture of her sitting on John Malkovich's back, for one. She enjoyed performing, but her emphasis was in costume design. She even took a math minor to help out. Why, you ask.

Well, now we have a costume shop specializing in full theater productions. During spring musical season she will put together around 80 fully costumed and designed productions for schools as far away as Maine, and North Dakota. We are in central Illinois and those are some of the farthest I recall. If she doesn't have it in stock she will build it. The math, algebra, geometry and such, come in when buying fabric and figuring how to get the most use and the least waste.

She uses her marh skills everyday, and I am still trying to figure out which train willarrive in San francisco first! Well, not really. Several years ago when I was working and using my degree as a chef, I had to use math everyday in executing as well as developing recipies. Now that I do martial arts full time, I have to use math when doing the tuition and all that icky business side stuff!

cguzik
10th July 2003, 19:29
My initial reaction to this thread was to reply with comments similar to what Umar said: Learning math helps people learn how to think.

A couple of additional points to note, however.

In spite of the fact that our educational systems try to impose requirements for mathematics, I don't see very many young people coming out of school who know how to do math with any level of competency. I don't see very many that can even think with any level of competency.

This would seem to indicate that the efforts to teach these things are not succeeding.

I think that part of the problem is that teachers of *any* subject should approach their job as that of teaching students to solve problems and think things through. Instead, we have teachers who believe that their job is to make sure that students know lists of facts, or how to generate certain answers to certain questions.

Different kinds of math teach different things. Geometry class is more about learning logic than it is about the subject of the axioms and theorems. Unfortunately, many students get passing grades as a result of memorizing properties of geometry. Algebra is more about learning to think abstractly than it is about how to solve for X and Y in a set of equations.

Some of these things can be taught just as well in other classes. For example, a debate class should teach logic nearly as well as geometry. The thing about math, though, is that it is more specifically focused on these ways of thinking than other areas. You can find logic in philosophy classes (it's integral), but it's not usually taught as directly as it is in mathematics.

Chris

Marc Renouf
10th July 2003, 20:31
I use math every day. I cannot escape it. I'm an engineer and a programmer, and calculus is pretty much at the heart of what I have to do.

Chris brings up a very good point about using math to teach critical thinking skills, but that situation works in reverse too. If you want to learn how stuff "works," you need to understand physics. Physics is rooted in math, and is an area where math can help you learn another kind of critical thinking: process interaction.

For what it's worth, I find abstract math much more difficult to understand than applied math, even if it's the same stuff. I struggled through Differential Equations in college, but I aced my structures and dynamics classes (structural deformation and dynamic response are described using differential equations). Once I had something "concrete" to wrap my brain around, the concepts became very easy to understand.

Oh, and I may have been Schroedinger's Cat in a past life.

Shitoryu Dude
10th July 2003, 22:23
Or maybe not. I'll go flip a quarter and see ;)

I always found math easier to work with when I had something to apply it to as well. Once I got past that mental roadblock it became easy to apply it to other situations.

The student's t test was for me a head smacker of a concept because parts of it works counter-intuitively when you first get exposed to it. I finally grasped it in it's entirety when I applied the test to determining how best to defog a windshield on a cold day and if there was really any statistical difference between using heat/AC and fresh/recycled air.

:beer:

PS - using the AC will defog the window faster than the heater. Fresh or recycled depends on the vehicle. Oddly enough, recycled usually works better.

elder999
10th July 2003, 22:29
Originally posted by Shitoryu Dude
The student's t test was for me a head smacker of a concept because parts of it works counter-intuitively when you first get exposed to it. I finally grasped it in it's entirety when I applied the test to determining how best to defog a windshield on a cold day and if there was really any statistical difference between using heat/AC and fresh/recycled air.

:beer:

PS - using the AC will defog the window faster than the heater. Fresh or recycled depends on the vehicle. Oddly enough, recycled usually works better.

Qout, Dude!

n=Wout-Win/Qin=Wnet/Qin

Shitoryu Dude
10th July 2003, 23:15
Can you believe I went through the silly math and setup of defogging a windshield over a silly disagreement with my wife? She always used the AC on full blast with the air on recirculate where I did the exact opposite - Heater on full blast with air on fresh. I based it on the assumption that heat and fresh air were needed to excite the water back into a gaseous state and to reduce the water vapor saturation level back down to the point where it wouldn't recondense on the windshield.

