# SAT anyone?March 24, 2012 10:35 PM   Subscribe

I love the first math question that totally blows his mind. It's q
posted by Mitrovarr at 10:42 PM on March 24, 2012

Quite possibly the easiest math question ever.

Also, what button on your keyboard will instantly post your half-finished comment if you happen to randomly flail into it? It's happening enough times now that I'm getting annoyed about it.
posted by Mitrovarr at 10:43 PM on March 24, 2012 [10 favorites]

You better get that worked out, the internet commenting section of the test is coming in a few years.
posted by furiousxgeorge at 10:45 PM on March 24, 2012 [42 favorites]

You may as well have asked me to climb Everest using a fork.

As a mature student presently taking Calculus, and a mediocre mountain climber, this sentiment hits home.
posted by klanawa at 10:48 PM on March 24, 2012 [8 favorites]

and if you were unfortunate enough to be some Polish kid with a 30,000-letter last name, you were dead and buried before you'd even reached the antonyms.

Gee, I wonder what that's like.
posted by tylerkaraszewski at 10:55 PM on March 24, 2012 [103 favorites]

What Happens When a 35-Year-Old Bro Retakes The SAT?

Evidently, he writes a self-righteous rant that incidentally reveals how frustrated people who were failed by public education get when faced with evidence of their own ignorance.

For the record, I'm not saying that every 35-year-old needs to know the relationship between a polygon's number of sides and the sum of its angles; I'm saying that the sign of becoming educated is to face such a problem with something other than tooth-grinding anger at the test itself.
posted by belarius at 10:59 PM on March 24, 2012 [54 favorites]

That second math question is a bastard. I can figure out how you get the size of the interior angles, but I have no idea how you'd ever proceed from that point without looking something up. I mean, if you just happen to KNOW the interior angles of the 6-10 sided regular polygons, or have the formula for calculating it memorized, you could do it, but that seems incredibly unlikely unless you memorized your geometry textbook for fun.
posted by Mitrovarr at 11:00 PM on March 24, 2012

I took my SATs under extreme duress and also hungover. I didn't want to take them at all but I was told I should and blowing them off would be a bad thing to do. I think I got a near perfect on the language part and did so so in math.

This writer is trying to hard by a factor of ten.
posted by The Whelk at 11:01 PM on March 24, 2012 [2 favorites]

Mitrovar, the interior angles of a regular polygon (or, I'm pretty sure, any entirely convex polygon) have to add up to 360. It you didn't know this (and I had forgotten it) can pretty confidently infer it from first principles if you just think about an equliateral triangle and a square, which are simple enough to work out visually.
posted by George_Spiggott at 11:05 PM on March 24, 2012 [2 favorites]

Please sum up the interior angles of a triangle and try that again.
posted by aspo at 11:06 PM on March 24, 2012 [24 favorites]

George_Spiggott: Mitrovar, the interior angles of a regular polygon (or, I'm pretty sure, any entirely convex polygon) have to add up to 360.

Really? The interior angles of a triangle sure seems to add up to 180 to me. Isn't 360 only true for a quadrilateral?
posted by Mitrovarr at 11:06 PM on March 24, 2012

Aw, beat to the punch.
posted by Mitrovarr at 11:07 PM on March 24, 2012

Mitrovarr: A regular n-sided polygon can be thought of as n isosceles triangles stuck together at the center point. So if the interior angles of the polygon are, e.g., 140 degrees, you've got a bunch of isosceles triangles that each have two angles of 140/2 = 70 degrees. The other angle of each triangle is thus 40, so there are 360/40 = 9 such triangles around the center point, hence 9 sides.

George_Spiggott: The only regular polygon whose angles sum to 360 is a square.
posted by zeptoweasel at 11:08 PM on March 24, 2012 [19 favorites]

That second math question is a bastard.

Mitrovar, the interior angles of a regular polygon (or, I'm pretty sure, any entirely convex polygon) have to add up to 360.

No, because once you get greater than 4 sides, you start having obtuse angles, and more than 4 of those is going to get you way over 360. The complimentary angles (the angle you have to add to the interior angle to get to 180) should add up to 360.
posted by LionIndex at 11:08 PM on March 24, 2012

Oh, for that edit/delete capability....
posted by George_Spiggott at 11:08 PM on March 24, 2012 [2 favorites]

I won't take the SAT because it's un-American. They want you to use a No. 2 pencil, and everybody knows we're No. 1.
posted by twoleftfeet at 11:09 PM on March 24, 2012 [8 favorites]

Maybe it's culture shock but he seems awful upset at having to fill in scantron and stuff, when I remember doing that in like second grade.
posted by The Whelk at 11:09 PM on March 24, 2012 [3 favorites]

Mitrovar, the interior angles of a regular polygon (or, I'm pretty sure, any entirely convex polygon) have to add up to 360.
I'm pretty sure the angles of a triangle add up to 180.
That second math question is a bastard. I can figure out how you get the size of the interior angles, but I have no idea how you'd ever proceed from that point without looking something up.
I was a little stuck, the 'cropped' polygon is a rhombus, which is made of two triangles, so the interior angles must sum to 360. Since we know the angles that match with the paper sum to 80, we have 280 degrees left. 280/2 = 140.

But, I didn't know the formula for figuring out what polygon that corresponded too, so I ended up looking it up
posted by delmoi at 11:09 PM on March 24, 2012

More about interior angles of polygons.

I didn't remember this stuff either, but I did remember that it's in the study guide. The SAT covers such a limited range of math that it's not terribly difficult to memorize the few formulas you might need.
posted by xil at 11:10 PM on March 24, 2012 [2 favorites]

Question 2:

1. Any regular 4 sided polygon has 360 degrees as the sum of its interior angles.
x + y = 80. So, the other two angles added together makes 280.

2. All angles and sides are equal, so, 280 / 2 = 140 degrees per angle

3. (n-2) × 180° / n (where n is the number of sides) is the formula to calculate the interior angle.

4. (9 - 2) x 180 / 9 = 140.

5. 9 sides.
posted by The Giant Squid at 11:11 PM on March 24, 2012

Does nobody like the isosceles triangle method? :(
posted by zeptoweasel at 11:12 PM on March 24, 2012 [2 favorites]

See, I don't remember those rules. All I remembered is that the sum of the angles has to be divisible by 180, because making a complete circuit leaves you where you started.. So I experimented. 140*6/180, 140*7/180, 140*8/180, 140*9/180, 140*10/180. Only 140*9/180 is a whole number. So I figure it's that.
posted by kafziel at 11:13 PM on March 24, 2012 [1 favorite]

The most interesting part is about the SAT grader who has to read all those essays. A real story there somewhere.
posted by stbalbach at 11:13 PM on March 24, 2012 [3 favorites]

Metafilter: trying to hard by a factor of ten.

Yes, now it's a verb. Shut up, that's why.
posted by joe lisboa at 11:14 PM on March 24, 2012 [10 favorites]

Also seriously man these are not difficult questions. I guess if you don't remember what a graph even is, maybe #16 will throw you? But even then it should be obvious that y=g(x) is just one higher than y=f(x), so the answer is B.

And I guess you need some vocabulary for the vocabulary question. Still, not hard to know what those words mean.
posted by kafziel at 11:14 PM on March 24, 2012 [1 favorite]

Is my 1360/1600 equal to 2040/2400, straight-up? I do not recall an essay, at all. (I took the test in the early 1980s.)
posted by maxwelton at 11:16 PM on March 24, 2012

After all that complaining, he still ended up at about the 96th percentile.

My theory: This is his way to finally get to brag about his high SAT score without being so boorish as to come out and say it directly.
posted by Winnemac at 11:19 PM on March 24, 2012 [12 favorites]

Another approach to solving the geometry question is to calculate the interior angle to be 140, which means the line changes direction by 40 degrees each angle. Since you know it makes a whole circle, you know it has to complete 360 degrees by the end. Divide 360 by 40 and you can determine that it turns nine times before the end, so it's a nine-cornered (and thus nine-sided) figure.
posted by Mitrovarr at 11:19 PM on March 24, 2012 [10 favorites]

They just instituted the essay a few (possibly many) years ago, and they've "adjusted" the scoring (I don't know when most recently, but a year or two after I took it in 1993 they did), so that your score from before those adjustments doesn't really correlate.
posted by LionIndex at 11:19 PM on March 24, 2012

Another approach to solving the geometry question is to calculate the interior angle to be 140, which means the line changes direction by 40 degrees each angle. Since you know it makes a whole circle, you know it has to complete 360 degrees by the end. Divide 360 by 40 and you can determine that it turns nine times before the end, so it's a nine-cornered (and thus nine-sided) figure.

Basically, there's so many ways to calculate the correct answer that it's really kind of baffling that he didn't think of or figure out any of them.
posted by kafziel at 11:21 PM on March 24, 2012 [3 favorites]

What an atrocious article.

No shit sherlock, you wouldn't be as up to date as a high-schooler who took math lessons last week.

The title should have been "35 year old man manages to coerce kids off of his lawn". Maybe I'd learn something from that.
posted by Sphinx at 11:23 PM on March 24, 2012

I feel him on the blue book. When I took some courses at community college they put me on a remedial English class based on a placement essay. I had taken multiple college level English courses before that point so it came as a bit of a shock. I stayed in the remedial class for half an hour the first day before the teacher realized it was a mistake. I'm pretty sure the problem was just that I have godawful handwriting and the grader did not look past that in a super quick grading of the essay.

posted by furiousxgeorge at 11:23 PM on March 24, 2012 [1 favorite]

It's probably the time limit - it took me a while to figure out a solution that didn't rely on a formula I didn't have memorized. I tend to be decent at math but I do it slowly, which hurt me on the GRE somewhat (not enough to keep me out of grad school, but it's a good thing I'm a Biologist, so the requirement wasn't so high).
posted by Mitrovarr at 11:24 PM on March 24, 2012

Divide 360 by 40 and you can determine that it turns nine times before the end,

Which bizarrely enough is exactly what I did to arrive at the answer. Then did a hasty shit job of explaining to myself what I had done and had the poor sense to post it.
posted by George_Spiggott at 11:24 PM on March 24, 2012 [1 favorite]

the 'cropped' polygon is a rhombus [link mine]

Actually, the quadrilateral isn't a rhombus in that the partially covered edges clearly can't be parallel. There's a minor possibility that it could have been a trapezium (or a 'trapezoid', as it is apparently called in en-US) judging by the shape, but really, we have no information on whether the edge of the paper is placed parallel to the only completely visible edge of the polygon. The _only_ information you have about the newly formed figure is that it's a quadrilateral.

Once you realize that, and understand that the only information you have is that the newly formed figure is a quadrilateral, you should be set to solve. :)
posted by the cydonian at 11:30 PM on March 24, 2012

I took the SATs for Sociology majors. It's quite different. For example, we had the following essay question:
If you arrange N triangles in a circle, sharing a common vertex, then the total sum of all that angles in all the triangles is N times 180 degrees, because there are N triangles and each one has 180 degrees. If you ignore all the angles around the central vertex, you are ignoring one circle's worth of angles, so you are ignoring 360 degrees, because it takes 360 degrees to go around the circle. How do the triangles feel about the angles that are ignored? What could be some of the ramifications for the community of triangles described in this problem? Suppose not every triangle had angles adding up to 180 degrees; how could you help these triangles?
posted by twoleftfeet at 11:37 PM on March 24, 2012 [41 favorites]

Eh, the guy's an idiot. I recently berated some idiot kid on my blog who claimed that the idea that the angles of a triangle added up to 180 required "faith" by providing him with a simple proof off the top of my head, and as for the question that exploded this dude's mind, the answer was rather very obviously b, g(x) = f(x) + 1, so.... yeah, dude's dumb as a box of rocks at 35, quite a tragedy. And I'm 43. I'm practically dead.
posted by smcameron at 11:44 PM on March 24, 2012 [4 favorites]

My theory: This is his way to finally get to brag about his high SAT score without being so boorish as to come out and say it directly.

I did really well on the SAT in high school. I didn't plan to, and in fact, had by that point resolved that I was not going to go to college, so I really didn't even want to bother.

But one of my good friends (alex) mother was concerned that I wasn't taking the SAT so she offered to pay for me to take it the same weekend he did. In practice that meant Alex spent the weekend studying for the SAT, and I spent the weekend sneaking shots of whisky from Jason's dad's liquor cabinet while we played D&D in dad's basement. Come time for the test, I basically rewrote the answer key and Alex got his ass handed to him.

I offered to fake him on the next attempt and, well, he got accepted into the UofM. I went on to get kicked out of the marines and he got a job repairing electron microscopes.

I don't know what the point is, except to point out that I wasn't ready for college even though I tested well, and my friends who didn't test well went on to excel at college and well, we all knew the system was bullshit from start to finish and we didn't give two shits about exploiting those weaknesses for our gain.

I had to take the ACT as an adult, and it was interesting to be a 30 year old dude in a room full of 17 year olds. I hadn't really felt my age in such a way before. I do all the time now, but I'm gonna be 40 in a college town.

Anyway, I did well, again, but it proved meaningless - I got rejected due to my poor HS grades. I spoke with the admitting secretary at the college of engineering and she told me what to do - go to community college, excel and apply - and win.

I did and I did. BSEE FTW. Fuck you, haters.
posted by Pogo_Fuzzybutt at 11:50 PM on March 24, 2012 [28 favorites]

I fumed about this article earlier this week. I guess I'm not over it yet, because I was angry just reading the title when it popped up here. There are many, many, many problems with high-stakes standardised testing, but this article doesn't address them in any coherent way. And sometimes his complaints are arse-backwards:
The SAT … front-load[s] most sections with a few softballs, so that stupid kids can get at least a few questions right… But as you get deeper into each section, the questions take a nasty turn. Like so.
That's exactly how it should work. The point is to allow students to demonstrate what they know and understand, which means questions at every difficulty level from piss-easy to fiendish, with the easy ones at the start so that people don't run out of time before getting to the questions they can answer.
Christ. Where do you even begin to figure out the methodology needed to solve this?
Perhaps by taking the class the test is associated with. It's been 11 years since I learned any maths, but I still knew the interior angles rule we had been required to memorise for exams back then. The fact that you need to memorise these kinds of things is one of the big failings of this type of assessment, but it's reasonable for the testers to assume you've studied the course, and if you haven't, then STFU about how it's impossible to work out the answer.
I guessed. I guessed wrong. That's the amazing thing about the SAT. YOU WILL NEVER GUESS RIGHT.
Actually, here's the thing about multiple choice tests: you WILL guess right, at least part of the time. If it was truly impossible to guess right, that would be a very good multiple choice test.

(I also think it'd be preferable that a 35yo man avoided gratuitous jokes about 15yo girls' panties, but that's me.)

Of course, this guy isn't the first adult to sit a high school test. Last year an experienced teacher and school board member took Florida's 10th grade maths and reading tests, and shared his experience:
“I won’t beat around the bush,” he wrote in an email. “The math section had 60 questions. I knew the answers to none of them, but managed to guess ten out of the 60 correctly. On the reading test, I got 62% . In our system, that’s a “D”, and would get me a mandatory assignment to a double block of reading instruction.

He continued, “It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate.

“I help oversee an organization with 22,000 employees and a \$3 billion operations and capital budget, and am able to make sense of complex data related to those responsibilities.

“I have a wide circle of friends in various professions. Since taking the test, I’ve detailed its contents as best I can to many of them, particularly the math section, which does more than its share of shoving students in our system out of school and on to the street. Not a single one of them said that the math I described was necessary in their profession.

“It might be argued that I’ve been out of school too long, that if I’d actually been in the 10th grade prior to taking the test, the material would have been fresh. But doesn’t that miss the point? A test that can determine a student’s future life chances should surely relate in some practical way to the requirements of life. I can’t see how that could possibly be true of the test I took.”

