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Aptitude Schmaptitude!: innumeracy in America
May 3, 2007 7:30 AM   Subscribe

Aptitude Schmaptitude! While the state of mathematical incompetence in this country has been much lamented, most famously in Paulos's brilliant 1988 book Innumeracy, it is still tacitly accepted . . . Being incompetent in math has become not only acceptable in this widely innumerate culture, it has almost become a matter of pride. No one goes around showing off that he is illiterate, or has no athletic ability, but declarations of innumeracy are constantly made without any embarrassment or shame.
posted by jason's_planet (140 comments total) 6 users marked this as a favorite

 
word word word word word!

Being in the process of raising children, I can tell you that some simple explanations/examples of what you are really doing when you, for example, add numbers can go a loooong way towards building skill and confidence in math.

I'll ask my at-the-time 5 year old what 15 plus 15 is and he'll have no idea. It's just these two big numbers. But then I point out that 15 is a 10 and a 5. So that's two 10s and two 5s. Now what's the total? Oh, 30! Pretty soon he can figure out that kind of thing himself, plus he knows he can figure out that kind of thing himself.
posted by DU at 7:40 AM on May 3, 2007


It is partly the fault of elitist approaches to mathematics. All the talk about "pure math"and "universal mathesis", for example, is enough to put off just about anyone. Where are the community numeracy programmes? Where is mathematicians without borders?
posted by No Robots at 7:42 AM on May 3, 2007


this may be, but i know a math dork who has the mandelbrot set tattooed on his back.
posted by entropone at 7:45 AM on May 3, 2007


I'm down for mathematicians without borders if anyone ever sets it up.
posted by zhivota at 7:45 AM on May 3, 2007


I'd be happy to get some kind of "here's what everyone oughtta know about math" list, similar to all the highfalutin' book lists that always come out, telling me what I oughtta read to keep up on the basics of Western literature. This guy keeps going on about how we're innumerate, but doesn't propose a basic level of math-aptitude towards which we should all strive. Does anyone know of any attempts to create that kind of Basic Everyman's Math Curriculum?
posted by Greg Nog at 7:48 AM on May 3, 2007


It is partly the fault of elitist approaches to mathematics. All the talk about "pure math"and "universal mathesis", for example, is enough to put off just about anyone.

I don't know about you but "impure math" or applied math is boring as hell. I always hated the "real world" questions when learning math. Obviously it's important to understand how all the equations map to real life, but unlike pure mathematics it's not fun at all.
posted by delmoi at 7:52 AM on May 3, 2007 [4 favorites]


This just sounds like people who are good at math are discriminating against those who are not. I think the abilty to read in incomparible to the abilty to do complex math. People are more exposed to words in every day life and it is easier to learn by hearing, reading and speaking.
posted by byronimation at 7:53 AM on May 3, 2007 [3 favorites]



Personally, I blame "Everyday Math".

My son (a 6th grader) has all sorts of difficulty following the inane lessons in the everyday math books.

For example, when dividing fractions, I was taught to invert and multiply. He is being taught some other process that makes no sense to me at all - and I've got a degree in electrical engineering...

I also think they should start algebra much sooner than they do. But I don't have a PhD in elementary education, so what do I know?
posted by Pogo_Fuzzybutt at 7:54 AM on May 3, 2007


Is our children learnin' math?

The No Chlid's Behind Left was supposed to be the magical Texas cure for math illiteracy, wasn't it?
posted by nofundy at 7:54 AM on May 3, 2007


The problem of innumeracy seems to be exacerbated by the fact that the bits you have to learn first are also now the most useless. Take the question mentioned in the post:
'Then I ask them to subtract one number from another for me, using a pen and a piece of paper I hand them: say -2and7/8ths minus 1and3/17ths. '

Now, if someone asked me to do that I'd probably not do it. I could do it, but it's a boring process that I can do much more quickly by finding a calculator.

Where innumeracy really has an impact isn't in those situations when people are stuck without a calculator and have to deal with seventeenths but when presented by statistics and probability - opinion polls, medical research results and assessing risks.

I wouldn't worry if I met someone whose arithmetic had declined to the point of needing a calculator to perform trivial tasks. I would worry if I met someone who uncritically accepted the results of a political opinion poll which mentions in the small print that it only sampled ten people.

I suppose I'm less worried about whether people can do maths than whether they can spot bad maths.
posted by edd at 8:03 AM on May 3, 2007 [6 favorites]


No one goes around showing off that he is illiterate,

Maybe not, but we sure as hell go around bragging about our aliteracy, at least here in Amurca.

Reading, writing, playing the piano, and doing math are highly unnatural activities (unlike speaking, say) which we are not naturally evolved to do. Instead, we take abilities we have evolved for other purposes and subvert them because it is so useful to learn these things.

That's a very interesting point.

