yeah. That's right.
From Mathematics:Birth of Numbers, by Gullberg
"Unfortunately very few people have this kind of apprecia-
tion of the true nature of mathematics. The most common
fallacy, even among otherwise well-informed people, is, as we have said, to confuse mathematics with elementary arithmetic, and thus to suppose that progress in mathematics consists of performing ever more complicated calculations with speed, dexterity, and accuracy. Thus, for example, Dustin Hoffman received an Oscar in 1989 for his portrayal of the autistic brother in the film 'The Rain Man'. This person is an 'idiot savant', capable of performing rapid, totally unmotivated mental calculations such as computing 341 x 127, or taking m to 10 decimal places. However, he is described by various critics, in their reviews of the film, as a genius. It is surely unnecessary for me to belabor the point further that
such an extraordinary ability, far from being evidence of
genius, is usually an indication of stupidity - as in this case.
There have been rare exceptions, such as the great German
mathematician, astronomer, and physicist Karl Friedrich
Gauss, the British civil engineer George Parker Bidder, and the statistician A. C. Aitken. However, it is interesting and significant to note that Gauss's powers of mental calculation declined as his genius grew, thus testifying to the antithesis between calculation and mathematical insight which we are claiming to exist. "
So why don't my teachers every give partial credit for my understanding of the problem?
How high level are the problems? If it's seriously high level math, they should be giving substantial partial credit for set up and comprehension, with minor deductions for trivial errors.
(I ask because I forget what math you are studying...sorry.)
I don't know what the math I'm studying is called, but it is mostly proofs of algebraic equations, series, and such. History of mathematics stuff.
Proof by mathematical induction, binomial theorem (re-hash for me but we are studying some other angle of it--haven't gotten to it yet), truth tables. Mostly algebra based but higher level. The focus isn't on the algebra, in other words. I forget some of the rules, so I get a nick here and there. It frustrates. I'll just keep kissing his ass.
Mm...that's why you lose points. Rules and proofs are the whole point of math like that. Memorization and rote application.
When you hit differential equations, they tend to care a lot less if you make a sign error.
(Please don't be offended - I'm not trying to belittle you here.)
I have to choose for next semester among
I think I'll wait on the stats.
Calc 2 is where it starts getting interesting, to me.
Discrete was ok. Depending on your prof, you get into some interesting stuff on graph connectivity and partitioning problems.
"Memorization and rote application. "
I don't see any of that. I haven't memorized anything except basic stuff. If you know the basics, you derive the rest.
I'm not offended, but whenever I talk math with certain kinds of people, it always ends up "well, that's the way it is supposed to be." rather than a reasoned answer.
I've had calc II and III, but I remember little of them so I'm re-taking. 20 years ago, wow. Let's see, 2006-1986. Yup. Twenty years.
Ah...yeah. I just did that. Sorry.
There should be points for setting up a proof overall, getting the framework right. Historically, though, there have been tons of proofs that had a minor hole in them that invalidated the whole frickin thing, so they tend to be sticklers about the details. The details do matter, of course, but not enough to go ballistic over like they seem to.
Here's a good quote about it from the same book:
"The usefulness of mathematics leads to other, related
abuses. Since mathematics is useful, its acquisition must be tested. Since, in the perverse view we are deprecating, it is a skill, it is tested as a skill. Since it is useful, it must be taught to all. Thus the testing problem becomes enormous, and grading by machine becomes commonplace. The result is that standard tests are applied that have almost nothing to do with the acquisition of mathematical understanding and put a premium on brute knowledge and memory, speed and slickness.
They provide no opportunity for the student to explain his or her answer and treat all 'wrong' answers as equally wrong. They are, in short, inimical to mathematics itself. "
Math gets easier when I figure out how to symbolize and apply my programming background to it. When I start listening to the teacher giving rote instructions, I stop learning.
I think a lot of people would be better at math if I had a teacher like Mr. Magee. Mr. Magee taught high school geometry and I absolutely loved him. He was entertaining and really TAUGHT. To demonstrate certain principles, he would make us all get up and physically get involved. Shortest distance, proving pythagorus, etc. That was the last time I had such a great math teacher.
If I can get through this program, maybe I'll consider being a Mr. Magee.
Sharky, I had the same problem with finite geometries. By the time I grasped the notion we had moved on. It hurt my grade in what was otherwise an excellent class for me, one that I understood and actually did well in, other than bombing the first third.