Here’s the clincher in what he wrote:

“If I’d been required to take those two tests when I was a 10th grader, my life would almost certainly have been very different. I’d have been told I wasn’t ‘college material,’ would probably have believed it, and looked for work appropriate for the level of ability that the test said I had.

“It makes no sense to me that a test with the potential for shaping a student’s entire future has so little apparent relevance to adult, real-world functioning. Who decided the kind of questions and their level of difficulty? Using what criteria? To whom did they have to defend their decisions? As subject-matter specialists, how qualified were they to make general judgments about the needs of this state’s children in a future they can’t possibly predict? Who set the pass-fail “cut score”? How?”

“I can’t escape the conclusion that decisions about the [state test] in particular and standardized tests in general are being made by individuals who lack perspective and aren’t really accountable.”
posted by robcorr at 11:53 PM on March 24, 2012 [36 favorites]

I didn't remember my polygon formulas, so I solved the problem by assuming the edge of the paper was parallel to top edge of the polygon. Narrowing the problem to this specific case made it easier to think about test cases.

Three easy cases to visualize are squares, hexagons, and octagons.
If it is a square, then x+y would be 180.
If it is a hexagon, then x+y would be 120.
If it is an octagon, then x+y would be 90.

So that narrows it down to a 9- or 10-sided polygon. Finding a simple formula that fits the three test cases suggests x+y = 720/n. Therefore n=9.
posted by ryanrs at 11:53 PM on March 24, 2012

BTW, the SAT isn't supposed to be relevant to "adult, real-world functioning". It's supposed to predict performance in college. That's why colleges care about your SAT scores but pretty much no one else does.
posted by ryanrs at 11:57 PM on March 24, 2012 [1 favorite]

I figured out the polygon one by pretending I was in a car driving around a giant chalk outline of the polygon on the ground. Obviously, to trace the polygon and get back to where you started, you'll always have to turn your car through 360 degrees, but the angle of each turn in the car doesn't match the interior angle of the polygon. Imagine an equilateral triangle where each interior angle is 60 degrees: when you drive up to that angle in your car, you're going to have to make a sharper-than-90-degree turn. Actually: (180 degrees) - (the interior angle of the polygon).

So, you can make a formula that looks like this:
sides*(180-angle) = 360

You can also use the same car analogy to figure out what 'angle' should be. Drive around the visible shape, and you'll have done your 360 degrees. Subtract the 80 degrees mentioned, and your remaining interior angles are 140 degrees each.

sides*(180-140) = 360
sides*40 = 360
sides = 9

I'm fairly confident that's correct.
posted by tylerkaraszewski at 12:00 AM on March 25, 2012 [2 favorites]

ryanrs: “BTW, the SAT isn't supposed to be relevant to ‘adult, real-world functioning’. It's supposed to predict performance in college. That's why colleges care about your SAT scores but pretty much no one else does.”

Colleges care about SAT scores because they've been marketed a pile of crap. SAT scores are not at all predictive of college performance. The studies showing that SAT scores are predictive of college performance are quite flawed, and it turns out that most good studies indicate that it's a very weak predictor of college performance.

The SAT is a pile of unmitigated nonsense that nobody should have to go through.
posted by koeselitz at 12:02 AM on March 25, 2012 [18 favorites]

me: “Colleges care about SAT scores because they've been marketed a pile of crap.”

Okay, I retract this bit. Colleges generally know that SAT scores are crap. They only use them because high school grades are even more crap for predicting college performance, and because they need something to use to eliminate people and make themselves look good to everybody else.
posted by koeselitz at 12:05 AM on March 25, 2012 [2 favorites]

posted by koeselitz at 12:06 AM on March 25, 2012

I LOVED the SAT. I really looked forward to taking it and I scored very, very well. But then I dropped out of college. Hmm, maybe you're right.
posted by ryanrs at 12:07 AM on March 25, 2012 [7 favorites]

Ha, I actually loved the SAT, too. I've always kind of had a knack for doing multiple-choice tests, so it was lots of fun. Then I went to a college where they didn't even look at my SAT scores. One of my classmates (who did much better than I did, truth be told) hadn't even finished junior high. I've come to feel as though my little knack for multiple-choice tests is pretty much meaningless. Colleges should ask for a good essay, interview applicants thoroughly, and just ask a lot of their students when they get there.
posted by koeselitz at 12:10 AM on March 25, 2012

Like many of you, I am eager to note the meaningless of the SATs, and also my own high scores.
posted by naoko at 12:13 AM on March 25, 2012 [64 favorites]

You'd really think that the SAT would be a better test than any individual school could put together; certainly, they have a lot more effort to spend on writing it, experts specifically devoted to writing test questions, and all the cumulative years of expertise from having done it so many times. Probably, it's just difficult to accomplish the task they are trying to do; predict future college performance from a single test that can't be too difficult to administer or grade.
posted by Mitrovarr at 12:13 AM on March 25, 2012

author:cranky pants::SAT:asshole tone
posted by mosk at 12:17 AM on March 25, 2012

That's the amazing thing about the SAT. YOU WILL NEVER GUESS RIGHT.

You will occasionally guess right. In fact, since there are five possible answers for each question, you will guess right about one-fifth of the time. That's not often, so it seems like you guess right very infrequently. Confirmation bias and people are bad at estimating probability, etc, etc.

All you do is tally up the number of questions you got right and the number you got wrong, multiply the number you got wrong by .25 (????), subtract that number from the number you got right for your "raw score," and then look up that raw score on a conversion table to get your actual score . . . I don't know why the test is scored like this.

And that's exactly why: given an average one correct guess out of five and the corresponding four quarter-points deducted for incorrect answers, this scoring system will tend toward a score of 0 for a random guessing strategy, instead of 20%.

The geometry problem aside, people with this level of ignorance cum contempt for math drive me up the wall as bad as people who misuse apostrophes.

It strikes me as yet another needless complication in an already needlessly complicated test.

Actually I remember this mantra clearly from being prepared for the SAT in high school: don't guess, unless you can eliminate one or more of the options, in which case do.

Not that complicated or hard to remember, but I do remember it driving me crazy that I was just told to do this, until my physics teacher helpfully explained the above.
posted by 7segment at 12:20 AM on March 25, 2012 [7 favorites]

Like many of you, I am eager to note the meaningless of the SATs, and also my own high scores.

Heh. IQ test threads are also fertile ground for this.

In 7th grade I got 760 on the Math section, pre-centering.

Still a peon code monkey today though.

posted by kmz at 12:26 AM on March 25, 2012

If random guesses tend towards a zero score, it does not hurt to guess even if you can't eliminate a choice. But I suppose your rule encourages the student to try to eliminate some choices.
posted by ryanrs at 12:28 AM on March 25, 2012 [2 favorites]

Yes, that occurred to me as I was typing that....

Or it encourages the student towards risk-aversion? Or to spend less time filling in the bubbles?
posted by 7segment at 12:36 AM on March 25, 2012

I don't think my score was especially good, but it wasn't bad, and I also dropped out of college. Maybe BECAUSE the test planted a lazy bomb in my brain. I am so suing.
posted by maxwelton at 12:37 AM on March 25, 2012

What I like about the math problem is that, since they imply it works for any angle of the paper, you can just assume the paper is parallel to the top side, which makes it much easier.

What I always liked about geometry is that you could get by by knowing, like, three facts, if you had a quick facility for putting them together in the right sequence, usually involving drawing some extra lines somewhere. My ideal in mathematics was imagining there was some best kit of facts and tricks, maybe a dozen, that would allow you to quickly solve almost anything. Obviously the axioms of geometry and arithmetic will allow you to do this in theory, but in practice, the set of most-useful tools is likely to include simple but slightly higher-level concepts -- though not too high. For instance, I could never remember the 5 axioms of geometry, but remembering that the sum of the angles of a triangle was 180, plus a willingness to draw triangles all over the place, allowed you to solve, like, 90% of the puzzles they gave you in geometry class. I miss those days of discrete, achievable puzzles.
posted by chortly at 12:42 AM on March 25, 2012 [1 favorite]

The way that made the most sense to me to solve the polygon problem:

Shaded area has 4 sides. 4 sided figures always have internal angles that = 360°.

The two unknown angles are the same because an n sided polygon is made up of isosceles triangles.

360°-80°= 280°. 280°/2 = 140°.

So each of the unknown angles is 140°. Knowing that each outer corner of each n sided polygon has an angle of 70°, half the inner most angle of the isosceles triangle is 180° - 90° - 70° = 20°. There are 360° if you rotate around the inside and each isosceles triangle has an inner angle of 40°.

360/40 = 9.
posted by Quack at 12:44 AM on March 25, 2012 [1 favorite]

Chortly, it's much the same in (high school) physics. If you're good with units, you don't have to memorize very many equations.
posted by ryanrs at 12:46 AM on March 25, 2012

I mean seriously, HOLY FUCK. My mind exploded when I looked at this.

Then you are stupid and you will die.
posted by flabdablet at 12:50 AM on March 25, 2012 [4 favorites]

What a dumbass. REALLLY easy to see why he only got a 4 on the essay, though.
posted by Joseph Gurl at 1:02 AM on March 25, 2012 [2 favorites]

My process for the polygon problem: it's obvious that angles x and y will sum to the same thing regardless of the tilt of the paper edge wrt the polygon, because any tilt that increases x will decrease y by the same amount and vice versa. So tilt the paper to make its edge run parallel to an edge of the polygon. Now x and y are equal, which makes them both 40°; that's also the complement of the polygon's interior angles, and since those complements must sum to 360° to make the polygon close and since the question specifies that the polygon's angles are all equal, there must be 9 of those angles and therefore 9 sides.

In fact, I would recommend that no one take the SAT ever. It's a sternly worded dinosaur of a test, graded in an arbitrary manner with outdated equipment, and it blows.

What a no-account whiner.
posted by flabdablet at 1:05 AM on March 25, 2012 [1 favorite]

This guy is 35? Judging from his writing style, I'm guessing he spent a good 10 years or so as a pothead living in his parents' basement.
posted by i_have_a_computer at 1:39 AM on March 25, 2012 [2 favorites]

Maybe it's culture shock but he seems awful upset at having to fill in scantron and stuff, when I remember doing that in like second grade.

I also remember scantrons from the second grade. I also Remember President Jimmy Carter and 8-Track tapes from the 2nd grade. It's actually kind of amazing that a bit of technology dating back to the 1930s is still the best thing going for it's specific use.
posted by billyfleetwood at 1:46 AM on March 25, 2012

So once again I'm the only one, except from the original poster perhaps, who liked this post?

Because it sure did capture my feelings about test and exam taking and the huge relief it was once I dropped out of uni not to be subjected to them anymore. Also all the little frustrations like having to write everything out in longhand, or indeed the feeling of being dropped cold in front of a maths question you have to think about to even understand what's being asked.

Now not being of the yank persuation I never had to take the SAT, though we had similar ones in Holland, so it surprised me to learn you were supposed to not skip questions but answer everything in order, had to wait between sections, couldn't use scratch paper to try out stuff, etc. My teachers actually expected us to do all these things, to skip questions we didn't understand and come back to them, to just read through all the questions at first then do those you feel confident about and you could always take a pee break and use scratch paper, you just couldn't take it with you at the end of the exam.

BTW, if you've commented about how dumb this guy was for not getting an obvious answer to an easy question, you fail reading comprehension forever. This wasn't about how easy or difficult the tests are, but about the subjective experience for quite a few people of taking it.

Proof of this left as an essay question on your next SAT.
posted by MartinWisse at 1:47 AM on March 25, 2012 [24 favorites]

Sure you had scratch paper, a calculator, and could answer the questions in whatever order you liked. Some tests are divided into timed section, for instance a multiple choice part and an essay part.

posted by ryanrs at 2:06 AM on March 25, 2012

There's a Hogarth-Hughes-on-espresso vibe in here.
posted by obiwanwasabi at 2:15 AM on March 25, 2012 [2 favorites]

He's not dumb, just miseducated. It's very easy to leave high school with a) the misconception that math is about memorizing formulas and b) having weak quantitative reasoning skills. The system failed him at a time when he had the most potential to learn this stuff.
posted by polymodus at 2:35 AM on March 25, 2012 [6 favorites]

I don't know what the big deal is - I got a perfect score on my Sat's. I mean Jesus, on the Internet why wouldn't you?
You also don't know that I am, in real life, actually a dog. Oh annonymity, you complete me.
posted by From Bklyn at 2:50 AM on March 25, 2012 [6 favorites]

I'm relieved that I was able to take the SAT before the essay requirement was added. Not only would I have done significantly worse, there would have been markers outside my house protesting my handwriting. As it is I put up with thinly-veiled threats of violence from teachers for years.

*hugs keyboard* thank you for allowing me to pretend I can string words together.
posted by vanar sena at 2:55 AM on March 25, 2012 [5 favorites]

I honestly feel baffled that anyone would fail to see how easy that question on functions f and g is. Now, the polygon one does need a bit of joined-up thinking to reach the answer, but those functions? Come on. No excuse.

It annoys me that there is almost a cultural acceptance of being no good at basic maths and science. It's almost as if it's somehow cool to say "OMG, I'm so bad at maths." yet it makes you an uncultured lout to say, for example, that you don't understand Shakespeare.

This needs to change. People should be as embarrassed to be scientifically and mathematically ignorant, and they should do something about it.
posted by Decani at 3:09 AM on March 25, 2012 [3 favorites]

This needs to change. People should be as embarrassed to be scientifically and mathematically ignorant

It would be easier to just accept that many people don't know a damn thing on any subject; they function on guesswork and lying. In the current political climate in the US, we are more than halfway there.
posted by GenjiandProust at 3:21 AM on March 25, 2012 [3 favorites]

I got a 790 verbal 500 math and a perfect English comp achievement test when I took it in HS. I am absolutely sure I would do much much better in math now but worse in English. Not breaking 1400 was a huge blow even though I did really well on the achievement test.

Anyway, I think most people do better as adults in general. My mom scored a perfect score GRE in her 50s even though she didn't break 1500 on the SAT in her teens.
posted by Ad hominem at 3:29 AM on March 25, 2012

Oh, whatever at the people going on about how easy the first math question is. I know lots of people here actually use math in their jobs and hobbies, but lots of people never do. Unfortunately, I don't even think I know what that question is asking. My math muscle has atrophied, because I haven't needed to use it for anything but simple arithmetic since school. It's like being illiterate only with hardly any consequences. I don't know, I kind of wish I knew about math, but whenever I try to go back to it it just doesn't seem worth all the misery. If Shakespeare made me feel that way I wouldn't bother with him either. I've heard what Decani just said about a million times on this site, and I wonder if it ever occurs to people like that to feel shame about all the things that are obvious and basic in other people's lives that they don't understand, can't do, and won't ever take the time to learn about.

That's the amazing thing about the SAT. YOU WILL NEVER GUESS RIGHT.

I cannot believe people are taking issue with this as if it were meant literally.
posted by two or three cars parked under the stars at 3:32 AM on March 25, 2012 [43 favorites]

if you've commented about how dumb this guy was for not getting an obvious answer to an easy question, you fail reading comprehension forever. This wasn't about how easy or difficult the tests are, but about the subjective experience for quite a few people of taking it.

I'm sure there isn't a student alive who has never faced a test question and had their head explode. I know I have. But when that happens, it's because I don't know the material.

Complain about the quality of your tutelage, or own up to your own lack of work. But unless the test question makes no sense to people who do understand the material, there's nothing wrong with the test and complaining about the test is stupid.
posted by flabdablet at 3:38 AM on March 25, 2012

From the article:

But I'll be goddamned if I can remember the last time I had to figure out how many sides a covered polygon has. That shit is useless. Unless you engineer planes or something.

Well, yeah. They're testing your ability to solve the sorts of problems that people who "engineer planes or something" would have to solve because this test will determine who gets to go to plane-engineer school.
posted by baf at 3:47 AM on March 25, 2012 [6 favorites]

It would be easier to just accept that many people don't know a damn thing on any subject; they function on guesswork and lying.

