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Author Topic: I Don't *Do* Math!  (Read 7356 times)

billy-jay

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I Don't *Do* Math!
« on: June 16, 2005, 04:48:17 am »

Forum post at Kim's place

Interesting post there.  I think that if I were a teacher and a student told me that, I'd fail them on the spot.
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mi6a2lm

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« Reply #1 on: June 16, 2005, 08:10:46 am »

Just for those who want to know the definition of an algebra:

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UnReconstructed

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« Reply #2 on: June 16, 2005, 10:24:49 am »

M16,

What the *hell* is that?

I *DO* math. Math is the key to being able to manipulate and understand the universe around you. Math and physics should *ALWAYS* be taught together, so that the student can actually APPLY the knowledge.

Unfortunately, skools 2day do not teach math with rigor. When my daughter was in gubbmint school, they seemed to encourage 'creative' math.....just like they did creative spelling.

Of course none of the teachers actually *USE* math to earn a living. They have little real world idea of what advanced math is good for. After all they opted to go to teachers school.....why? Well probably in part because they did not have the desire (aptitude) to do advanced math.

OOOPS rant alert rant alert........
« Last Edit: June 16, 2005, 10:39:28 am by UnReconstructed »
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Bear

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I Don't *Do* Math!
« Reply #3 on: June 16, 2005, 11:15:37 am »

Kim was too polite. Given that this happens with college students, I'd say something
like the following (and probably get fired):

"You don't do math? That's too bad. You will be vulnerable to fraud and cheating
by anyone who isn't as lazy as you. You had better marry someone who will take
care of you, as you certainly aren't enough of an adult to live on your own."

Bear
 
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Scarmiglione'

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« Reply #4 on: June 16, 2005, 11:57:22 am »

I'm one of those people who was taught to hate math by the PS.  My brain never "got" multiplication until years after I had passed it.  The consequences of that were really bad.  As a result the highest math I've ever been taught was HS Algebra.  I found ways out of the rest.

My job as a programmer put math right in my lap quite often.  I found myself on the internet doing research into HS math and teaching myself.  I'm no guru, and no high math either.  I did a lot of wheel reinventions.  But I guess one could say that while I 8do* math, I don't *know* math.

Thanks GovSchool!
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Bill St. Clair

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« Reply #5 on: June 16, 2005, 12:10:13 pm »

Quote
M16,

What the *hell* is that?
 
Looks to me like M16 really does math, not just the arithmetic that most people call "math". I took a graduate Abelian Algebra course during my senior year of college. They talked about the Sieve of Primes of the Kernels of Homomorphisms, or something like that. I had always been pretty good at proofs, but I realized in this course that I had been working before with a blindfold on. Because the undergraduate proofs I had been asked to do were like walking around a small room and bumping into the furniture, I could handle it. This graduate class, however, was more like being asked to find a teacup on a football field. Without a better mathematical intuition, some way to remove the blindfold, I couldn't do it. Being stoned all the time didn't help either.  I dropped the class.
« Last Edit: June 16, 2005, 12:10:36 pm by Bill St. Clair »
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Joel

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« Reply #6 on: June 16, 2005, 12:50:04 pm »

From that forum...

Quote
Does society allow a person with a college degree to say, "I'm sorry, I don't DO punctuation?" Or "I know it's difficult to read the memo, but you know me! I just don't DO complete sentences!" What has given these students the idea that basic math has become optional?

The answer to his first question, is "hell, yes, it does!"  And the person with the college degree can be quite well paid for it, and indeed seems to hold his 'not DOING punctuation (or grammar, or spelling, or whatever)' as a lodge pin for his profession.  Ever work with engineers?

I have no college degree.  Part of my JOB is to proofread and correct very basic English on the part of my "better-educated" - and much better paid - "superiors."  What gave THEM the idea that being able to communicate in their own language - on a very basic level - is optional?  I'll tell you what - the fact that they get away with it en masse, and on a daily basis.

It ain't just math.
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Bear

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« Reply #7 on: June 16, 2005, 01:08:55 pm »

I'd better clarify what I meant. My 'bone to pick' with the attitude is not that the
woman couldn't do math, but that she wouldn't do math, and thought
it was beneath her.

Bear
 
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mi6a2lm

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« Reply #8 on: June 16, 2005, 01:42:10 pm »

Quote
Quote
M16,

What the *hell* is that?
 