And the price we must pay is that they are not always a great joy to do. Just as one must learn one's ABCs or practice one's scales, one must also memorize one's times tables, and I cannot think of a way to make that particularly interesting.

Well, there's your problem. If it's not fun, we ain't doin' it. Or, as a friend's students often say, "Why do we gotta learn this shit?"
posted by scratch at 8:07 AM on May 3, 2007 [2 favorites]


edd- I think the point that the article was trying to make is that there's a certain amount of slogging which is required to achieve this kind of fluency.

It seems to me that a lot of schooling nowadays is predicated on being interesting and capturing the imagination of pupils. I, on the other hand, am of the opinion that learning to sit down, STFU and get on with the task in hand is also a valuable lesson. There is no shortcut for learning basic maths and literacy.

On another note, the Stevinus link in the original article is also quite interesting.
posted by Jakey at 8:09 AM on May 3, 2007 [2 favorites]


Obviously it's important to understand how all the equations map to real life, but unlike pure mathematics it's not fun at all.

I have a degree in applied math, so obviously I disagree on the fun part, but yes, applying all but the most simple math can be a real bitch. But the most simple math desperately cries for application so that kids know what they are doing is actually not totally abstract craziness.

Mathematics, more than any other discipline I'm aware of, is brutally sequential. If you fall behind and fail to grok fractions or algebra or trig or calculus, you are stuck. You need these things to move on, and in the education systems I've had access to, there is generally no way to catch up once you've fallen behind, and no way to go forward.

So there you go.

But I, too, am a little confused by the pride many take in not understanding even simple math. Having a degree in math, I run into this all the time. More than half of the time, telling people what my college major was gets me a variation of the "God I suck at math, and I'm proud" speech.

I wonder if it is at least partly an ego thing: we all tend to blame subjects we hate, not our own failings, even when the latter is obviously what's at play. I know I tend to do that (*ahem*, biology, *ahem*, business), and I try hard to stop it.
posted by teece at 8:09 AM on May 3, 2007 [2 favorites]


I think the abilty to read in[sic] incomparible[sic] to the abilty to do complex math. People are more exposed to words in every day life and it is easier to learn by hearing, reading and speaking.

Learn what, I might ask? Learn how to understand what the best policy is? Learn what the benefits of taking one course of action over another is? Learn how to handle a budget effective? Those all require and understanding of mathematics and a general intuition for numbers.
posted by deanc at 8:14 AM on May 3, 2007


Well, heck, I sucked at math long before it was fashionable to suck at math, and though I never made it a point of pride, I was never especially ashamed of it either. To me it was just the inalterable nature of my fundamental wiring. My hair was brown. I sucked at math. Now my hair is turning gray. I still suck at math. Got through life pretty much ok anyway...
posted by flapjax at midnite at 8:16 AM on May 3, 2007


Being proud of sucking at something is about self-acceptance. The fact is, some people didn't get the math bug. Some people (hmmm...ME for example?) put all their shot into the literacy-pile, and they have allowed themselves to be happy about it. It's called specialization. But on the other side, hating on math is stupid. We innumerates lean on numerates all the time, and are wise to thank you for it.
posted by gorgor_balabala at 8:21 AM on May 3, 2007


I was trying to figure out a trivial problem based on a movie scene, and something my girlfriend said struck me. I always reduce a problem to first principles if I don't know how to solve it immediately, try to figure out exactly how the parts interact. She was looking for a formula to put the numbers into, and neither of us could really grok the others' train of thought.

I wonder if there is a concrete difference in learning styles there, or simply an artifact of different educational backgrounds. If that's not taken into account, I can easily see quite a lot of resistance and animosity developing towards a subject that just doesn't click as taught.
posted by Skorgu at 8:21 AM on May 3, 2007 [1 favorite]


And I also agree with the slogging part. I always read my math texts first, when I learn a new math discipline. In most of the other areas I study (English, history, poetry, photography, etc.) that would be enough to get me an 'A' in class [ of course, to actually practice poetry or photography or whatnot requires real work].

But having just read a math text is nowhere near enough. I have to drill on the information in the text. I have to explore theorems and do homework sets and write ideas out on paper and follow them through. Reading a proof is rarely, if ever, sufficient: I have get out pencil and paper, and work through the proof as if I were actually doing it myself if I want to really understand it.

So there is a lot of drill in math, and it can be boring. But, math is very sequential, as I mentioned above, and very unnatural, so it is not something you can "fake." So if you are lazy with it (as I was all through junior high and high school), you get punished for it. And then you often have no viable way to get back on track.

For many kids, this happens in the 3rd, 4th, or 5th grade. They get fucked that early.
posted by teece at 8:23 AM on May 3, 2007 [4 favorites]


'edd- I think the point that the article was trying to make is that there's a certain amount of slogging which is required to achieve this kind of fluency.'