MeTa

I liked they essay better than most of you, but this discussion is great! I now feel confident I can figure out the number of sides of a polygon given just a single point on one of the sides.
posted by TedW at 5:04 AM on March 25, 2012

I used to teach for one of the big test prep services. The instructors tend to view the test with withering cynicism, and the trend is to instill that in students as well. The first session is basically about the structure and procedure of the test, and it's hammered home that the SAT is not a test of how smart you are. Just look at the acronym. Know what it means? Well it used to be "Scholastic Aptitude Test," only research showed it doesn't actually predict aptitude, so they switched it to "Scholastic Achievement Test," only research showed it doesn't actually predict that either. So now it's just "SAT," an empty acronym, which tests one thing and one thing only: how good you are at taking standardized tests.

But there's a reason these companies exist, and it's not just because the SAT and ACT are overblown parts of most Americans' academic careers. Rather, it's because it's possible to game the tests. Because there's a trick to designing these tests, there is also a trick to taking them. In short, the way to take these tests is at least as much about spotting and eliminating obvious wrong answers as it is trying to come up with the right one.

There are all sorts of regular tricks. Say the correct answer involves a two step calculation, say calculating an average. First you add the series together, then you divide by the number of elements in the series. I guarantee you that one of the wrong answers is going to be the sum. A lot of students, again, working quickly, will get the sum, see that they just got a number that appears as an answer, mark it, and move on. I kid you not, I've seen it happen.

This is true, to a lesser extent, with the reading and grammar sections. These are actually even harder to come up with wrong answers for, because the answers have to be both superficially plausible and objectively wrong. With math, an answer is either right or it isn't. But the SAT almost never tests comma use, or tests it only lightly, because commas are discretionary in any situations. There will never be an SAT question on the Oxford comma, for example. The test format won't permit a question with more than one right answer, which eliminates a huge amount of potential questions and answers.

But there are still tricks. A very common one crops up when asking for the definition of the word. Say they give you a sentence: "I really tried to apply myself to Latin, but it don't answer," and they ask you what "answer" means in this context. The correct response would be something like "To serve satisfactorily," which is a fairly archaic but entirely legitimate use of the word. But I guarantee you that "To respond" and "To be responsible for," neither of which makes much sense in context, but both of which are more common uses of the word. A student, working quickly under pressure, will be very, very tempted to say "Hey, yeah, that word means that. Got it," when it's really the third or fourth definition which is correct.

Here's the thing though: while figuring out these tricks can dramatically improve one's score, it's completely useless for just about anything else. Multiple choice questions exist only in the context of multiple choice tests. So as a predictor of success in college, the test doesn't actually do very well. I have personally improved students' scores by over 250 points in ten weeks. If the test really had anything to do with a student's intellectual preparedness or fitness for higher education, that shouldn't be possible.

You know what would make a far more effective admissions tool? Interviews. Numbers on a page don't mean much. Sit a kid down in a chair and ask him questions for fifteen minutes? Hard to fake that. Even better, hand him an intro to philosophy textbook and just have him read aloud for five minutes. If he's marginally literate, you'll know right away. You could even enlist alumni volunteers in various cities to run a sort of intensive, Saturday intake, where they run through a few hundred kids in an afternoon.
posted by valkyryn at 5:11 AM on March 25, 2012 [46 favorites]

Yeah, because, um, "alumni volunteers" can't be bought...

(caveat: I own a test-prep company that games the hell out of the test and has delivered three perfect 2400's in the last few sittings)
posted by Joseph Gurl at 5:43 AM on March 25, 2012

stbalbach: "The most interesting part is about the SAT grader who has to read all those essays. A real story there somewhere"

Here ya go.
posted by Red Loop at 5:43 AM on March 25, 2012

I had the joy of teaching a class in how to take the SAT math 8 years ago. The school I was in was awful in terms of wasting students' time in classes like these. However, you can prep for the SAT math as there are only like 6 classes of problems. Most are just variations on a theme and if you know how to handle the theme, it's a cake walk. Calculators? If you're using one, you're doing something wrong. I don't think that I encountered a problem that couldn't be solved faster without a calculator.

Now, when I took the SATs, back when dinosaurs roamed the earth, I got a 620 in math, IIRC, and I was the poster child for what not to do. I took the test one, at the last available opportunity and I stayed up a lot of the night before (it was a great band, what can I say?). Turns out that if you take the test a scant few times under lower pressure and with a good night's sleep, you do hella better.

I challenged my students - if they could *all* in a practice test do better than I did, then I would dye my hair purple. A sucker bet, to be sure.

I took the tests at the same time as my students and found that with college math and many years of software engineering, that I could get a consistent 780/800 using half the allotted time and without checking my work.

What does this say? If you actively use math beyond arithmetic (and I do) and have emotional maturity, the SAT math section is straightforward. This author clearly neither uses math nor has emotional maturity. Or maybe that's his bitter sense of humor.
posted by plinth at 5:44 AM on March 25, 2012 [3 favorites]

I have personally improved students' scores by over 250 points in ten weeks. If the test really had anything to do with a student's intellectual preparedness or fitness for higher education, that shouldn't be possible.

This. Actually everything valkyryn said. I have never had a kids score improve by less than 150 points after tutoring them, and it's usually much more. The kids do not get smarter, just more cynical.

But I should add that many students now take both the SAT and the ACT, and many of the tricks that work for one test do not work for the other, so wheeeee, more tutoring! For example, on the ACT sentence correction, more often than not, the response with the fewest words in it is correct. Nine times out of ten, it's the response with the fewest words that makes any sense whatsoever. The SAT likes to be a bit more verbose.

The fact that you can spend a few hundred bucks to improve your child's score by 10-15% is monumentally stupid and unfair. A kid who can only afford to take the SAT once and gets a 1350 has fewer opportunities than the kid who got 1350, but whose parents can spend \$1000 on tutoring (what my old agency charged for SAT prep, there were more expensive options available) and have him retake the test and get a 1600. Neither kid is smarter or better prepared for college than the other, but one gets huge preference over the other in admissions.
posted by Garm at 5:45 AM on March 25, 2012 [3 favorites]

Yes. Taking the SAT always felt like I was playing a peculiar sort of game or solving a puzzle. I never took a test prep course, so I'm not sure what they teach, exactly. But I remember having fun spotting the tricky wrong answers, checking that I've used all the facts in the question to arrive at my answer, etc.
posted by ryanrs at 5:46 AM on March 25, 2012

this isn't to say there should be a man with a cattle prod hanging over you

That's an absolutely terrible sentence containing an absolutely terrible mixed metaphor. He's mashing together an image of the Sword of Damocles with an image of a man with a cattle prod. What you get is an image of a cowpoke hanging upside down.

It's interesting that the guy isn't the least bit chastened or humbled by his results. He's a fool and can't see it.
posted by painquale at 5:46 AM on March 25, 2012 [4 favorites]

Evidently, he writes a self-righteous rant that incidentally reveals how frustrated people who were failed by public education get when faced with evidence of their own ignorance.

Congratulations. You have a head for math. Some people have utterly no ability in math, no matter how well they've been served by formal education. Math isn't something that all people naturally grasp.
posted by Thorzdad at 6:15 AM on March 25, 2012 [8 favorites]

A kid who can only afford to take the SAT once and gets a 1350 has fewer opportunities than the kid who got 1350, but whose parents can spend \$1000 on tutoring [...] and have him retake the test and get a 1600. Neither kid is smarter or better prepared for college than the other, but one gets huge preference over the other in admissions.
I would say the student who has enough money to game the system is demonstrably better suited to college life.

The SAT and ACT work perfectly as intended.
posted by fullerine at 6:18 AM on March 25, 2012 [2 favorites]

I have personally improved students' scores by over 250 points in ten weeks. If the test really had anything to do with a student's intellectual preparedness or fitness for higher education, that shouldn't be possible.

Why? Your experience seems totally consistent with the general consensus that SAT scores capture some kind of mixed-up amalgam of intellectual preparedness for college with "good at multiple-choice test" gamesmanship.

Also, you should know that you were extraordinarily good at test prep; if improving student scores to that extent in a ten-week course were routine, the SAT would have big problems. My sense has been that the effect size is typically much smaller; e.g. this study finds a mean improvement of 11 to 15 points on math and 6 to 9 points on verbal.
posted by escabeche at 6:21 AM on March 25, 2012

I can't believe anyone over the age of 25 remembers their SAT scores. I took the SAT, ACT and GRE and I can't remember any of my scores (I'm 37). I totally fucked up the GRE because I thought you had to complete both essays in 45 minutes (or whatever they give you) and I couldn't go back and edit either. I have incredible test anxiety, though. One of the best testing experiences I ever had was when I had a hastily slammed beer beforehand. (I hadn't yet been prescribed anti-anxiety meds.) It was a history exam, there were six (SIX!) essay questions over two hours, and I got an A+.
posted by desjardins at 6:28 AM on March 25, 2012

Congratulations. You have a head for math. Some people have utterly no ability in math, no matter how well they've been served by formal education. Math isn't something that all people naturally grasp.

Most people. Even people who are really good at it. It takes a lot of work to understand math, for pretty much everyone. If it were intuitive, we wouldn't need to drill it into our heads from the age of five.
posted by empath at 6:45 AM on March 25, 2012 [1 favorite]

I honestly feel baffled that anyone would fail to see how easy that question on functions f and g is.

I'm baffled that you would be baffled by this! It's easy if you've really understood how a curve in the plane corresponds to a function, and what functional notation means. But neither of these is themselves obvious or easy. The first, in particular, was one of the great achievements in the history of mathematics.
posted by escabeche at 6:48 AM on March 25, 2012 [2 favorites]

"Right from the start, I tell our kids, 'I'm not a teacher. This isn't school. I'm not going to teach you English. I'm not going to teach you math. I'm going to teach you the SAT.' I tell the kids that they're not competing with each other, they're competing with ETS. And the mindset is: let's blow these assholes away."
— Test prep pioneer John Katzman, quoted in None of the Above: Behind the Myth of Scholastic Aptitude by David Owen. If you want to read a fantastically funny and vicious takedown of the SAT and the Educational Testing Service, this 1985 book is the one to get.
posted by How the runs scored at 6:49 AM on March 25, 2012 [2 favorites]

I aced the sats, but I'd say maybe a few hundred points were just from being good at multiple choice tests, a skill I had developed from years of not studying for tests.

It's also served me well for getting tech certifications, but 'check all that apply' questions completely throw me.
posted by empath at 6:49 AM on March 25, 2012 [2 favorites]

I'm on the last day of a ten-day window scoring SAT essays.

By the end of today, it'll have been about 2000 essays this week. Let's just say I don't think it's terribly interesting. I am sooooo weary.

The Reddit answerer did all right, but if you have something you want to ask directly, go ahead.
posted by RedEmma at 6:55 AM on March 25, 2012 [1 favorite]

It's easy if you've really understood how a curve in the plane corresponds to a function, and what functional notation means. But neither of these is themselves obvious or easy. The first, in particular, was one of the great achievements in the history of mathematics.

No doubt.

Plus, about half of my calculus students don't know the difference between "f(x+h)" and "f(x) + h". I have a hard time believing that nearly everyone in this thread does.
posted by King Bee at 7:01 AM on March 25, 2012 [1 favorite]

Congratulations. You have a head for math. Some people have utterly no ability in math, no matter how well they've been served by formal education. Math isn't something that all people naturally grasp.

I do not believe this. I imagine that there are people who have a "math disability" akin to dyslexia (or possibly including dyslexia), but I think the majority of people can grasp the basics of math with little problem. I think they are generally taught poorly, because a setting of 30+ students with a harried teacher (who may or may not have a particular orientation for the material) trying to satisfy a range of standards while getting all the students to a minimal fluency to pass the next test is probably not the best way to do it. Additionally, our culture (and I am talking about the US here) actively discourages accomplishment in math as fit neither for men (who it emasculates) or women (who it defeminizes).* Kids pick up on this really early, and there is a strong pressure not to learn the material and belittle those who do. Additionally, it's a type of thinking that we don't do a good job of a) valuing (see above) or b) explaining why kids should when no one else does. Hell, "I can't do math" is almost a point of pride with a surprising number of people.

So I don't buy the idea that large numbers of people are just naturally amathematical, any more than I believe that large numbers of people "can't get Shakespeare" or "are incapable of understanding societal privilege." A fairly small number of people will like and engage with each topic more than the average person, but the vast majority of people can "get" the concepts if they are even slightly motivated and learn in an appropriate environment.

*I am not really sure how that is supposed to work, but, go figure, cultural gender norms are not exactly rooted in rigorous logical process.
posted by GenjiandProust at 7:02 AM on March 25, 2012 [7 favorites]

Plus, about half of my calculus students don't know the difference between "f(x+h)" and "f(x) + h". I have a hard time believing that nearly everyone in this thread does.

Me too. But that's not because they're stupid, it's because math is in fact hard.
posted by escabeche at 7:07 AM on March 25, 2012

Me too. But that's not because they're stupid, it's because math is in fact hard.

True, but then so is literature and sociology and chemistry and pretty much every area of human endeavor, assuming you are doing it right and not just skating by. It's not like math is some special class of "magically incomprehensible knowledge." Hell, it has the advantage of being more or less regular and arising clearly from simpler principles unlike, say, English grammar.
posted by GenjiandProust at 7:11 AM on March 25, 2012

Well, and also your brain is fairly efficient at weeding out 'useless' information, so if you aren't actively reinforcing knowledge by using it, you are going to forget it eventually.

Though that doesn't explain why I still know the code to fight Tyson in punch out on the NES.
posted by empath at 7:12 AM on March 25, 2012 [3 favorites]

> This writer is trying to hard by a factor of ten.

The correct answer was "too hard." You get zero points.
posted by cjorgensen at 7:13 AM on March 25, 2012 [2 favorites]

He didn't know 180 degrees make up the interior angles of a triangle and he made the 96th percentile?

He makes trenchant analysis such as: Hip hop is the genre. Rapping is the vocal style performed WITHIN that genre. This is the whitest question ever.

The genre and the vocal style can both make commentaries. It was a stupid white question for completely different reasons.

And what the hell does this mean? an expense plenty of nutjob helicopter parents are happy to throw down.

To have helicoptering parents tossing down money would be really cool.

This is a style of writing where anti-intellectualism tries to pass as hipness. I hate it.
posted by dances_with_sneetches at 7:17 AM on March 25, 2012 [4 favorites]

Though that doesn't explain why I still know the code to fight Tyson in punch out on the NES.

Saki had a story where a person is asked whether he knows the difference between good and evil, and he says yes, he did, his mother had taught him when he was a child, but he had since forgotten. The aghast interrogator demands to know how he could have forgotten the difference between good and evil, and the character responds that his mother had also taught him three ways to prepare lobster, and you can't remember everything.

You have probably forgotten both math and the difference between good and evil to remember that code.
posted by GenjiandProust at 7:20 AM on March 25, 2012 [9 favorites]

I also abhor this style of writing. The internet loves this kind of stuff though.
posted by Ron Thanagar at 7:28 AM on March 25, 2012 [1 favorite]

Is nobody else besides me wondering how he could struggle so much with the math section, only get a 4 on the essay, and end up in the 96th percentile? That just doesn't add up.
posted by COD at 7:32 AM on March 25, 2012 [1 favorite]

True story.

I suck at taking standardized tests but am otherwise, I think, a fairly intelligent person capable of complex thought and analysis.

I took the PSATs and the SATs twice.

My first score on the SATs was:

Verbal 580
Math 480

My second score on the SATs was:

Verbal: 580
Math 490

I didn't even break 1100 at the time 1600 was the max score, and this just floored my teachers and a number of my peers. But I had a history of not performing to my potential on standardized tests, and I quite frankly didn't give a damn.