She just said her way worked faster and left it at that. :laugh:

So I started thinking that all you had to do was get an average defog time using her method you could change each of the variables in turn and get a new average defog time and crunch the numbers. Damned if she wasn't right. Every now and then in the fall I try to explain how blowing cold air over a fogged up windshield works better than heated air but I can't. I must not be accounting for something.

:beer:

elder999
10th July 2003, 23:24
It's an equilibrium, difference in temperature problem.
For fogged up due to cooling by rain, or somewhat lower temperatures, AC does work best-these are probably what you get most of the time.

Anyone from Colorado or New York that deals with excessively cold temperatures knows that hot air-on recirc-works best for those situations.

Here in New Mexico we get both, and arguments like you wouldn't believe!

Shitoryu Dude
10th July 2003, 23:30
That would explain it - I grew up in places where it got biting cold or blistering hot with little in-between. Running your AC to defog the windshield would likely make it freeze up :laugh:

Seattle is so temperate though: hot is 80 degrees, cold is below 50. Snow only once or twice every few years, and it hardly ever breaks 95 degrees in the summer. Lots of semi-cool rain most of the year. Hardly anybody owns a real winter coat and nobody gets a tan without a little help from technology or travel.

:beer:

Cody
10th July 2003, 23:48
For a lot of people, math is just a tool of problem solving. It can be their life-saver and at the same time, it can be borning as hell. (Go argue with any student in my statistic class).

For me... I only do math for fun. I lose my interest in it as soon as I find something useful about it. I used to thought pi was the most interesting number on earth, until I learn more about cryptography...

Not surprisingly, I agree math is like art, poem or even music. It's most symbolic of human intellect. Really, there are a lot of fun, math thing you can amuse yourself with, with just the most basic math skill (algebra, geometry...).

I posted a "just for fun" type math problem on budo fun once, but it wasn't very well received. I think it really reflects how a lot of people automatically reject math as something dry, geeky, abhor... which is a shame. If you think about it, it can be as humanly witty as a poem or a sonata!

Just my humble two cents.

-Cody

A. M. Jauregui
11th July 2003, 00:00
Logic that stems from mathematics would help a lot of students get better grades. How you might ask... Any time there is a sequential multiple part multiple choice quantitative question a simple matrix will solve it more often then not. Test makers (not me I’m mean) generally assume that students will not think out of the box and solve the problem in that fashion so they do not make multiple sequences of correct answers.

elder999
11th July 2003, 00:08
Originally posted by Cody

I posted a "just for fun" type math problem on budo fun once, but it wasn't very well received. I think it really reflects how a lot of people automatically reject math as something dry, geeky, abhor... which is a shame. If you think about it, it can be as humanly witty as a poem or a sonata!

Just my humble two cents.

-Cody

Well, I appreciated your question, but it's pretty bogus when there are only 7 four digit vampire numbers and you listed five of them....while there are lots of vampire numbers with more than 4 digits, it's well known that real vampires only have two fangs....:D

David Dunn
11th July 2003, 00:10
As a mathematician, I thought I'd better chime in here.

In a nutshell, maths is the study of numbers, or sets if you want the abstract version (numbers can be represented as sets). Since we observe nature through numbers (magnitudes, dimensions, directions, time) and changes in these numbers over time or space, maths is the way in which we express our understanding of nature. Maths and logic are almost inseperable since most of maths is expressed as propositions. These can be true or false, and logical deductions can be made from propositions. If we can express laws of nature mathematically, that logical reasoning can predict nature, and therefore we can test our theories. Basically for me maths is the language which we do science and engineering with, stripped of all the ambiguities of human subjectivity that characterises ordinary language, literature, history and so on.

Is maths 'discovered', in that it pre-exists humanity? Or is it invented by us? I think the latter on the whole, although there is plenty to suggest that children think in sets, quantities and so on intuitively. In that sense it might be considered a honing of our innate methods of categorising the world that we sense.

One of the great benefits of learning maths is that you have to learn abstract reasoning, remove yourself from the sensory world and subjectivity, learn how to employ your critical faculties and construct watertight arguments. That's on a personal level. On a societal level, we would be living in caves without mathematics.