Looks to me like M16 really does math, not just the arithmetic that most people call "math". I took a graduate Abelian Algebra course during my senior year of college. They talked about the Sieve of Primes of the Kernels of Homomorphisms, or something like that. I had always been pretty good at proofs, but I realized in this course that I had been working before with a blindfold on. Because the undergraduate proofs I had been asked to do were like walking around a small room and bumping into the furniture, I could handle it. This graduate class, however, was more like being asked to find a teacup on a football field. Without a better mathematical intuition, some way to remove the blindfold, I couldn't do it. Being stoned all the time didn't help either.  I dropped the class.
The above definition is from this book at Amazon.

The author was my prof for two mathematical physics classes.  One day during a review session he asked for students to write-in suggestions for the class because he was using a proof version of his undergraduate text and he wanted some feedback.  Some of the students wrote in that it would be better to use more numbers in the examples.  He seemed to get slightly agitated and went into a discourse on why numbers really didn't matter that much when you are doing math and physics.  He wrote the number 57 on the board and asked what information or usefullness that conveyed.  Answer:  Not much.  Then he wrote an equation on the board and asked what information that conveyed.  Answer:  A lot!  And you could stick any set of numbers in the equation and get numerical answers or derive further important results without using numbers.    Being able to manipulate the symbols and derive further results are the important things.

Of course, numbers are important for real-life applications.  I don't think he was implying that they weren't - but most math and physics and any science derived from these do not need numbers until the final result.  

I note that the blog entry focuses on arithmetic, which I find too mechanical.  If I can avoid crunching numbers I do - I don't think it requires much analysis.  Once you learn the algorithm it just becomes tedious to keep track of what numbers go where.

It's interesting that while some of my profs would grade just as hard for an incorrect numerical answer (for example, I always make numerical mistakes in matrix multiplication), others wouldn't care at all just as long as the derivation was correct.  After all, anyone can do arithmetic.      :)

When I used to teach (as a teaching assistant) a 100-level physics lab, the students would always get hung up on using numbers first.  For example, take Hooke's Law as it relates to the standard weight-on-a-spring experiment:

F = ma = -kx

Given the mass, acceleration and the distance the spring is stretched, what is the spring constant, k?  Well, they'd start getting confused by trying to start plugging in numbers.  No!  Solve for k first, then stick in the numbers.  Don't worry about the numbers until the very end!  (This would confuse some of them - it seemed it wasn't arithmetic as it was the simple algebra that got them.)  Once I got it through to them how to get 'k by itself' they were able to solve, with a little nudging, other algebraic equations.

--------------------------------------------------------

Here's a bunch of tutorials on very theoretical probability.  No numbers here, either.  (This stuff is beyond me - maybe someday I'll learn enough to start studying it.)

http://www.probability.net
« Last Edit: June 16, 2005, 01:44:51 pm by mi6a2lm »
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debra

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« Reply #9 on: June 16, 2005, 01:56:28 pm »

How cool -- I understood everything from the statement, "The dimension of the vector space..."   B)  
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Joel

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« Reply #10 on: June 16, 2005, 01:58:29 pm »

Quote
Unfortunately, skools 2day do not teach math with rigor. When my daughter was in gubbmint school, they seemed to encourage 'creative' math.....just like they did creative spelling.

Of course none of the teachers actually *USE* math to earn a living. They have little real world idea of what advanced math is good for.
This was my problem with math in school.  Arithmetic was easy; I could see what it was good for, so it was worth my time to bend a few synapses into place so I could use it.

Algebra was agony.  I saw the logic of it.  It wasn't hard to do.  But what was it FOR?  It just seemed to be this pointless, Talmudic exercise with no application.  For years, I asked teacher after teacher to please tell me how to apply this esoteric nonsense to the real world.  Most reacted with annoyance, and NONE could/would provide a single example.

Years later, in tech school - I was now in my late twenties - I took a required Applied Math course while studying to be an auto tech.  I encountered a formula I'd seen a million times:  [well, I can't do the symbols here, but it's pi times the square of r, times the height]  All the ejukated people here immediately recognize this as the volume of a cylinder.  Assume the height is the stroke of a piston, multiply the result by the number of cylinders, and you've just calculated the cubic inch displacement of an internal combustion engine.