When I applied to grad schools I didn't end up attending, I took the GREs at a testing center on a computer where if you answered a question incorrectly, the next question was easier, and if you answered it correctly, the next was more difficult. I didn't get to back and check my work or change my answers on the GREs the way I was on the SATs. The computer program didn't allow for it.

My score on the GREs nearly 5 years after taking the SATs?

Verbal 580
Math 490

The Princeton Review is a provides useless metrics, and these types of standardized tests should be done away with completely. The college I went to didn't even require SATs to be submitted. I didn't submit, got in, and did just fine.
posted by zizzle at 7:32 AM on March 25, 2012 [1 favorite]

I have mixed feelings about the SAT. On one hand, I think the test, and the concept behind it, is total bullshit. On the other hand, I did well enough that I overcame my so-so high school grades and got into a decent university. So yeah, we should figure out something better, but we probably won't.
posted by LastOfHisKind at 7:38 AM on March 25, 2012

The fact that you can spend a few hundred bucks to improve your child's score by 10-15% is monumentally stupid and unfair.

In fact, I wonder how much of the SAT's predictive value comes from its ability to pinpoint kids whose parents are involved and invested in their education. Parental involvement is one of the predictors of future success that really does work reasonably well. Colleges can't just use it directly as a factor in making admission decisions. But if the SAT ends up serving as a proxy for parental involvement, then what the hell, why not use the SAT?

None of which is to deny that it's still stupid and unfair if we're actually serious about meritocracy or social justice.
posted by nebulawindphone at 7:44 AM on March 25, 2012 [2 favorites]

Back in the 60's, I earned the high 700's in verbal and math, and dropped out of college after two years. On the other hand, I paid for graduate school by being so good at the GRE's that I qualified for a fellowship. My kid had a perfect verbal score, and it helped her get into college. We gamed the system very nicely thank you. None of it is fair, and I think the test is bullshit.
posted by Peach at 7:47 AM on March 25, 2012

I felt bad to see him so baffled by the function question. He looks at the graph and the curve and totally flips his shit, when to answer that question you don't actually need to know anything about calculus, just need to notice that one curve is exactly one unit higher on the graph than the other one.

Like, one of my great shames is that I don't know calculus. Homeschooled, self-taught myself math through algebra and a little trig (Ah, Saxon math), and that was it. Immediately forgot almost all of it, and I feel bad about that, too. I have a lot of math shame in general, honestly.

But one of my favorite ideas in math is that you can have an operation characterized in traditional notation, and then graph that operation and really see, really feel how it works as you slide it over values. So while you don't need to know any actual calculus to answer that question, you do need to know about functions, and what f(x) means, conceptually. Then you'll see that the intimidating-looking wavy curve there is a total red herring, that the only important piece of information on the graph is the fact that g(x) is higher on the graph than f(x), and that there's no other useful information to be gleaned from it.

I don't feel particularly smart for seeing the answer, because it's a bullshit question that you don't actually have to understand anything important about to get right.
posted by pts at 8:14 AM on March 25, 2012 [1 favorite]

> A kid who can only afford to take the SAT once and gets a 1350 has fewer opportunities than the kid who got
> 1350, but whose parents can spend \$1000 on tutoring (what my old agency charged for SAT prep, there were
> more expensive options available) and have him retake the test and get a 1600. Neither kid is smarter or
> better prepared for college than the other, but one gets huge preference over the other in admissions.

OTOH working your way conscienciously through one of those SAT cram books (the thick kind that has the short content review sections as well as the practice tests) costs \$15 and has the same effect. Substitute effort for money, you can. Better yet, blow \$30 on two of 'em from different publishers, work through both, and hit the 99+ percentile. (Merely doing all the practice tests so that you become thoroughly familiar with the form and mechanics of the tests is worth 200 points a side, easily.)
posted by jfuller at 8:18 AM on March 25, 2012 [3 favorites]

Good lord people. It was played for the Lulz. Chill the fuck out with calling the guy an idiot because he forgot a little basic geometry and algebra. He's a dude who writes dick jokes on the internet for money.
posted by JPD at 8:22 AM on March 25, 2012 [13 favorites]

> graph that operation and really see, really feel how it works as you slide it over values.

Very first epiphany after learning enough BASIC to plot equations on X,Y axes on my first PC (8-bit generation.) I graphed hundreds of 'em. I am far more an arts/humanities type than any sort of math geek and would never ever have done that with pencil and paper, or even calculator and paper.
posted by jfuller at 8:26 AM on March 25, 2012

Plus, about half of my calculus students don't know the difference between "f(x+h)" and "f(x) + h". I have a hard time believing that nearly everyone in this thread does.
posted by King Bee at 7:01 AM on March 25 [+] [!]

I'm not a teacher, so I guess I don't understand why this would be hard to teach. Can you please explain to me what is so hard about this?
posted by 200burritos at 8:32 AM on March 25, 2012 [1 favorite]

He's not dumb, just miseducated. It's very easy to leave high school with a) the misconception that math is about memorizing formulas and b) having weak quantitative reasoning skills. The system failed him at a time when he had the most potential to learn this stuff.

Yeah, I have to agree with this. I was lucky in that most of my grade and high school education was theory based. Learn the theory and the proofs and all that stuff, and you'll be able to figure all kinds of things out. Most of my peers who went to other schools were taught in the rote memorization style. As was, I'm assuming, this guy.

It's really disappointing to see the results of the different styles over time. The people taught in the memorization style have zero ability to figure stuff out. "I don't remember" = "impossible" as far as they are concerned. (They tend to vote republican, too, but that's a kettle of fish for another day.)

But the other positive thing about my schooling was that we did a LOT of standardized testing over the years. As a result, there wasn't a whole lot of test anxiety among us. It wasn't a Big Important Thing That You Will Screw Up Your Life Over, it was just another day where we didn't have to go to normal classes.
posted by gjc at 8:34 AM on March 25, 2012

But one of the few upsides of being an adult is that you NEVER have to take the SAT again.

No, but you may have to take the GRE, the LSAT, the GMAT, the LCAT... The standardized testing bullshit doesn't end at high school for everyone.
posted by arcticwoman at 8:37 AM on March 25, 2012

I don't remember the math questions being that hard. But it was 1988 and I only got 1080 (650 Verbal, 430 Math).
posted by jonmc at 8:38 AM on March 25, 2012

It's basic order of operators and parentheses stuff that you learn in grade school. It isn't that it's hard to teach, it's that it is baffling that someone can make it to calculus not knowing it. And at that point, it probably IS hard to teach, because the students must have built up some wickedly bad habits trying to compensate for not knowing such a thing.
posted by gjc at 8:39 AM on March 25, 2012

Because there's a trick to designing these tests, there is also a trick to taking them. In short, the way to take these tests is at least as much about spotting and eliminating obvious wrong answers as it is trying to come up with the right one.

LOL I can tell it's test season, since there's another argumentative post about the NYSED ELA 8 elsewhere on MeFi.

Anyway, that comment reminds me of one of my favorite Japanese short stories, it's in the anthology "Monkey Brain Sushi" and it's called something like "English Proficiency Exams for Earnest Students." If you think the culture of ACTs and SATs is bad, you ought to see the high school final exams in Japan. Everyone has to take them, and they basically determine your future. You get one shot, and that's it. Everyone tries to game the system, everyone goes to prep schools.

I remember one of my Japanese instructors showed us a section of the English Proficiency exam. We passed it around the class, and none of us (all English native speakers of course) could correctly answer a single question, not even as a group effort. And there was more than one grad student working on PhDs in Linguistics, some had TOEFL certificates. The test seemed intended to test whether you understood how English was taught, rather than how it was used.

So.. the short story was amusing, it was a series of dialogues between a student and an instructor teaching him the tricks of the test. It's been a long time since I read it, but IIRC it says this: There are 4 multiple choice answers. One of them is obviously right, that is not the correct answer. Three are wrong. One is obviously wrong, that's not it either, that would be too easy. So of the two remaining answers, look for the one that is the most irrelevant, off topic, or that expands the range of the question so the answer is meaningless. That is the correct answer.

I blame this test for screwing with my head seriously during my own prep for the Japanese Language Proficiency test. It's a good system. Instead of just giving you a score 1 through 4 (1 is native level proficiency, 4 lowest) they give 4 tests, pass fail. All my friends who had lived in Japan longer than me tried for Level one, thinking it would be more prestigious to have a high failing grade on L1 than a passing grade on L2. I took L2. I took multiple example tests from past years, and aced them all. I studied extra hard and was in the study group for L1. It was seriously important to take practice tests, or you would have spent time trying to figure out how to answer the questions, or in fact, what the question was.

When I got the results, we were all astonished, the test was harder than in past years, they had unexpectedly raised the difficulty of the questions. All my L1 friends flunked badly, barely getting above 50%, which almost anyone could do by guessing. I aced every section on the L2 but the Listening Comprehension, which I would have passed if I had answered two more questions correctly. Dammit!

Anyway, I will advocate for this sort of testing. I have done so partly because I score tests as a temp job and I make money at it, but barely enough to avoid starving. More testing means more money for me. But more than that, testing reminds me of what my Mom said, to convince me to go back to school 20 years after I dropped out and finish my degree. She said that I was getting crappy jobs because I didn't have my degree. A degree would tell employers that you were able to sit down for 4 years and follow someone else's set of instructions and do them. It would demonstrate your long term ability to work according to a system you have no control over.

And I think that's true for testing, and even more so for students who take test prep. I think they should be rewarded for the effort they take trying to understand how the test works, even more if they expend extra effort in a prep class. That shows they have the ability to not just work according to the rules an arbitrary system, but to discern the hidden rules.
posted by charlie don't surf at 8:59 AM on March 25, 2012 [6 favorites]

This essay has it all! Pride at not knowing math AND the "omg did he really say that" snark-writing of 2005's Internet! Maybe more, but I stopped reading! Fuck!
posted by Legomancer at 9:17 AM on March 25, 2012 [1 favorite]

These are actually even harder to come up with wrong answers for, because the answers have to be both superficially plausible and objectively wrong.

Hire Herman Cain.
posted by benito.strauss at 9:19 AM on March 25, 2012 [1 favorite]

So while you don't need to know any actual calculus to answer that question, you do need to know about functions, and what f(x) means, conceptually. Then you'll see that the intimidating-looking wavy curve there is a total red herring, that the only important piece of information on the graph is the fact that g(x) is higher on the graph than f(x), and that there's no other useful information to be gleaned from it.

I agree with this - it wasn't that the first math question was particularly hard, it's that it was dressed up in a way that obfuscated the actual question. Most people don't have to use anything like the f(x) notation standard in their lives, so they forget what it means once they're out of school. And the graphs - if you've made it to trig or algebra 2 in high school, you may not know the function that produces those wavy lines, but you know it's going to be some complicated sine shit and not some y=x+3x or something. So, that question is really just frontin' and trying to intimidate you such that you don't realize you actually know the answer to it, and people who aren't totally confident in their math skills can get panicked over all the stuff in the question that doesn't matter.
posted by LionIndex at 9:42 AM on March 25, 2012 [5 favorites]

I don't feel particularly smart for seeing the answer, because it's a bullshit question that you don't actually have to understand anything important about to get right.

My heart is kind of broken by this sentence, because it's preceded by an articulately phrased and completely mathematically sound paragraph which makes it utterly clear that you do understand the mathematical principle the problem is trying to test, a principle which is deeper and more important than any trig identity. And yet something about your schooling has failed you so badly that you think a math question is "bullshit" because you could get it right by virtue of understanding something important about math.
posted by escabeche at 9:47 AM on March 25, 2012 [6 favorites]

If you get every question wrong, you still get 200 points on each section, just for showing up and putting your name on your test. Though if you got every question wrong, you probably fucked up that part as well. I don't know why the test is scored like this. It strikes me as yet another needless complication in an already needlessly complicated test.
Why is the lowest possible score 200 rather than 0? I've always wanted to know this.
posted by grouse at 9:54 AM on March 25, 2012

The article resonated with me, because I love goofing on things that are, in my opinion, ridiculous. Like the SAT. The commentary was hilarious. Thanks OP for posting this.
posted by sundrop at 9:58 AM on March 25, 2012 [1 favorite]

Then you'll see that the intimidating-looking wavy curve there is a total red herring, that the only important piece of information on the graph is the fact that g(x) is higher on the graph than f(x), and that there's no other useful information to be gleaned from it.
...
So, that question is really just frontin' and trying to intimidate you such that you don't realize you actually know the answer to it
I thought that was the best part of that question! I work in software--a math-relevant profession--and I'd say 90% of my time is spent just trying to figure out which stalk of hay in an irrelevant-information haystack is actually a relevant-information needle.

To me, a question with a simple answer obfuscated by complicated-looking irrelevancies is an accurate simulation of using math in the real world.

except in the real world the math problems are framed in your native tongue and you're allowed to go to the bathroom and when you find out you were wrong you can go back and fix it and you can use whatever tools you feel are necessary
posted by I've a Horse Outside at 10:02 AM on March 25, 2012

Also, readability.org! Holy crap! Why didn't anyone tell me!
posted by I've a Horse Outside at 10:02 AM on March 25, 2012

I honestly feel baffled that anyone would fail to see how easy that question on functions f and g is.

I'm sorry that my stupidity baffles you. It's not like I like being this fucking stupid, either. I wish I could do math well. Apparently when I was very very young, like 2nd grade and earlier, I had decent math skills... but then I went through some significant childhood trauma, switched elementary schools at least annually (a couple of years I switched schools right in the middle of the year), and had some truly lousy teachers. And then in 9th grade my district switched all high schoolers over to the College Preparatory Math system, which failed many of us. When they brought back "regular" math the next year, with actual textbooks and seasoned teachers instead of mimeographed pamphlets full of story problems taught by inexperienced teachers straight out of college themselves, it was too late for me. (Doesn't help that I went to an extremely poor school in a very underfunded district. My high school doesn't even exist anymore, its campus is now the site of three "charter" schools funded by a grant from the Gates Foundation. Because it's near the airport, one of the charter schools specializes in getting kids ready to work in the hospitality/travel industry.)

I ended up taking Algebra I/II twice, and Geometry I/II twice, and only eking out a D in each class the final time around. Not for lack of trying, either. I tried so fucking hard. I went home most days and cried -- I knew I was really bad at math and that it could keep me from graduating, and nobody in my life was trying to help me succeed. Because I was smart at other things, everyone assumed I was just being a lazy wastrel and not actually trying to learn. Lots and lots of beratement thrown my way. Tons of shaming. No offer of help from my teachers, who treated me like a waste of their time.

I did graduate, but I never went to college. Recently I had a full neuropsychological evaluation (I have severe ADHD and many comorbid disorders run in my family, so I needed to find out what's going on in my brain)... turns out that I have a significant math impairment. One hemisphere of my brain is extremely overpowered in its functionality, and the other hemisphere is average at best. The disparity creates HUGE problems in the way my brain functions, and I literally cannot learn new maths concepts without a ridiculous amount of work, like tons of repetition for instance. Once I knew that, it finally made sense that I forgot how to do long division over the course of two summers in a row.

So anyway. I'm sorry that my stupidity is so dismaying. Trust me, it's dismaying to me, too. It doesn't feel good at all to look at a math problem and not understand a single whit of it. It doesn't feel good to be this fucking stupid. I hope no one makes you feel like this about the things you don't do well.
posted by palomar at 10:08 AM on March 25, 2012 [24 favorites]

I just _knew_ the answer to the polygon question the way most people know the answer to 12X12. Read the question and *bing* 9 popped into my head. It sure is interesting what sticks in our brains. Reading all the derivation stories has been interesting.

kafziel writes "Also seriously man these are not difficult questions. I guess if you don't remember what a graph even is, maybe #16 will throw you? But even then it should be obvious that y=g(x) is just one higher than y=f(x), so the answer is B."