Just my tup'pence ha'penny worth, and many mathematicians would disagree with me.

elder999
11th July 2003, 00:20
Originally posted by David Dunn
Is maths 'discovered', in that it pre-exists humanity? Or is it invented by us? I think the latter on the whole, although there is plenty to suggest that children think in sets, quantities and so on intuitively. In that sense it might be considered a honing of our innate methods of categorising the world that we sense.

One of the great benefits of learning maths is that you have to learn abstract reasoning, remove yourself from the sensory world and subjectivity, learn how to employ your critical faculties and construct watertight arguments. That's on a personal level. On a societal level, we would be living in caves without mathematics.

Just my tup'pence ha'penny worth, and many mathematicians would disagree with me.

See? Mathematicians are weird...and I mean that in the nicest way, really!:p

Thank you Mr. Dunn....

David Dunn
11th July 2003, 00:33
I know Aaron. I'm just an applied mathematician. You should see some of the pure maths people :D

Shitoryu Dude
11th July 2003, 01:36
Speaking of tests - I do write test questions. And I make them damn tough - typically I put in at least one wrong answer for those who do the question incorrectly in one of the more common ways (must remember if it is a population or a sample). I toss in bogus answers that seem correct, I create questions around obscure answers that seem improbable, I do everything I can to f*** you up - if you don't know your sh*t, then be prepared to get blasted out of the water. :cool:

I wrote many, many questions for the ASQ's certification exams. Keeping it tough keeps out the lightweights. The last thing I want is a batch of watered-down dweebs working around me that don't know their job.

:beer:

A. M. Jauregui
11th July 2003, 02:48
As a student I beat tests left and right - 1560 SAT with higher math then verbal :rolleyes: . Every test has some logic behind it, most people just do not look for it. Mathematics definitely helps logic...

For the tests that I write which are not mathematical in the slightest, I use simple but effective psychological mind games. The newest one was drawing a page long S shaped line down the center of the students blank paper which if written on equates to an instant fail. Stopped the old pre-write and switch. *Diabolical laugh* two kids went from A work to D...

Shitoryu Dude
11th July 2003, 04:27
I'm afraid I don't know much about cheating on tests - it always seemed to me that the amount of effort that went into a good cheat was more than that required to just know the subject well enough to pass. But then, I blew through most subjects even while I practically slept through classes.

MA Chicks with high SAT scores are HOT :cool:

:beer:

A. M. Jauregui
11th July 2003, 05:11
I was an alternate for the Royal Court of the 104th Annual Tournament of Roses Parade too. :cool:

I know the the boys in my class that cheat are intelligent and if they did focus their efforts there would be no need to cheat. Sadly the only way they are going to learn is the hard way - failing grade after failing grade and humiliation among their peers. E.g. having them grade there own papers and then informing them that I will be comparing the test they are handing back in to post test photocopies that i made..

Charlie Kondek
11th July 2003, 14:00
Ana, this is not going to keep the e-budoka from asking to see a PIC!

:D

Charlie Kondek
11th July 2003, 14:15
Thanks for chiming in here, guys. Here's another question, and David, I'd love to hear what you think.

Does math deserve the priority it gets in our school curriculum? From what I'm hearing here, it does. When I was in school, the smart kids took reams and reams of math, even if they went on to become lawyers or business-people. My high school guidance counsellor, bless him, realized I was right brained and urged me to take art classes. Yes, I was AP in English, but not science or math.

Did the emphasis on math in these kids' education help them in later life? You've pointed out that it enhanced their reasoning and problem-solving skills and I buy that, but I wonder (and I'll have to ask some of them next time I see them) if they could have changed their curriculum, would they have done it differently?

For example, instead of advanced math, wouldn't they have benefited from advanced computer courses (I graduated in '90, so we were just starting to get computer labs), CAD courses, business courses, work-studies, or other courses that prepared them for college or the professional world?

cguzik
11th July 2003, 14:49
Charlie,

I am interested to see what David thinks, but I'll add my two cents worth as well.

If by computer classes, you mean computer science classes, then I think they could accomplish the same things as math classes if taught with the right emphasis. (Computer science is applied mathematics).

However, as I alluded to in my earlier post, I doubt that it would in most cases be taught with an emphasis that would achieve the same results. Math has a way of distilling the subject matter so that the right emphasis is enforced.

Chris

cguzik
11th July 2003, 14:53
Anybody here a fan (or critic) of Douglas Hofstadter?

Some of his questions about the limits of computation, math, and mind were the catalysts that eventually led me to develop an interest in MA.