That was one of those classes where finding a quiet place to study was paramount. One night I exhausted a friend's apartment, the dorm lounge, and even the locked storeroom in the basement that I'd used for most of the semester. It took a lot of concentration, but I felt that it was definitely worth it.
I can relate. I'm really slow. I figured out a problem on the homework completely on my own, but it took two days of thought. He worked it out in class because no one got it. If I always had that much time, I would be pretty good. But since I don't...well.
I've taken to studying math with classical music on. It really helps me focus. I code better with it too.
What classical music are you using?
September 27th, 2006 10:36pm
Right now it is mostly Leila Josefowitz on this Ann Rice album playing some Hungarian sounding violin solos, along with my favorite Tchaikovsky solo, and Paganini violin solos featuring who knows who playing some wickedly difficult music.
I really wish I knew how to pick cello solos.
For those that want to know, here are the topics in my syllabus
1. Logic of Propositions, Expressions and Tautologies, and Quantifiers
2. Methods of Proof including, direct, indirect, and contrapositive
3. Operations on Sets
4. Proofs by Induction
5. Relations, including equivalence relations and compositions of relations
6. Functions as relations
Teacher just posted everyone's grades from homework assignments (I can see everyone's grades), but the points aren't weighted so that you can compute your exact grade. So a homework assignment might be 140 points, the exam worth 100, but all the homework is only 10% while all the exams are worth 30%. So I really don't know what my grade is.
I'm not sure here but I think algebraic equations and proofs are required to be practiced. Aren't they like chords and scales in guitar? Though they themselves don't make songs but we need to work on them to progress to songs. But if the focus isn't on Algebra, what else can it be on?
You think it won't make any difference if you skip this stuff and go to Calculus?
September 28th, 2006 12:43am
Pi is good. Euclid is good. Lie algebra is good. Using Cartesian ccordinates to figure out your own grade is not good. No, it's not. No.
Revolt against the tyranny of the ruler. The autarky of the compass, the hegemony of the Peano postulates. Revolt fair lass. Peace. (And pi.)
September 28th, 2006 3:11am
sharky, try the YoYo Ma or the Casals version of the Bach Cello Suites (you *have* to at least hear the Casals). good recordings of the 48 too (try glenn gould).
Bach's instrumental music in general is great for studying. Or just great. The violin suites, or a *good* recording of the flute/harpsichord/viola de gamba stuff. (there is one with Janet See on Harmonia Mundi that is killing ... *don't* buy some smartass french speed merchant flute version.)
learning to solve DE's is cool, but will melt your brain. I could do it 20 years back, but I felt I needed more time to digest it, and before I knew it we were on to Laplace and stuff, where I started to lose it. Fourier Transforms are the shit though. That says so much about so much.
September 28th, 2006 4:30am
"Casals version of the Bach Cello Suites (you *have* to at least hear the Casals)."
I have that one. I must have a bad recording or something because it doesn't sound good to me.
"You think it won't make any difference if you skip this stuff and go to Calculus?"
Who said anything about skipping? Who starts college at algebra? You would review it on your own. Which I do.
You're 40 and still thinking about the grade. You *really* need to reconsider the essential purpose of education. Stop wasting time and energy begging for partial credit and worrying about the weight of a quiz vs. a homework.
September 28th, 2006 12:14pm
Good points. However, you either don't live in the USA or you have not a clue about the financial situations that put us in places we don't want to be.
1. 40 is approaching. Nobody is dying to have me in a good grad school
2. I don't have the money for a good grad school
3. As a minority female, if I want to go to a good grad school and get money to do so, I have to earn a scholarship or grant of some kind.
I must get decent grades. Sure, I could get all C's and cruise, learn a bunch, have a good time. Or I could do better and increase my options. With the clock ticking, my options are fewer and fewer.
This is why it is called a mid-life "crisis". We are under pressure to do something with our lives before we die. We can only hope we have chosen wisely, understood ourselves well enough to go in the appropriate direction, and perform well enough so that our work is not all for naught.
Oh, and no one need preach about what education is. I've suffered at the hands of many an ambitious professor who could give two shits about whether they were actually teaching anything of consequence.
Keep it up, sharkfish. You have a super spirit...
September 29th, 2006 1:23am