This is the sort of thing that real life doesn't really prepare you for most of the time. Last year I had to take a basic Math and English entrance exam for entry into my trade program. Luckily the college I was attending used a standard test rather than rolling their own and prep material was available or I would have done very poorly on the math section. In 20 years since leaving high school I've never needed to factor a quadratic equation or all sorts of other basic math stuff that anyone in high school math does regularly but someone cranking AutoCAD 40 hours a week doing design work which is math heavy doesn't ever use.

"“I have a wide circle of friends in various professions. Since taking the test, I’ve detailed its contents as best I can to many of them, particularly the math section, which does more than its share of shoving students in our system out of school and on to the street. Not a single one of them said that the math I described was necessary in their profession."

The author is a teacher and school board member; I really wonder how diverse his poll was. Did enquire this of plumbers, electricians, architects, truck drivers, programmers, waitresses, engineers, pharmacy techs etc.

This would be a nightmare. At least with the SAT the test your teacher teaches you is the same in this town as the town one state over. If everyone wrote their own test not only would the tests on average be poorer out of state students would have a tougher time than the locals.

Decani writes "I honestly feel baffled that anyone would fail to see how easy that question on functions f and g is. Now, the polygon one does need a bit of joined-up thinking to reach the answer, but those functions? Come on. No excuse."

See above. You need to know the structure of a function statement to get that question. If that's something you haven't done in 20 years and maybe weren't all that good at it in high school you might not remember and that's going to make it a very difficult question. Unlike the polygon question which with some sweat you can derive answer the function question needs you to have fairly obscure terminology knowledge.

valkyryn writes "You know what would make a far more effective admissions tool? Interviews. Numbers on a page don't mean much. Sit a kid down in a chair and ask him questions for fifteen minutes? Hard to fake that. Even better, hand him an intro to philosophy textbook and just have him read aloud for five minutes. If he's marginally literate, you'll know right away. You could even enlist alumni volunteers in various cities to run a sort of intensive, Saturday intake, where they run through a few hundred kids in an afternoon."

Really tough to structure interviews so that they are free of sex, gender, race, class, and ethinic biases. I'd guess it's pretty well impossible.
posted by Mitheral at 10:21 AM on March 25, 2012 [1 favorite]

The circlejerk in here is overwhelming.

I love metafilter for the most part. There are some truly great discussions. Then pieces like this get posted and the pretentiousness just gets turned to the max. Holy shit.
posted by CancerStick at 10:24 AM on March 25, 2012 [15 favorites]

I just wanted to say that I thought the passage from 1909 that he derides as the "worst thing ever written" was in fact quite good. Not sure what he didn't like about it. The subject? That doesn't mean it's bad writing.
posted by ultraviolet catastrophe at 10:25 AM on March 25, 2012 [1 favorite]

someone cranking AutoCAD 40 hours a week doing design work which is math heavy doesn't ever use

After figuring out the polygon thing in my head I went and drew it in AutoCAD to make sure.

posted by LionIndex at 10:35 AM on March 25, 2012 [2 favorites]

Regarding the Orange County School Board Member who said this: “It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate.

Here is what is wrong: He is innumerate. Two of those degrees are in education and one is in education psychology. I can't imagine these programs were even minimally quantitatively challenging.
posted by borges at 10:43 AM on March 25, 2012 [2 favorites]

You know, if you're going to spend a perfectly good Saturday and however many dollars the SAT costs nowadays, perhaps you should at least read through the free booklet so you know the goddam format of the test.
posted by maryr at 10:56 AM on March 25, 2012

the passage from 1909 that he derides as the "worst thing ever written"

Which is from The Glory of the Conquered, Susan Glaspell's first novel, in case anyone cares. It does seem pretty soppy and overwritten in that characteristically turn-of-the-century way, not that Drew Magary is entitled to talk about anyone else's overwriting.
posted by RogerB at 11:10 AM on March 25, 2012 [1 favorite]

maryr writes "You know, if you're going to spend a perfectly good Saturday and however many dollars the SAT costs nowadays, perhaps you should at least read through the free booklet so you know the goddam format of the test."

He didn't actually pay for a sitting; he just did a sample test in simulated conditions.
posted by Mitheral at 11:20 AM on March 25, 2012

I took the SAT a grand total of one time when I was in dipshit prep school.

As I was reading this article by a 35 year old man who's descriptive vocabulary mostly consists of "dick" and "asshole", I came to truly respect the quality of his prep school. They turned out a quality dipshit.
posted by Tell Me No Lies at 11:34 AM on March 25, 2012 [3 favorites]

I still remember how indignant I felt when I discovered that there were CLASSES I could have taken to help me prepare for the SAT. I did okay, but I bet if I'd had any idea what the test would be like, I'd've aced it.

Sort of like when we moved to a bigger town in my senior year (too late for college applications) and discovered that at this school you could get greater than a 4.0 grade point average. And no, the classes weren't harder, despite what the teachers thought.

The inequity in our school system between rural and urban is disgraceful.
posted by small_ruminant at 11:38 AM on March 25, 2012 [1 favorite]

I imagine that there are people who have a "math disability" akin to dyslexia

It is called dyscalculia.
posted by mlis at 11:43 AM on March 25, 2012 [1 favorite]

I kind-of did this. I took the SAT's in 1969, got an 800 in math and not too bad on verbal, and ended up going to a college that wanted the ACT instead. In the mid-'80s, one of my kids was taking the SAT's and I got a practice (?) version that I took. I didn't get an 800 this time, but my overall score was higher.
Anyway, I don't think it's the same thing. I wasn't in a hot room with an asshole proctor and it didn't really count. There was no pressure.
posted by MtDewd at 11:47 AM on March 25, 2012

I realize that one big reason I struggled with math in grade school and never became much more than minimally competent at it -- barely functional, basically -- is because I had the misfortune to encounter math teachers who were almost (not quite, but almost) as contemptuous, impatient, and dismissive as some of the commenters in this thread and who had no time for losers like me who couldn't keep up -- and who were more than content to stand there while kids in their classes flailed and fell behind and drowned.

Fortunately, I was strong in other areas of my education, but I'm still ashamed after all these years that I'm so shitty at math.
posted by blucevalo at 11:49 AM on March 25, 2012 [4 favorites]

Actually, the quadrilateral isn't a rhombus in that the partially covered edges clearly can't be parallel. There's a minor possibility that it could have been a trapezium (or a 'trapezoid', as it is apparently called in en-US) judging by the shape, but really, we have no information on whether the edge of the paper is placed parallel to the only completely visible edge of the polygon. The _only_ information you have about the newly formed figure is that it's a quadrilateral.
Yeah, trapazoid is what I meant. I took Geometry in highschool, had that been a more recent experience I might have remembered the rule.

Sometimes it's possible to re-derive the formulas. When I was in highschool learning physics, we were taught the laws of motion as formulas for figuring out stuff like, if you throw a ball in the air with velocity x where it land, where will it be at time T, etc.

When I was in college once, years after that I had a calculus test where they asked a similar question and told you to assume that gravity accelerated things at 10m/s2. The point was, you were supposed to use the calc you were learning to re-derive those formulas. At that point, it was actually easy for me to do. You just take the anti-derivative of a straight line with a slope of ten to get the velocity formula, then do the same thing again to get the position formula.

But, remember, on the SAT you have to do 20, 30 questions like that. Even if you can re-derive the interior angles rule in a couple minutes, you're still fucked because there are however many more questions like that. You have to solve it quickly

I don't remember exactly how many questions were on that calc test, maybe 5-10? You could spend 5-10 minutes on each one.

The first question was crazy easy, though.
most good studies indicate that it's a very weak predictor of college performance.
The biggest problem, IMO is the fact that in the 'real world' you have resources in front of you. I was able to lookup the interior angles thing with a few seconds of googling. What's important in this day and age is the ability to quickly lookup formulas, etc. Memorization can be helpful, but really if you use something all the time you're much more likely to have it memorized.

But it sounds like the real key is to study methods to beat the test. If I knew all the formulas that might come into play on the SAT and how to recognize the situations they might come up, of course it would be easy.
Colleges should ask for a good essay, interview applicants thoroughly, and just ask a lot of their students when they get there.
I actually think essay questions are a terrible way to judge people. Especially a one that's graded in 60 seconds. And writing longhand? Might as well shoot myself in the head. Ugh. At least they don't grade on spelling.

---

The guy Robcorr quotes is kind of a dumbass, though.
“I have a wide circle of friends in various professions. Since taking the test, I’ve detailed its contents as best I can to many of them, particularly the math section, which does more than its share of shoving students in our system out of school and on to the street. Not a single one of them said that the math I described was necessary in their profession.
The thing is, the kid of math that this guy learned in highschool probably involved lots of pencil and paper arithmetic. Something that's even less necessary today then what was likely on the test. If kids who did well on that test tried to take the kinds of tests that he took as a student, likely they'd flunk.

If kids do poorly on the math portion of the tests, it's because they didn't learn the math they were being taught. What's important these days is being able to apply concepts and 'encode' ideas mathematically, not crunch through arithmetic. In fact, on the SAT at least you can actually use a calculator. So testing someone's arithmetic would be completely useless. You might as well just drop the math requirement entirely.
“If I’d been required to take those two tests when I was a 10th grader, my life would almost certainly have been very different. I’d have been told I wasn’t ‘college material,’ would probably have believed it, and looked for work appropriate for the level of ability that the test said I had.
Yes, and if you wanted to become a scientist or engineer today that would likely be correct. It would mean you weren't able to absorb the math you'd been taught.

This guy should sit through a couple hundred Khan Acadamy videos, take good notes, and then re-take the test with notes.
posted by delmoi at 11:50 AM on March 25, 2012

Regarding the Orange County School Board Member who said this: “It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate.

Here is what is wrong: He is innumerate. Two of those degrees are in education and one is in education psychology. I can't imagine these programs were even minimally quantitatively challenging.

Nope.

Can't address the math part, but let's look at his 62% in reading.

I got a perfect score on the PSAT verbal and a 710 on the SAT verbal in the mid-80s. I can punch above my weight in any verbal standardized test in english and the romance languages. I took the WaPo sample test and got all 10 (or wev) right, easily.

But when I got into K-12 education and had to start reading all the technical shit that comes with educational pedagogy (teaching reading and cooperative learning and analyzing statistics and so forth) I had to pretty much learn how to read all over again. Reading literature is not the same as reading informational text is not the same as reading analytical text, etc etc. How well does your lit degree prepare you for using Haynes Manuals?

The school board member is quite competent at reading content that pertains to his profession, and good for him. What he's saying is that the FCAT tests your ability to read and analyze poetry, and then based on that, tells you whether or not you're fit to go to college *for any specialty*.

That's what's wrong.
posted by toodleydoodley at 11:56 AM on March 25, 2012

Gonna propose a new Blue posting rule - if its posted on Kottke.org first, most of us have seen it already, you can leave it alone.

There's an incredible amount of stuff posted there, and showing up here a day later.
posted by C.A.S. at 12:39 PM on March 25, 2012 [2 favorites]

200burritos: I'm not a teacher, so I guess I don't understand why this would be hard to teach. Can you please explain to me what is so hard about this?

Trying to teach something to someone when they think they already know it but they are wrong is impossible. Absolutely impossible.

Since the "f(x+1)" versus "f(x) + 1" thing is so remedial their eyes, they assume they have it right even if they have it wrong. If I tell them they have it wrong and that they need to change, they get huffy and upset. Then I'm told "well, this is the way my other teachers did it".
posted by King Bee at 12:45 PM on March 25, 2012 [1 favorite]

I have no idea what kottke.org is and appreciated this posting.
posted by benito.strauss at 12:46 PM on March 25, 2012 [3 favorites]

I have no idea what kottke.org is and appreciated this posting.

Same.
posted by kafziel at 1:06 PM on March 25, 2012

//if its posted on Kottke.org first, most of us have seen it already, you can leave it alone.//

I quit reading Kottke because stuff shows up here the next day, with intelligent commentary added. Usually.
posted by COD at 1:44 PM on March 25, 2012

Here is what is wrong: He is innumerate. Two of those degrees are in education and one is in education psychology. I can't imagine these programs were even minimally quantitatively challenging.

Depends on your definition of "minimally", I guess, but I certainly had to take stats papers as part of my psych degree, and I'd hope and assume that the same was true in his case.
posted by Infinite Jest at 1:47 PM on March 25, 2012

C.A.S. writes "Gonna propose a new Blue posting rule - if its posted on Kottke.org first, most of us have seen it already, you can leave it alone.

"There's an incredible amount of stuff posted there, and showing up here a day later."

It's like we are filtering the good stuff on the web and posting it here.
posted by Mitheral at 2:28 PM on March 25, 2012 [10 favorites]

Also, you should know that you were extraordinarily good at test prep; if improving student scores to that extent in a ten-week course were routine, the SAT would have big problems.

I wasn't. That kid was an outlier. The average improvement was closer to 100. Which isn't as impressive, but is still nothing to sneeze at. I'm given to believe that the organization expects results in about that range.
posted by valkyryn at 3:49 PM on March 25, 2012

The most interesting part is about the SAT grader who has to read all those essays. A real story there somewhere.

I've done it too, as have a few other MeFites as charlie don't surf mentions above [and in this comment]. I've also worked for The Princeton Review and spend a lot of time geeking out about both standardized testing and the travesty that No Child Left Behind is. One of the things we did for TPR was take standardized tests, a lot. Most teachers got to the point where they could get near perfect scores on the SAT and the GRE though the LSAT was a bit more tricky. I assert, as others have, that they mostly prove how well you can learn the set of things that these tests test for and everyone knows that the only thing, literally the only single thing, these tests scores correlate with is family household income.

if improving student scores to that extent in a ten-week course were routine, the SAT would have big problems.

The improvements are routine, for kids who study, and yes they're about what valkyryn indicates. However the people who prep are a really small subset of All The Kids even if they may seem ubiquitous in more affluent areas. I found the article amusing because yeah that stuff is tough if the last time you interacted with a lot of it was twenty years ago. For a lot of people in the educational biz, they wish they could be this surprised by what was on those tests.
posted by jessamyn at 4:32 PM on March 25, 2012 [3 favorites]

escabeche: “Your experience seems totally consistent with the general consensus that SAT scores capture some kind of mixed-up amalgam of intellectual preparedness for college with ‘good at multiple-choice test’ gamesmanship.”

This doesn't seem true to me. As far as I can tell, there were studies funded by the College Board which seemed to indicate this, but most of those have been discredited, and the consensus nowadays seems to be that the SAT does not in fact indicate intellectual preparedness for college. I gave some links for this above. I understand I might be wrong, however; this is just my feeling having read a little about the issue. I think the SAT warrants a good deal of skepticism, for several reasons.

pts: “I don't feel particularly smart for seeing the answer, because it's a bullshit question that you don't actually have to understand anything important about to get right.”

escabeche: “My heart is kind of broken by this sentence, because it's preceded by an articulately phrased and completely mathematically sound paragraph which makes it utterly clear that you do understand the mathematical principle the problem is trying to test, a principle which is deeper and more important than any trig identity. And yet something about your schooling has failed you so badly that you think a math question is 'bullshit' because you could get it right by virtue of understanding something important about math.”

This gets right to the heart of the issue, I think. The current educational system can sometimes teach people about certain facts and concepts; but there are many times when it's apparent that it's utterly failing to teach the import or meaning of those facts and concepts, to convey their importance, or to instill in its students any kind of reverence or love for education. In a significant sense, the current educational system really is 'bullshit.' And one of the central reasons for that is the systematic removal of meaning through such mechanized rituals as the SAT and other standardized evaluation tools.
posted by koeselitz at 4:59 PM on March 25, 2012 [1 favorite]

Gonna propose a new Blue posting rule - if its posted on Kottke.org first, most of us have seen it already.