That was all it took; I felt like I'd found god.  I went around for a week, showing this elegant thing to everybody I knew.  Everybody I knew thought I had gone crazy, of course, because they already knew that.  But after that one example, which I still remember 25 years later, I couldn't get enough.

That was all that those benighted teachers would have had to tell me.  But they couldn't conjure even this everyday example, to answer an honest question that crippled me for years.
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UnReconstructed

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« Reply #11 on: June 16, 2005, 02:26:16 pm »

M16,

Thanks for the pointers to what that was......I got as far as Linear Algebra and Diffeq.....that was enough for the engineering degree. So it is probability theory......And I thought Tensors were hard......

John,

Yepper, I know the aha moment there well...I was sitting in the first few days of a Systems I class (once upon a time in a universe far away). The prof was going over laplace transforms ad nauseum. Although it was sorta interesting, I couldn't for the life of me figure out WHY he was doing this.......the class was supposed to be about systems...like servos and stuff.

So finally I asked him in class "Why are we doing all this stuff with Laplace Transforms?"

He looked at me as if I was sitting in the class naked .....and then thanked me for asking the question.

He replied:

"Because Systems are modeled with differential equations. You cannot easily solve Differential Equations, in fact, you may not be able to solve some of them at all. But you *CAN* solve an algebraic equation....and Laplace Transforms are a way to convert a differential equation to an algebraic equation"

Ding ding ding...the light went on. NOW I understand.........but I knew better than to try to explain it to my wife  B) ...she has listened to me rave about all kinds of things, and although she would nod her head sagely, and smile in the right places...............

and boy oh boy do I know about Engineers not being able to write or spell....it drives me up a wall......highly educated intelligent people....who cannot communicate effectively......
« Last Edit: June 16, 2005, 02:32:55 pm by UnReconstructed »
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H.M. WoggleBug, T.E.

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« Reply #12 on: June 16, 2005, 02:29:50 pm »

We're preparing to build a house. Boy, talk about applying geometry, algebra, and trigonometry! I'm going to inflict as much as possible on my two older kids.

I'm going to let them know that if the calculations are off, and we waste money, it's going to affect what we can place in THEIR ROOMS.

I want some rounded stuff, just so I can inflict that as a lesson. :)

Of course I won't TELL them that's what I'm doing. It'll just be natural.

My 11 year old already is becoming interested in programming, using Mindstorm. I am one of the few programmers that I know that actually uses UML to aid in design and programming. Mindstorm basically uses a variant of flowcharting to do its programming. My son is always excited to see my UML charts and identifying portions of it that are similar to Mindstorm.

I also use regular flow charting to flesh out some of the aspects of this [very large] project. He understands switches, if-then-else, loops, etc. I figure I can start using him in about a year, and pay him $.50 / hour. :)

Math is everywhere, and very useful. People don't like math because either they couldn't apply it, or they're afraid of it. Math was dreadfully boring for me until trigonometry. I had a use for trig at the time, so I became interested. Arithmetic should be taught carefully, math should just be everywhere.

'Bug
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Bill St. Clair

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« Reply #13 on: June 16, 2005, 02:38:42 pm »

Quote
So finally I asked him in class "Why are we doing all this stuff with Laplace Transforms?"

He looked at me as if I was sitting in the class naked .....and then thanked me for asking the question.

He replied:

"Because Systems are modeled with differential equations. You cannot easily solve Differential Equations, in fact, you may not be able to solve some of them at all. But you *CAN* solve an algebraic equation....and Laplace Transforms are a way to convert a differential equation to an algebraic equation"
 
I learned that on a test. We were studying Fourier Transforms. The test question was an electronic circuit with a simple feedback loop. We had not yet studied that kind of circuit. The secret was to realize that doing a Fourier Transform of both sides of the equation, switching from time to frequency, turned it into a simple algebraic equation. Then, after solving for the desired quantity, transform back to the time domain, and you're done.

Some people solved it with infinite series. Much harder to do that way, but it works.
 
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RagnarDanneskjold

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« Reply #14 on: June 16, 2005, 08:36:53 pm »

Interesting commentaries on math epiphanies in this thread, I have my own, but for now I just want to state - WTF - did anyone here read to the end of that article by Jay Odaffer?
Quote
The thrust of her argument seemed to be that calculators and spreadsheets make arithmetic unnecessary and that she will have no use for anything more advanced in her chosen career.

She is going to be a teacher.
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