(Actually, they weren't really his questions, but he has a very eloquent way of expressing them...)

Enfield
11th July 2003, 23:32
Originally posted by Charlie Kondek
Does math deserve the priority it gets in our school curriculum? From what I'm hearing here, it does. When I was in school, the smart kids took reams and reams of math, even if they went on to become lawyers or business-people. My high school guidance counsellor, bless him, realized I was right brained and urged me to take art classes. Yes, I was AP in English, but not science or math.Charlie, think of math as the suri-ashi of engineering and science (including social and computer sciences) kendo. If you can't do the math without much thought, then the rest just doesn't quite work right.

As to the CAD type stuff, I'm a grad student in mechanical engineering. I've TAed my department's undergrad and graduate numerical methods classes. There's a noticeable difference between the people who know how to use software to solve equations, and those who know how to solve equations and use software to do it. The former know how to get an answer out of the magic box. The latter know when to trust it.

A. M. Jauregui
11th July 2003, 23:59
The plurality of AP English only students that I knew seem to have went on to either become writers or lawyers, hmmm. I bet that a study or two has been done my some sociologists tracking variables such as AP course selection and career paths.

As for the picture Charlie, most likely not, even though I have two were I am wearing a borrowed coronet from one of the girls that was selected to precipitate. My attire is just too weird - I am hardly believe that I dressed like I did. :rolleyes:

Shitoryu Dude
12th July 2003, 00:15
AP English was a snap. While I hold secret delusions of someday being a writer, I'm currently an engineer. But then, I took AP courses in just about everything.

:beer:

Iain
12th July 2003, 05:30
I'm math-tarded (really, there was a 14 point differential between my highest and lowest scores on the wexler IQ test). Subsequently I don't use math for anything. This causes me to question exactly how useful it is. I don't really see the point of teaching linear algebra, differential equations, fractals, and such to students in highschool unless they plan to go into a post-secondary programme where it will be of use.

Yes, math does an amazing job of explaining nature, but if you're too much of a dunce to understand the math, it doesn't do you much good. I think a more comprehensive highschool education involving ethics and such would serve to better integrate adults exiting highschool into society at large.

Shitoryu Dude
12th July 2003, 06:16
Now I understand why we have such a problem arguing economics with you all the time.

:beer:

Iain
12th July 2003, 11:53
Originally posted by Shitoryu Dude
Now I understand why we have such a problem arguing economics with you all the time.

:beer:

Probably. I understand how economic theory is supposed to work, just not why it works. Economics also strikes me as a bit of an abstraction as you're not dealing with concrete physical objects as much as you are their ascribed or percieved values attributed to them by society at large. People are flawed and don't always act rationally, so any economic prediction is going to be subject to human error.

Then there's the information technologies sector. People using math to invest in things that function using math... that has to be the devils work.

seskoad
14th July 2003, 16:45
something just come up in my mind. Have you ever seen movie "beautiful mind". And how easy he solve problem when he's crazy. :D

Charlie Kondek
15th July 2003, 14:46
Haha! Too right, Umar.

I'll tell you why I bring it up in the first place. I'm going to start taking some classes and working on teacher certification, and in about four-five years that'll be my next career. I'd like to be a high school English/History teacher (while still trying to publish). Anywho, to that end, I had to take the MTTC Basic recently - this is a test for would-be entrants to any Michigan college of ed. that tests basic skills in reading, math and writing.

So I was doing a bunch of math and got to thinking about it. By the way, I hate standardized testing. Maybe with a few more education classes under my belt, I won't hate such things, but I doubt it.

Here's a funny thing. I'm smart but was always a mediocre unmotivated B student and I hated Math. The older I get, the better a student I become. And when I was studying for this MTTC I started having flashbacks to the frustrated nights of tears shed over algebra homework; I just couldn't do it. With a little practice, though, I found that I could do it now, and didn't mind it so much. In fact, I'm thinking of getting some old algebra and geometry text books just to practice at it, to keep the old brain fresh.

I'm not sure what the point of all that is except to note that I am pleasantly baffled at what a good student I am at 31, as opposed to 14. How can I use this to become a good teacher?

A. M. Jauregui
15th July 2003, 23:04
Charlie it could be that your brain is now fully developed and you now have your priorities better adapted to your goals in life.

I also think that it is wonderful that you are looking into a career as a teacher. :)