The only time I ever hear about that site is when people on metafilter complain about people posting stuff here that they saw there first.
posted by empath at 5:38 PM on March 25, 2012 [4 favorites]

I'm pretty sure it's been years since I've seen kottke.org. According to Quantcast it reaches around 80k people a month, and has a rank of around 21k. metafilter reaches 2.6 million a month and is the 579th most popular website in the US.
posted by delmoi at 6:11 PM on March 25, 2012 [1 favorite]

koeselitz: In a significant sense, the current educational system really is 'bullshit.' And one of the central reasons for that is the systematic removal of meaning through such mechanized rituals as the SAT and other standardized evaluation tools.

And yet -- the reaction I meant to convey is that when I saw that question, my response was "that's nice, the people who write standardized tests are no fools; this question actually tests something meaningful that I care whether people know."
posted by escabeche at 6:46 PM on March 25, 2012

You know what would make a far more effective admissions tool? Interviews.

But there are plenty of reasons someone might interview well or poorly that are also unrelated to how well they'll perform in college, like shyness, or social anxiety, or even just a personality mismatch with the interviewer. And further, since people tend to prefer people like themselves, weighting a single social interaction might have unintended consequences re: race/class, even if there's no conscious or explicit discrimination as there was in the early 20th century:
The personal interview became a key component of admissions in order, [Jerome Karabel] writes, "to ensure that "undesirables' were identified and to assess important but subtle indicators of background and breeding such as speech, dress, deportment and physical appearance." By 1933, the end of Lowell's term, the percentage of Jews at Harvard was back down to fifteen per cent. (from this Malcolm Gladwell piece)
This isn't at all to suggest that the SAT is some wonderful equalizer of racial and class inequality, of course. But shifting to a system that heavily favored interviews would give me pause.
posted by en forme de poire at 7:32 PM on March 25, 2012 [1 favorite]

per delmoi's link: 31% of mefite households make \$150K or more per year?
posted by desjardins at 8:35 PM on March 25, 2012

Why is the lowest possible score 200 rather than 0? I've always wanted to know this.

IIRC, their rationale was:
(1) everybody is familiar with the 0-to-100 scale and has preconceived notions of what a score on that scale means
(2) they wanted a completely different scale that nobody else had ever used, that would be associated only with their tests, so it would mean only what they wanted it to mean
(3) being very bright professional test-makers, they created a 200-to-800 scale, and that has stuck over the decades
posted by exphysicist345 at 9:02 PM on March 25, 2012 [1 favorite]

en forme de poire: “This isn't at all to suggest that the SAT is some wonderful equalizer of racial and class inequality, of course. But shifting to a system that heavily favored interviews would give me pause.”

This is the issue – why?

I understand that it's a difficult thing, evaluating students selectively and accurately determining which will perform to an exact level. And if that's our goal, then we have a difficult task ahead of us.

But why is that our goal? And if it weren't, what would that look like? There is this notion in the college world that selectivity, that this strict and careful acceptance of only the top students, is the only way to broadcast a college's quality. But I'm not sure that's a good marker of the quality of education.

The problem here is that education is supposed to make students better. A more realistic marker of the quality of a college education would be if a school took the worst students and graduated a high percentage of the best – then it could be known that that school was really doing its job.

That seems like a great length to go to, and I don't see any social incentive to have students tested at graduation. However, I do think it would really benefit colleges to give up the emphasis on selectivity and make more of an effort to collect a diverse body of thoughtful students that seem ready and willing to put in the work to learn. As I said above, I was out-performed in college by someone who didn't even finish junior high; needless to say, she was not prepared for an SAT, although she had her own reading habits by the time she got to college. It seems like a bad idea to weed out people like that.
posted by koeselitz at 9:32 PM on March 25, 2012 [1 favorite]

Shockingly, little about the SAT has changed since I set foot in that classroom. Most students still have to take the test using bubble sheets and a No. 2 pencil, which is insane to me. They've managed to digitize VOTING, for shit's sake. And yet here's the SAT, still feeding test sheets into the Scantron machine like it's 1982. Maybe the only differences with today's SAT are the essay question (barf), the higher maximum score (2400), and the hugely metastasized frenzy over the test. Wired reports that as recently as 2009, the test-preparation industry had earnings of over \$4 billion. Private tutoring from a Kaplan expert to study for the test can cost you close to \$5,000, an expense plenty of nutjob helicopter parents are happy to throw down.

There are many, many problems with the SAT. Using a pencil is not it. (Also, digitizing voting ain't the best example of progress.)

But no wonder he was flummoxed by the reading comprehension and essay tests -- he says that almost nothing has changed...then references some pretty significant changes. And sure, the test-prep industry has grown (uh, not really "metastasized") but c'mon, I graduated high school in 1991 and there was moaning over the expensive test-prep classes and tutors and books then.
posted by desuetude at 9:43 PM on March 25, 2012

I honestly feel baffled that anyone would fail to see how easy that question on functions f and g is. Now, the polygon one does need a bit of joined-up thinking to reach the answer, but those functions? Come on. No excuse.

Okay, let's do a sort of verbal skills test. Why don't you explain how your reply above is ignorant and self-absorbed?
posted by desuetude at 10:02 PM on March 25, 2012

31% of mefite households make \$150K or more per year?

That's visitors, not members.

But frankly there are quite a few well educated members here, a notable portion of whom work in finance, technology, and law. There's also a slant towards a lack of children, which statistically puts a higher percentage of people in dual income situations.

Last but not least a huge proportion of the most active posters appear to sit in front of an unmonitored computer screen all day. That does not speak of minimum wage employment. Unemployment perhaps, but not minimum wage.
posted by Tell Me No Lies at 10:34 PM on March 25, 2012

The SAT is bad. I know it inside and out. It's been my career.

But interviews aren't the answer (and at many schools are already part of the app process). Without even going into the many, many problems with making interviews more important than they currently are, we can see that they are not a suitable replacement for the SAT for one reason above all others: the SAT is valuable to colleges because it is the one thing they can use to objectively compare every applicant (I mean there's no subjectivity in SAT scores, not that the test itself is an objective measure of anything, of course). GPAs vary by school, grades by teacher, activities by region and resources, experiences by wealth, but the SAT is the same for everyone.

Now I'm not remotely convinced it's a very GOOD exam (the writing section, especially, is broken by design), but unless something better comes around, most schools will need it.
posted by Joseph Gurl at 11:54 PM on March 25, 2012 [1 favorite]

In a related vein, here is what happens when parents take their third-grader's reading test (found via this commentary).
posted by TedW at 12:22 AM on March 26, 2012

I imagine that there are people who have a "math disability" akin to dyslexia

There generally are, but not nearly as many as think they do.

I could go on for paragraphs, having trained as a math teacher and had to listen to how much everyone hates math and how useless it is (I was even told this by an education professor in front of my class, where I was the only math-ed person.)

Math is different from other subjects. In history you can goof off and flunk the 16th century and then buckle up and do okay on the 17th. But in math, since it all scaffolds, if you louse up pre-algebra, you don't have much of a shot at algebra unless you actually go back and learn the stuff. This annoys people, so they simply claim they "just can't get it". Anything else they want to get is fine, but math? It's simply impossible for them.

It's not impossible for most people to do high school math. But it's become acceptable to say you simply can't.
posted by Legomancer at 5:00 AM on March 26, 2012 [5 favorites]

Legomancer is correct. In Korea, where I live, literally every student I've ever taught has great math skills--and it's not genetic, people. Math, like anything else, is doable. The whole "humanities/STEM" division of personality & learning types is pernicious and false.
posted by Joseph Gurl at 5:27 AM on March 26, 2012 [2 favorites]

“If I’d been required to take those two tests when I was a 10th grader, my life would almost certainly have been very different. I’d have been told I wasn’t ‘college material,’ would probably have believed it, and looked for work appropriate for the level of ability that the test said I had."

I have long said this about Florida's FCAT exam. I believe it's the WORST standardized test I've ever seen. I taught the damn thing and I couldn't get a handle on it. The Reading Comprehension is especially horrible.

I too have a degree in literature and an advanced degree and I struggled with it.

As for the SAT, GRE and GMAT. Screw them. Talk about old fashioned, although I belive that I did take the GRE on a computer. That's 4 hours and \$100 bucks I'll never get back.

And what's at the end of all of this? Idiots who can't read for comprehension, write for shit or work complex mathematical problems. College Freshmen.
posted by Ruthless Bunny at 6:29 AM on March 26, 2012

There is this notion in the college world that selectivity, that this strict and careful acceptance of only the top students, is the only way to broadcast a college's quality.

Then there's that other notion that colleges shouldn't have to waste limited teaching resources on running remedial programs for people who couldn't be arsed to learn the difference between f(x + h) and f(x) + h.
posted by flabdablet at 6:36 AM on March 26, 2012 [1 favorite]

Why I went to an art college which said "we don't look at ACT/SATs. We look at grades and portfolio of talent. Choose math OR science related to your field"---see below (I have zero f-in clue what any of these mean.

Question 2:

1. Any regular 4 sided polygon has 360 degrees as the sum of its interior angles.
x + y = 80. So, the other two angles added together makes 280.

2. All angles and sides are equal, so, 280 / 2 = 140 degrees per angle

3. (n-2) × 180° / n (where n is the number of sides) is the formula to calculate the interior angle.

4. (9 - 2) x 180 / 9 = 140.

5. 9 sides.
posted by stormpooper at 6:36 AM on March 26, 2012

There will never be an SAT question on the Oxford comma, for example. The test format won't permit a question with more than one right answer, which eliminates a huge amount of potential questions and answers.

PISTOLS AT DAWN, SIR.
posted by Mayor West at 8:16 AM on March 26, 2012

There will never be an SAT question on the Oxford comma, for example. The test format won't permit a question with more than one right answer, which eliminates a huge amount of potential questions and answers.

Oh but there IS. The SAT Writing test has an essay section. Yes, they do look for correct usage of Oxford commas, which is a sign of higher level grammar abilities. I've scored elementary school essay exams that grade on Oxford commas. The School Boards often decree only one type of usage is correct, because that's what they teach.
posted by charlie don't surf at 8:28 AM on March 26, 2012

Joseph Gurl: “Now I'm not remotely convinced it's a very GOOD exam (the writing section, especially, is broken by design), but unless something better comes around, most schools will need it.”

Again – why? Need it for what?

me: “There is this notion in the college world that selectivity, that this strict and careful acceptance of only the top students, is the only way to broadcast a college's quality.”

flabdablet: “Then there's that other notion that colleges shouldn't have to waste limited teaching resources on running remedial programs for people who couldn't be arsed to learn the difference between f(x + h) and f(x) + h.”

This presumes that colleges want to teach undergraduates advanced knowledge, so they desire the students they accept to be advanced students who have acquired a standard set of knowledge already. But I disagree with this, for at least two reasons.

First of all, I don't believe knowledge is linear in this way. Knowing how to manipulate functions is not the same thing as understanding what they mean, and understanding probably isn't something that can be tested for in the standard ways. This is particularly true in the realm of calculus; when I got to college, I'd done the advanced calculus classes, and I could manipulate derivatives very well, but I had no idea what they meant. I don't think anybody in my advanced calculus class did, honestly – I don't even think the teacher did.

But the college I went to insisted that all students begin over again, from the very beginning – that is, with Euclid, and then working our way up. When we did calculus my junior year using Newton's Principia Mathematica as a textbook, for the first time in my life I actually understood what calculus meant. It made sense. I could finally see the point of all those derivatives and all the other nonsense. And because we'd all gained that understanding, the college I went to could bring us through Maxwell's formalization of Faraday's experiments in the senior year and then follow it up with Einstein's papers on relativity. None of that would have been possible, I think, if we hadn't started over from the beginning and worked toward understanding rather than functional capability.

Second of all – I really don't think an undergraduate education can possibly grant expert knowledge of a subject. Nor is it expected to in the real world, as far as I can tell. So the assumption that colleges have to get a head start by only admitting students who already have advanced knowledge seems flawed, because it assumes that colleges must get somewhere specific in the space of four years. Higher education is better off starting from the beginning and making sure students understand. Specialized expert knowledge of a field comes from graduate school.
posted by koeselitz at 8:54 AM on March 26, 2012 [1 favorite]

koeselitz, my good man, "need it for" determining whom to accept--there are alwazs far, far more wonderful applicants than there are spaces, and, like it or not, name value education (even if we toss aside the possibilitz that it offers "better schoolin´") unequivocallz offers better job opportunities, a fact that is verz important to manz people. Without at least one ingredient that is flatlined for all applicants, the US admissions process would be even more of a clusterfuck than it alreadz is, and that´s sazing something.
posted by Joseph Gurl at 11:32 AM on March 26, 2012

Nobody's going to link to the "Arcade" episode from season 3 of Newsradio? That's the straight-up plot. (A 35-ish-year-old man retakes the SAT to see how much stupider he's gotten.)

"It's been a long time, Stargate Defender."

"Indeed it has, Dave."
posted by mrgrimm at 1:44 PM on March 26, 2012 [2 favorites]

There will never be an SAT question on the Oxford comma, for example. The test format won't permit a question with more than one right answer, which eliminates a huge amount of potential questions and answers.

PISTOLS AT DAWN, SIR.

Shouldn't that be:

PISTOLS, MUSKETS, AND SABRES AT DAWN, SIR!
posted by TedW at 1:45 PM on March 26, 2012 [2 favorites]

I found the article both hilarious and insightful about the weird fascist tone and lack of utility of the SAT. Then I came to read this thread, and it's just utterly bizarre. I'll admit I finally started skimming after the first 60 or so comments calling the author an idiot, so maybe it got a lot better, but jeez. A whole lot of people in here seem weirdly upset that some guy on the internet doesn't remember much geometry.
posted by rusty at 2:28 PM on March 26, 2012 [2 favorites]

I took the SAT twice, first in 7th grade -- I don't remember the exact score, but it was higher than my pre-algebra teacher had gotten when she took it -- and again as a senior in high school, also did pretty well then. I have a knack for standardized tests, more than anything else. FWIW, I was told after my 7th grade experience that one oughtn't guess on the SAT and was terribly surprised, since that was my main method for getting through the experience.

I actually found the article hilarious.

I did very well in math all through school, was in a special after-school math class at a fancy private school, took AP Calculus, and enjoyed it. BUT...I haven't used any math beyond algebra in the 19 years since I took Calc II in college. And for somewhat odd reasons, I never actually took geometry. So yeah, the math questions: strange and baffling.

It's like looking at the contents of this time capsule I made in junior high*: I know it means something, and I know that I used to know what, but now? ::shrug::

* SO MUCH WTF. All the 5s from a deck of cards? A broken bookmark? A peach pit? Girl, who were you?!
posted by epersonae at 2:55 PM on March 26, 2012 [1 favorite]

I find it hurtful that so many people in this thread are basically being huge bullies about "how easy" those math questions are.

I do not consider myself to be an idiot and have done very well in life so far, regardless of my inability to comprehend even basic math - so I stand firmly in the camp of people who would resent that assertion.

I have read every explanation to those questions in this thread and I still don't understand either of them. I can memorize laws and equations and regurgitate them but I can never, ever, it seems, intuitively understand them. The fact that I don't understand these "simple" math problems makes me feel as stupid today at age 29 as it did when I was back in high school - and the smug attitudes on display in this thread only exacerbate that sting. If only condescension helped me understand math I would have figured it out years ago.