Yes, which was sort of what I was thinking when I posted. It's unfortunate that you have to go through that stage, but I can't think of a good way round it either.
posted by edd at 8:23 AM on May 3, 2007


jason's_planet posted "No one goes around showing off that he is illiterate, or has no athletic ability"

Well, to be fair, that was written in 1988, before the Internet, where you could be exposed to the astounding number of geeks (myself included) who brag about their lack of athletic ability.
posted by Bugbread at 8:25 AM on May 3, 2007


'Then I ask them to subtract one number from another for me, using a pen and a piece of paper I hand them: say -2and7/8ths minus 1and3/17ths. '

-(3 + 143/136ths). I was able to come up with that in my head (no guarantees that it's right). What I did was multiply 17 and 8 by adding 8*10=80 + 8*7=56 = 136. Then I converted the fractions into 136ths by multiplying 3*8 = 24, and (8-7)*17 = 136-119. that got me to -2 + 119/136 – (1 + 24/136). Ignore the signs and add, then negate.

The interesting thing about this is that I never would have been able to do that after elementary school, and probably not after high school either, rather simply doing lots of algebra over the years has gotten me more used to moving things around while preserving equality. I never would have been able to do that using the rote "arithmetic" I learned in elementary school, and I don't even remember what I learned.

Solution: teach people algebra earlier. We should also not be teaching kids that there is one "right way" to solve a problem. I talked to a girl who said she couldn't do math and hated it because there was no creativity. Nothing could be further from the truth. Doing math, especially higher math is very creative. Kids should be taught lots of different methods, and maybe they will learn something they like more.
posted by delmoi at 8:25 AM on May 3, 2007


The interesting thing about that is that you left the 143/136 top-heavy.
posted by edd at 8:30 AM on May 3, 2007


My partner forced me to watch Are You Smarter than a Fifth Grader last week, and I think the show kind of demonstrates the whole problem.

The candidate seemed relatively bright, being able to identity Mark Twain as the pseudonym of Samuel Clemens and generally doing quite well. He avoided the one math question on the board until last, and it was very trivial (12 + -14). For the million dollar question, he only had one math problem and he took the money rather than attempting.

To put that in perspective, he turned down $500,000 rather than even see the question. Granted, if he had gotten it wrong, he would have lost that amount of money, but the question was really easy (name the only prime factor of 16)
posted by aubin at 8:32 AM on May 3, 2007


But having just read a math text is nowhere near enough. I have to drill on the information in the text.

And that's the real root of the problem. It isn't maths, it's the hard work required to learn them. In America, similar shortcomings exist in foreign languages, geography, history.... And it's not just the kids. It's the too busy parents who have no time to spend educating their kids. T-ball and football (both sorts) and baseball and swiming and play group are all much more fun to do (and require less effort from the parents) than sitting down with your kid and struggling through long division.
posted by three blind mice at 8:34 AM on May 3, 2007


I also think they should start algebra much sooner than they do. But I don't have a PhD in elementary education, so what do I know?
posted by Pogo_Fuzzybutt at 10:54 AM on May 3


I completely agree. I have absolutely no recollection of math from 4th -6th grade. We learned multiplication and division in 3rd grade, and pre-algebra in 7th, but the intervening years are a blank.

Furthermore, this would be easy. When kids are in first grade and they have to learn "2+___ = 5" where the blank is a balloon or a sheep or something, it could just as easily be 'x'.
posted by Pastabagel at 8:38 AM on May 3, 2007


the question was really easy (name the only prime factor of 16)

"That 2 is a prime is often exasperating, but nothing can be done about it." - Arthur Mattuck
posted by deanc at 8:39 AM on May 3, 2007


I blame Teen Talk Barbie.
posted by kirkaracha at 8:39 AM on May 3, 2007


Now, I know that there are people who actually do not know how to do basic math the same as there are people who cannot read at all. But I get the impression that that's not the type of person this article is about, which is kind of what drives me crazy. Illiterate people cannot functionally read. Innumerate people should be people who cannot functionally do any math.

I'd be interested in knowing what precisely qualifies as innumeracy, and precisely how many americans are innumerate. The reason I ask this is because I don't personally know anyone who can't add, subtract, divide and multiply. I do, however, know plenty of people who can't do long division without pen and paper handy. And I suspect that the people who simply cannot do any math (and who aren't discalculate) mostly suffer from a deficient education in a lot of regards. If you told me that someone who went to a horrifically bad inner city public school has difficulty reading a newspaper and can't confidently figure out how much change he should get back when he buys it, then I'd say the problem isn't innumeracy but a poor education in general.

Of course, that also doesn't seem to be the type of person this article is talking about. It seems to be talking about the well educated who can't do calculus. Either that or this guy is so completely incapable of understanding the nuances of the English language that when someone says "I can't math my way out of a paper bag," he thinks they're literally saying that they couldn't add 2+2 if they had to.