Back in the day I had two different math tutors and also went to the teacher every week for help with math homework. I tried as hard as I could and I still got C's. I was a rockstar in most other subjects...but math? I still can't do most math despite wanting to understand it and I really resonate with this guys article (which, by the way is tongue-in-cheek...relax here people). The frustration of not being able to understand, despite putting in my best effort, what is to so many people "basic" and "easy" is immense. My only saving grace was that while I couldn't do math I was given a talent for drawing...but I wouldn't lord that over people who can't ...so go easy on people who can't do math and stop assuming that it's clear for everyone, or that if it's not that they must be idiots. That attitude isn't going to help anyone learn math and it's that attitude that stops people from even trying.
posted by jnnla at 5:02 PM on March 26, 2012 [3 favorites]

The fact that I don't understand these "simple" math problems makes me feel as stupid today at age 29 as it did when I was back in high school

OK. You're not stupid, or you couldn't have written what you just wrote. So let's try to unwind a bit of the "I am too stupid to get math" self-defeat here.

Go grab the f(x) and g(x) question again so that what I'm about to explain has something to make sense about.

There are really only two ideas you need to understand to answer that question, and neither of them is complicated. They're really good ideas, but not complex ones.

The first idea is functional notation. The way to read "f(x)" is "f of x" and all it means is "the result of taking some value x, and altering it in some predefined way f".

For example, if f was defined to mean adding fifteen to something, then f(3) would come out to 18 and f(12) would come out to 30 and so on. And if g was defined to mean dividing something by two, then g(6) would be 3 and g(9) would be four and a half and so on.

So by now I'd expect that one of two things is happening in your head. The reaction I'm hoping for is the one that says "OK, that's not so hard, I get that. What's the other good idea?" But the one I'm actually expecting is "oh fuck OFF fucking MATH FUCK YOU you FUCKING FUCK".

Let me know which is closer to the mark before we go any further.
posted by flabdablet at 5:52 PM on March 26, 2012

Math is different from other subjects. In history you can goof off and flunk the 16th century and then buckle up and do okay on the 17th. But in math, since it all scaffolds, if you louse up pre-algebra, you don't have much of a shot at algebra unless you actually go back and learn the stuff. This annoys people, so they simply claim they "just can't get it". Anything else they want to get is fine, but math? It's simply impossible for them.

Understanding history doesn't require scaffolded knowledge? (We call it "context.") People who have a hard time understanding math are lazy? What are you, my firth-grade teacher?

Yeah, math is special. It's special in that it's taught in a way that is utter gibberish to a fairly significant subset of people, many of whom are not masochistic enough to keep asking questions when the answer is always "look at this one example and then just...figure out the problem. Work harder, you'll get it." It's special in the delusion that "word problems" are great examples of applied mathematics, when really they're just the same old worksheet problems made even less understandable through tortuously contrived verbiage.

Attempting to get through math classes for me was like being expected to find an address in Paris with nothing but a London street map. What's the difference -- there are streets, they intersect, there's a subway, what do you mean you don't understand, it's the same principle, don't you get it?
posted by desuetude at 6:06 PM on March 26, 2012

For example, if f was defined to mean adding fifteen to something, then f(3) would come out to 18 and f(12) would come out to 30 and so on.

Functions I can explain; arithmetic? Not so much. In fact f(12) would be 27, not 30. Sorry to confuse.
posted by flabdablet at 3:13 AM on March 27, 2012

flabdablet: Some people have dyscalculus. It's like dyslexia, but with math. If that's the case here, your patient explanation isn't going to help, any more than explaining phonics would to a dyslexic. Regardless, it's kinda condescending of you to assume that you can teach someone math here on Metafilter that two tutors and lots of hard work were unable to in school. "It's just a simple idea, you see?" Yeah, please don't do that.
posted by rusty at 5:24 AM on March 27, 2012 [3 favorites]

Functional notation is a simple idea.

An x-y Cartesian graph is a simple idea.

Both ideas, though simple, are also deep, powerful and useful.

Understanding neither of these ideas requires the kind of stepwise digit manipulation skills that dyscalculia makes so difficult.

I've always found that given a patient and willing explainee, a patient and willing explainer can eventually communicate any simple idea. So if jnnla does in fact come back here and express an interest in understanding these things, I will feel quite free to ignore your rather condescending suggestion that further exploration of them would be a waste of time.
posted by flabdablet at 6:28 AM on March 27, 2012

Then you are stupid and you will die.

What a no-account whiner.

...own up to your own lack of work

Then there's that other notion that colleges shouldn't have to waste limited teaching resources on running remedial programs for people who couldn't be arsed to learn the difference between f(x + h) and f(x) + h.

--flabdablet, from the rest of this thread.

I'm sorry, you were saying something about "condescending?"
posted by rusty at 7:03 AM on March 27, 2012 [1 favorite]

OK, fine, I get it, I'm a complete prick and you win at the Internets.

Be that as it may: if anybody doesn't understand the f(x) and g(x) question but would like to, I'm happy to try to help. And if I can't help, even given patience and willingness on both sides, I would appreciate finding out at first hand why not.
posted by flabdablet at 7:25 AM on March 27, 2012

rusty, the point I think flabdablet is trying to make is that many mathematical ideas are actually intuitive and easy to understand. I think he's right.

Looking at those pictures of those curves, can you tell me in English words what's going on? I think most people can. Both of those curves look the same, one is just the other shifted upward. Most people can see that. The problem isn't asking you to describe that with words, though. It's asking if you know the mathematical notation we use to describe that. Is it f(x) +1? Is it f(x+1)? Something else? This where a lot of people shut down, because once we right something "in mathematics", people begin to get turned off. I know what forks and knives are, but if you told me in Japanese to get a fork and a knife from the drawer, I would stare at you and probably do nothing. You might think I'm an idiot, but you'd be better served thinking "well, he doesn't understand Japanese. He probably knows what forks and knives are."

The same goes for music. There are many people who can play and write beautiful music, but shut down when you show them sheet music with all of its wacky symbols. Does this mean they're worse musicians than those who can? Not necessarily. It really just means they can't be arsed to learn the rigorous, standardized way that we write music notation. They'll be hindered in some sense, but they wouldn't ever say they can't understand music, they just want to play and write it. Why? Because it's beautiful and they like doing it. They don't give a damn about the details behind it all. They just want to play music.

My favorite example of an "easy to understand" mathematical idea is the intermediate value theorem. I was about 4 feet tall when I was 10, but now I'm 5'8". Does that mean sometime between then and now I was 5'2"? Of course, that's how people grow. I may have been growing faster or slower at some points over the last 20 years, but I couldn't "skip over" being 5'2". That's absurd.

If I write "if f is a continuous function on [a,b], then for each W between f(a) and f(b) there exists a point c between a and b such that f(c) = W", people get upset, and possibly rightly so (depending on where they are in their mathematical development). The height example is a special case of this statement (my height being the function). I don't blame folks for thinking they can't understand the intermediate value theorem as it is written, but I do get on some folks for saying that they cannot understand the intermediate value theorem. This is false. Most folks do.

This is what mathematics should be like, but mostly, we spend too much time forcing children to understand the alchemy of the symbols we use to represent it. These people then grow up thinking they can't understand math, when most of the time, it's that they don't care about the symbols behind it.

So, I link to this PDF almost every time someone talks about mathematics education on this website, and maybe people are sick of it. I think more people should read it, so I'm linking to it again.
posted by King Bee at 7:34 AM on March 27, 2012 [4 favorites]

King Bee, I hadn't seen that before -- how wonderful! It actually reminds me (in a good way) of the special after-school math class that I loved so much, despite the fact that it was insanely hard. (And now I understand why it didn't include a formal geometry section.) He did teach us enough of the "formal" stuff that we wouldn't be hosed in standardized testing, but it was also taught in a way that engaged our minds in the ideas of math. Makes me feel really lucky.
posted by epersonae at 9:46 AM on March 27, 2012

I think that's what Khan academy does that makes it so easy to understand his videos -- he always, always starts with 'intuition', and explains where formulas come from before he ever gives you formulas and notation. And he always changes up notation, too, which makes it even easier to understand that the symbols aren't really the important thing, but the ideas that they represent are.
posted by empath at 9:59 AM on March 27, 2012

Keep linking, King Bee. I hadn't seen that before and it looks really good.
posted by benito.strauss at 1:36 PM on March 27, 2012

Ergh, I actually tutored high school geometry briefly. Maybe I'd blocked this out when I took it, but I was gobsmacked by how much of it was just endlessly memorizing the names of stupid theorems. Also, for each chapter you were supposed to use one and only one "trick" -- maybe some fact about triangle medians, for instance -- so even if you could actually do it several different ways, only one was "correct" by the standards of the textbook and the teacher. I felt like it made it really hard to communicate how all the pieces fit together, and that all of the theorems were basically only one or two steps away from simple things that made sense (despite their grandiose titles).
posted by en forme de poire at 3:19 PM on March 27, 2012

Understanding neither of these ideas requires the kind of stepwise digit manipulation skills that dyscalculia makes so difficult.

Isn't functional notation a way of manipulating numbers? And when you have a not-great sense of spatial reasoning, graphs make a whole lot less sense.

But that Lockhart article is terrific, King Bee. Any time I hear math discussed in terms of philosophy and art I realize that I'm actually pretty fascinated conceptually. This is how it came to be that Tom Stoppard's play Arcadia gave me a solid understanding of iterated algorithms, yet I have trouble reading analog clocks.
posted by desuetude at 8:28 PM on March 27, 2012

The only reason I remember my SAT score is because I remember Buffy "The Vampire Slayer" Summers's SAT score, and the only reason I remember Buffy Summers's SAT score is because it was EXACTLY 100 points HIGHER than mine, the injustice of which burned because SHE WAS TOTALLY TOO BUSY KILLING THINGS TO EVER STUDY, PEOPLE.

In other news, Buffy's pinnacle of paid employement was as a burger jockey at the Doublemeat Palace, which is pretty depressing when I'm jobhunting.
posted by nicebookrack at 8:38 PM on March 27, 2012 [2 favorites]

Isn't functional notation a way of manipulating numbers?

No. It's a way of attaching a name to a predefined set of manipulations so that you can reason about them without needing to keep the precise details of those manipulations straight at every step along the way. Provided the manipulations can be precisely and reliably defined, the things so manipulated and the results of those manipulations don't actually need to be numbers; they could be sets or groups or vectors or any other kind of mathematical object imaginable.

In the SAT question under discussion, x and f(x) and g(x) do in fact stand for numbers. We know that because they're represented as curves on a standard x-y graph. But we don't know exactly what manipulations f and g are defined to do in order to turn any given value for x into its corresponding f(x) or g(x) results. We're only shown a pair of curves that represent those results for all values of x between -2 and 2.

The point of the functional notation used in the question is that we don't need to know what manipulations f and g perform on x to produce f(x) and g(x); we can happily leave those secrets wrapped up in the undisclosed definitions of f and g. What the graph shows us is the relationship between those two secrets. The fact that the g(x) curve is identical to the f(x) curve except for being displaced upward by 1 unit means that whatever f might do to any given x, g does the same thing and then adds 1.

The point of posing the question is to make sure that the person presented with it understands that g(x) = f(x) + 1 is the right way to express that notion symbolically.

The other multiple-choice alternatives are

(A) g(x) = f(x + 1), which would mean that doing g to any given x has the same effect as adding 1 to x first and then doing f to the result. Putting that another way, doing g to any given x has the same result as doing f to the number that falls 1 unit to the right of x on the graph's x axis. So, graphing that relationship would show two identical curves with the g(x) curve displaced one unit to the left of the f(x) curve, not above it.

(C) g(x) = f(x + 1) + 1 means that doing g to any given x has the same effect as adding 1 to x first, then doing f to the result, then adding 1 to the result of that. Graphing that would show two identical curves with the g(x) curve displaced one unit up and one unit to the left of the f(x) curve.

(D) g(x) = f(x - 1) means that doing g to any given x has the same result as subtracting 1 from x first, then doing f to it. Graphing that would show two identical curves with the g(x) curve displaced one unit to the right of the f(x) curve.

(E) g(x) = f(x) - 1 means that doing g to any given x has the same effect as doing f to it, then subtracting 1 from the result. Graphing that would show two identical curves with the g(x) curve displaced one unit downward from the f(x) curve.

I remain happy to help anybody who doesnt get this, but would like to, do so.
posted by flabdablet at 8:22 PM on March 28, 2012

flabdablet: “It's a way of attaching a name to a predefined set of manipulations so that you can reason about them without needing to keep the precise details of those manipulations straight at every step along the way.”

This is the central problem with modern algebra. Testing people in their knowledge of algebra is basically like testing Americans in their knowledge of Mandarin, and then chiding them for not knowing it – it's just a complicated language that exists largely to create a barrier to understanding. And not only does that cause massive social problems by making mathematics inaccessible to most people; it even makes mathematics inaccessible to the people who know it by making them thing they're doing math when actually they're just manipulating symbols.

The pretentious assumption in this thread that anyone who hasn't bought this bullshit is therefore an idiot is pretty ironical, if you ask me.
posted by koeselitz at 9:51 AM on March 29, 2012 [2 favorites]

it even makes mathematics inaccessible to the people who know it by making them thing they're doing math when actually they're just manipulating symbols.

Abso-tive-posi-fucking-goddamned-lutely.

If I could explain to folks in my college mathematics courses that the fact that they've "always been good at math" actually might mean that they can't do mathematics at all, I would be happy. Can you come in and talk to my classes for me, koeselitz?
posted by King Bee at 10:19 AM on March 29, 2012 [1 favorite]

it's just a complicated language that exists largely to create a barrier to understanding.

That isn't why it exists.
posted by escabeche at 4:01 PM on March 29, 2012 [2 favorites]

The thing is, it can go either way. A formal language can aid communication, by letting you specify what you mean in precise and well-defined terms. And that leads to improved understanding when it works. But it can let you fake understanding, or fool yourself into thinking you've understood something you haven't, by giving you a set of rules to shuffle the symbols around without really grasping what the symbols are supposed to mean.

I'd say the problem isn't so much algebra as it is formal education, and specifically the importance that we place on grades. What's the name of the management principle I'm thinking of here? If you rate people's performance based on a certain metric, they won't work to cultivate the qualities you care about, they'll just work to manipulate the metric? If you rate people based on their algebra grades, it creates a skewed set of incentives where they no longer really want to grok algebra, they just want to get good at mindlessly shuffling the symbols around.

And the thing is, there is something to middle-school algebra beneath the symbol shuffling. It's a very small something, but it's important. The core principles ("if two things are really identical, and you do the same thing to of them, then they stay identical"; "space is like quantity, and distances are like numbers") are really deep and elegant, and they're reuseable — they crop up again in geometry, in logic and computer science, in all sorts of higher math. But you can't grade students on whether or not they've grasped the core principles, whether they've really hung out with them and rolled around in them and appreciated their beauty. All you can grade them on is the symbol-shuffling, so that's what kids end up focusing on.

But, I mean, you get the same problem in any other academic subject. English classes make people hate writing — or make them pointlessly proud of their mastery of arcane "rules" of "grammar" and style, so that they can make it through the rest of their life, identifying as good writers the whole time, without stopping to ask whether their prose is clear, beautiful or useful. Geography classes make people hate geography — or fill them up with lists of states and capitals and distract them from caring about what other parts of the world are really like. Our educational system is really useful for giving people basic literacy and arithmetic and a baseline of world knowledge, but it sucks at steering anyone towards a deep understanding of anything, and that's a hell of a tradeoff.
posted by nebulawindphone at 4:38 PM on March 29, 2012 [1 favorite]

it's just a complicated language that exists largely to create a barrier to understanding.

Is there a better substitute?
posted by flabdablet at 4:41 PM on March 29, 2012

Is there a better substitute?

I think the point is that there is no need for the formal language in mathematics when you're just starting out learning it. I don't need to talk about functions F(x) and G(x) and how to write down transformations when I really just want to look at curves in the plane and move them around. I don't need to say "AAA" when I want to talk about two triangles being "the same" (similar) but one is a scaled up (or down) version of the other.

I can just play with these imaginary things, have them talk to me, and talk about them to other people without having to muck it all up with symbols all the time.

I go back to the music analogy. I can play and write a song on the guitar, and then show you what I'm up to, and I don't have to write it down on a staff with specific notes in specific places and figure out exactly what the fucking time signature is. I can just say, "listen, it goes like this ---" We don't have to take all the joy and fun and beauty away from music by forcing everyone to learn how to read sheet music. I understand and appreciate music and play and write a bit myself, just for my own amusement, without understanding how to read sheet music. Isn't this OK?

Now, if I wanted to delve deeper, and share my ideas with people around the globe, it helps to have a formal language so that we all know we're talking about the same thing. That should come after understanding.
posted by King Bee at 4:56 PM on March 29, 2012 [1 favorite]

I think the point is that there is no need for the formal language in mathematics when you're just starting out learning it. I don't need to talk about functions F(x) and G(x) and how to write down transformations when I really just want to look at curves in the plane and move them around. I don't need to say "AAA" when I want to talk about two triangles being "the same" (similar) but one is a scaled up (or down) version of the other.

Of course, the SAT isn't supposed to be for people who are "just starting out". It's for people who are coming off of a twelve year education in mathematics and math notation.
posted by kafziel at 5:08 PM on March 29, 2012

Yes, but the conversation has shifted from the SAT to the topic of mathematics education in general, and that was what I was speaking to.
posted by King Bee at 5:12 PM on March 29, 2012

Our educational system is really useful for giving people basic literacy and arithmetic and a baseline of world knowledge, but it sucks at steering anyone towards a deep understanding of anything

Before I go any further, let me make it clear that my experience is with Australian primary school education, and that within a fairly small sample of schools. And if the differences between Australian school education and American school education are as profound as those between Australian public health care and American public health care, it may well be that my observations are not applicable where you live.

I work as a school IT technician. Every time I go to work I get to see primary school education in action, close up and personal. And I don't think the major problem is with the educational system. I think it's inherent.

I have now been at this school for long enough to have seen a couple of cohorts go all the way from prep (the year between kindergarten and Grade 1 in the Victorian education system) to year 6 (the last year of primary school), and it seems to me that the kids who do best are pretty much the ones who have shown signs of wanting a deep understanding of the world since prep. These are the kids whose curiosity shines through above all else. They're the ones who have the gumption to ask questions. By and large they're the ones who just knuckle down and get the work done instead of creating disruption in classes and playing petty power games at recess. And their attitude is pretty much consistent, all the way through from prep to 6.

So I don't think it's the education system that beats the spark out of kids. I think there are wider forces operating.

It seems to me that the kids who do well at school are the same kids who are lucky enough to have stable and happy lives at home, and parents who display a clear interest in working with the school to help their kids get what they need from it. I was one of those, and I do feel incredibly lucky.

It also seems to me that learning does proceed stepwise to a fairly great extent, and that failures of understanding in the earlier steps pretty much doom efforts to build on those. And as long as something like classes exist - which they will do unless we reorganize ourselves to that every single student can have access to personalized, skilled tuition in whatever field they fancy - then it's absolutely unfair on students who do already understand the prerequisites to make their teachers spend their class time on bringing students who don't up to speed.

So while I agree that teaching kids the best way to game a standardized test is a crappy use of their time, I disagree that the fault lies in the standardized test itself, on in the requirement to be able to pass a standardized test in order to gain access to further tuition.

if I wanted to delve deeper, and share my ideas with people around the globe, it helps to have a formal language so that we all know we're talking about the same thing. That should come after understanding.

My own reaction on first exposure to algebra - to the idea that symbol manipulation in a formal language makes it possible to tackle problems that would otherwise drown me in complexity - was profound delight. And I remember having the same reaction when first shown simultaneous equations, and again on being shown the general solution to quadratic equations, and again when I first encountered calculus. Handwaving geometry is not the only source of raw mathematical delight, and messing about with algebra can be as pleasurable as messing about with any other form of creative writing.

So I don't agree that learning formal mathematical language should come after understanding, because so much of it comes with understanding.

But I do agree that attempting to force people to rote-memorize slabs of it without understanding is a tragic waste of time.

But here's the thing: surely that can only happen when students are put in a position of attending classes designed to communicate material for which they do not grasp the prerequisites and/or the rationale? And how are we to find out whether anybody does grasp something without doing some form of testing?

And how are we to help students whose desire for a deep understanding has been beaten out of them at home before they even come through the school gates?
posted by flabdablet at 5:49 PM on March 29, 2012

Handwaving geometry is not the only source of raw mathematical delight, and messing about with algebra can be as pleasurable as messing about with any other form of creative writing.

Mathematical rigor isn't in the symbols you use to talk about it. I'm not talking about "handwaving", I'm talking about letting people write mathematical arguments in their own words, rather than being tied unnecessarily to specific ways of representing ideas.

So I don't agree that learning formal mathematical language should come after understanding, because so much of it comes with understanding.

I do agree with this to some extent. I have no idea how one would talk about the Lebesgue integral and certain convergence theorems without all the symbols. However, be reminded that no mathematician in the world, and probably even throughout history, has memorized theorems as they are stated with all the symbols. They remember what they say.

I do have a really hard time with figuring out how to get people interested in mathematics at the start. I think that by holding off on some of the more unnecessary notation at the outset could help not scare away so many folks. It would also help a lot if we had teachers who were passionate about mathematics, understood it more as an art and less of a tool for scientists, or cared to ever have produced a piece of mathematics in their lives.

A major problem with education in mathematics (at least here, in the US) is that most mathematics teachers do not understand the subject at any level deeper than the one they are teaching it. When I hear future "teachers" tell me that they are upset that they have to take calculus when "I just want to teach algebra to elementary school kids, why should I have to take calculus", I want to stab myself in the heart. Would you want someone who could only read at the level of the "Dick & Jane" books teach your children how to read? After all, that's the level the children are reading at, why should you, as a teacher, have to understand anything else? It's preposterous.

There needs to be an attitude shift, and I'm not sure how to bring it about. I'll just keep linking to Lockhart's article on internet forums and showing it to any colleague of mine who might give a damn.
posted by King Bee at 6:09 PM on March 29, 2012

flabdablet: “Is there a better substitute?”

Of course there is. Geometry.

“Handwaving geometry is not the only source of raw mathematical delight...”

I don't really understand what this means. 'Handwaving' geometry? Geometry is what algebra is supposed to describe. The problem with algebra is that it allows you to do mathematics whilst completely forgetting the geometry that underlies it – and therefore miss its actual meaning much of the time. I went through regular and advanced calculus in high school, could derive just about anything like a snap; but I had no idea what I was doing. I could never have understood the calculus of fluid dynamics and Maxwell's equations if I hadn't read Newton's Principia Mathematica and seen him construct calculus geometrically.

And, as I said, I think geometry is closer to the truth than algebra – I don't buy that they're simply alternative ways to describe the same thing. Language matters. The way we describe things matters. The broad impact of algebra on the world we live in has been so massive that it's difficult to appreciate it adequately, but I think the central impact it's had is on formalizing the language of science. I think that can be very problematic, because it leads us to assume that the world works in mathematical ways; the fact that we seem to see mathematical patterns in the world surely doesn't mean that they're there automatically. Geometry, which describes the purest form of mathematics as the study of one and many, encompasses this much better than algebra, because it is entirely explicit; it doesn't involve symbol-based shortcuts that remove the true meanings from the things that mathematics is trying to talk about.
posted by koeselitz at 11:21 PM on March 29, 2012

me: “... it's just a complicated language that exists largely to create a barrier to understanding.”

escabeche: “That isn't why it exists.”

Every shorthand exists largely to create a barrier to understanding. The assumption is that understanding the components all at once would be too difficult – otherwise, why would one need a shorthand symbolic system? – so one forgets about the contents of the components and focuses instead on the relationship between them. Isn't that how algebra works?
posted by koeselitz at 11:28 PM on March 29, 2012

Every shorthand exists largely to create a barrier to understanding.

Do you think that Newton came up with dot notation to make Calculus harder to understand? I think it's a lot more likely that he just got tired of writing 'the derivative of X with respect to time'.

It's perfectly possible to write out all of your equations in long hand, and people frequently did when they developed these systems. It doesn't make it easier to understand at all. Frequently, rolling up a whole bunch of complicated functions into one symbol makes the bigger picture much easier to understand.

Shorthand exists so that people who already know what they are doing can work faster.
posted by empath at 6:30 AM on March 30, 2012

Geometry, which describes the purest form of mathematics as the study of one and many, encompasses this much better than algebra, because it is entirely explicit; it doesn't involve symbol-based shortcuts that remove the true meanings from the things that mathematics is trying to talk about.

Try doing math in more than 3 dimensions with just geometry and see how far you get.
posted by empath at 6:33 AM on March 30, 2012

Would you want someone who could only read at the level of the "Dick & Jane" books teach your children how to read?

No, but I'm completely at ease if my kid's kindergarten teacher devours Hunger Games and has no interest in Alice Munro.

I think geometry is closer to the truth than algebra – I don't buy that they're simply alternative ways to describe the same thing.

I can't make you buy it. All I can say is that I do algebraic geometry for a living, and the point of view that geometry and algebra are alternative ways to describe the same thing, two points of view which we have to be able to switch between fluently and frequently, has driven a tremendous flourishing of understanding.

Every shorthand exists largely to create a barrier to understanding.

Yes, I long for the days when I used Roman numerals and really understood number theory. Better still was when I just used heaps of pebbles.

Now of course it is true that Arabic numbers make it possible to get addition problems "right" without understanding what the + sign refers to. But that's not the purpose of Arabic numerals. That's not why they exist. And it would be truly weird to expunge Arabic numerals from the K-5 math curriculum and teach it all with heaps of pebbles.

Now you might say -- but shouldn't you then teach heaps of stones first, then introduce arithmetic operations on numerals when kids understand what addition and multiplication actually mean? Sure -- and that's why that's what schools already do. Same for algebra -- the idea of asking questions like "I'm thinking of a secret number, you multiply it by 2 and add 5 to it and you get 11, what is it?" are introduced long before the notation 2x+5 = 11.

But without the notation, or the shorthand, you just can't understand that much. It's the opposite of a barrier. We understand geometry a hell of a lot better than Euclid did, or for that matter Poincare, and the reason is largely because we now understand that geometry is not "the real thing" of which algebra is merely a convenient description. They're both real and they each describe each other.
posted by escabeche at 6:47 AM on March 30, 2012 [5 favorites]

It would also help a lot if we had teachers who were passionate about mathematics, understood it more as an art and less of a tool for scientists, or cared to ever have produced a piece of mathematics in their lives.

I'm pretty sure I read a study someplace that elementary education majors reported being most "afraid" of math of any college students. This would seem to be a huge barrier to improving math education in general.
posted by epersonae at 11:36 AM on March 30, 2012

empath: “Try doing math in more than 3 dimensions with just geometry and see how far you get.”

I have. You can get pretty damned far, actually.
posted by koeselitz at 4:02 PM on March 30, 2012

escabeche: “Yes, I long for the days when I used Roman numerals and really understood number theory.”

Roman numerals are actually a relatively recent anomaly. Normal base-ten number systems are much more common. People were using base-ten number systems three thousand years ago, and I don't think it's likely that any mathematician ever worked primarily in Roman numerals.

me: “I think geometry is closer to the truth than algebra – I don't buy that they're simply alternative ways to describe the same thing.”

escabeche: “I can't make you buy it. All I can say is that I do algebraic geometry for a living, and the point of view that geometry and algebra are alternative ways to describe the same thing, two points of view which we have to be able to switch between fluently and frequently, has driven a tremendous flourishing of understanding. ”

Insisting that it is indeed a "flourishing of understanding" isn't an argument – you know that, right? I claimed it was a misunderstanding. Just contradicting me isn't the same as presenting rational reasons why. And this is the difficulty we face generally in this; mathematics, as delineated by algebra, has become an integral part of science, to the degree that people assume that it is an absolute reflection of the way the world works. When you ask people whether this is really true, they say "of course it is! Look how much we know now!" But an assumption can't be proven by pointing to one's faith in conclusions drawn from that assumption.

This is the problem I see, and I'm only pointing it out because I think it needs examining – it's almost completely ignored today. Algebra is a symbolic language which was adopted on the assumption that it exactly expressed the contents of geometry, with a one-to-one correspondence. But the study of that symbolic language has now utterly surpassed the study of its referent, to the point where the vast majority of people who use the symbolic language aren't very familiar with the thing that it's supposed to describe. Moreover, that symbolic language has taken a central place in scientific discovery. Scientists don't familiarize themselves with geometry except in a very general sense – particularly if they aren't dealing with anything macroscopic. This is why Faraday's experiments had to be translated, not into geometry, but into algebra for them to be scientifically acceptable and 'useful.'

So it's clear that algebra, and its use, have a fantastic importance. I guess you'll probably agree on that. What we disagree about is whether algebra is actually directly equivalent to geometry in meaning. It isn't, I think, for one central reason: algebraic equations assume that we're talking about numeric equations – and incommensurate geometrical lengths are not expressible in numbers. I understand that it's common to believe they can be today, in the sense that even if a string of decimal places is infinite it can be estimated or rounded or sometimes even just expressed with shorthand graphically with the knowledge that we're accurately expressing some length. But this is shaky stuff, and I think that's particularly true because it relies on Richard Dedekind's essays establishing the number line, which (as I think I've said before here) I disagree with strongly.
posted by koeselitz at 4:29 PM on March 30, 2012

escabeche: “But without the notation, or the shorthand, you just can't understand that much. It's the opposite of a barrier. We understand geometry a hell of a lot better than Euclid did, or for that matter Poincare, and the reason is largely because we now understand that geometry is not ‘the real thing’ of which algebra is merely a convenient description. They're both real and they each describe each other.”

We understand geometry better because we 'know' that algebra and geometry are real and describe each other, whereas they didn't 'know' that? Maybe you can point me toward a proof that geometry and algebra are both real and describe each other; I have a feeling you can't. Until you can, it's safe to say that you don't understand geometry better than Euclid; it's just that you disagree with Euclid. There's nothing wrong with disagreement, but don't act as though that disagreement is a badge that proves you're better. It's easy to pretend that you're better than dead people, and that may be a very popular pastime these days, but that doesn't make it a scientific or correct way to approach old works.
posted by koeselitz at 4:35 PM on March 30, 2012

incommensurate geometrical lengths are not expressible in numbers.

That strikes me as an extraordinarily large claim. Why not?
posted by flabdablet at 4:38 PM on March 30, 2012

koeselitz, I can only say that from what you've written I can't even tell what you think geometry is; I think we must just be talking about different things. E.G.

Maybe you can point me toward a proof that geometry and algebra are both real and describe each other

is opaque to me. What would a proof that geometry is real looks like? When I said both are "real" I simply mean that it's not the case that one is somehow primary, and the other merely a means of representation. It seems to me that you disagree -- you see algebra as something whose nature is to symbolically represent geometry. But what would a proof of that claim look like?

Until you can, it's safe to say that you don't understand geometry better than Euclid; it's just that you disagree with Euclid.

I don't think I disagree with Euclid in any way, so I'm not sure what you mean here. And I also don't understand in what sense modern geometers don't understand geometry better than Euclid. We know lots of things he didn't know, right? We know that a quartic curve in the real plane has at most 28 bitangents; I don't think Euclid knew this, and I think it would have been immensely hard for him to prove it using the methods available to him.
posted by escabeche at 9:11 PM on March 30, 2012 [3 favorites]

Koeselitz is being a bit time-cube-y for some reason, which is somewhat out of character for him.

Algebra and geometry are equivalent because they give the same answers to the same questions. But algebra is far, far more flexible than geometry is. You would have a really hard time, for example, solving systems of four equations with four variables with pure geometry, when you could solve them rather easily with linear algebra, even though there are obviously geometric interpretations of all the matrix manipulations.
posted by empath at 6:10 AM on March 31, 2012

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