God, I hate this article. Who on earth is he talking about?! Who are these people that he's speaking to when he says "Even the social sciences cannot exist without math anymore, and you cannot have any deep sense of political and economic issues if you are completely innumerate?" Who the fuck is telling this guy that they can't understand a simple percentage or a fraction? What qualifies as "completely innumerate?" I really can't tell if that phrase means "can't add and subtract" or if it means "once knew how to do trigonometry but forgot how by now because no one uses more than simple arithmetic in their daily lives."

If it's the latter, then I would like to heartily extend an invitation to the author to go fuck himself until he can come back to me with either a 30 page paper on Thomas Mann's "Death in Venice" or translate the original text into English for me (since he apparently took German in high school). We all forget the more advanced things we learned in high school as we focus more on the fields we specialize in. I couldn't tell you the first thing about chemistry. Should I be called "Dischemistrate" and have a movement started to make sure I remember my chemistry homework for the rest of my life? Or better yet, let's all start a grassroots program to make sure your every day joe understands the technical and aesthetic processes that went into Bergman's The Seventh Seal. Why? Because that's MY pet topic that most people don't know enough about and I insist.
posted by shmegegge at 8:40 AM on May 3, 2007 [9 favorites]


delmoi,
I don't think it requires algebra, just the basic functions. You did it the way I was taught in late elementary school/middle school (can't remember exactly), and it's really not a hard method. Just use multiplication to get the denominators the same, then add the fractions, then reduce to the lowest denominator.

aubin,
Your example illustrates exactly what teece was saying, which is exactly right. People saying they "suck at math" is a defense mechanism to protect their egos, like someone who isn't good at basketball saying it's a stupid game anyway. I'm not trying to be an elitist ass, I just really think that very few people are truly incapable of completely not getting basic math. It's just a lack of effort. Some people might understand math very easily and some less so, and so some people might need to try harder, but everyone can get it. I'm talking about the basic things, like addition, subtraction, etc, or the concept of negative numbers, in this case.

Being proud of sucking is not self-acceptance, gorgor_balabala, it's self-denial. It's like someone saying they suck at drawing, when what they're really saying is that they don't want to/haven't put in the time to learn how.
posted by Sangermaine at 8:45 AM on May 3, 2007


Illiterate people cannot functionally read. Innumerate people should be people who cannot functionally do any math.

I would define innumerate people as people who do not actually understand math.

I would say that someone is innumerate if you regal a listener with the following facts, and have him be shocked by the revelations that:

"Half of people are below average!"

or

"40% of sick days are taken on a Monday or a Friday!"

If the person cannot recognize that you are telling him a joke, in some way, then that person is effectively innumerate. Sure, he might be able to add and subtract, but what good does it do him?
posted by deanc at 8:46 AM on May 3, 2007


I was going to add my 3 cents worth, but shmegegge nailed it pretty well.
posted by BozoBurgerBonanza at 8:46 AM on May 3, 2007


Who the fuck is telling this guy that they can't understand a simple percentage

Several of my family members have absolutely no idea how to work percentages. Not idiots, but functionally innumerate. They can and subtract, and divide and multiply, but not anything else.

I've heard a guy on a sports show profess to having no idea which was bigger: the 5/8th inch cleat or the 1/4 inch -- he didn't like algebra, I think he said.

But I agree with you, I'm not all that fond of this article.
posted by teece at 8:48 AM on May 3, 2007



As an aside, when I was going to enlist in the Marines, I took the ASVAB.

There's a part where you have like a minute to do 100 simple math problems (1+4, 5-3, etc.).

Well, I was in HS and had just finished a semester of AP physics and AP pre-calc/trig and when I go that part I froze completely.

I was in a total panic "Where's the x, what am I solving for ? I don't know what to do!!" Only then did I fully appreciate the plight of Marvin the Robot.

Yeah, good times.
posted by Pogo_Fuzzybutt at 8:52 AM on May 3, 2007 [1 favorite]


To put that in perspective, he turned down $500,000 rather than even see the question. Granted, if he had gotten it wrong, he would have lost that amount of money, but the question was really easy (name the only prime factor of 16)

Fuck, man... I would have taken the money rather than attempt to answer that question. Why? Because that's five-hundred thousand dollars that is definitely yours if you don't answer that question.

It's a matter of probability. Chance of getting the question wrong if you have to answer it: greater than 0%. Chance of getting it wrong if you don't have to answer it: 0%.
posted by odinsdream at 8:55 AM on May 3, 2007 [1 favorite]


I was in a total panic "Where's the x, what am I solving for?

When I'm working a hard math problem, I make it a rule to keep as much symbolic as humanly possible -- I will get the algebraic manipulation right; I will solve the differential equation correctly; I will make the correct statistical inference.

I will almost always fuck up the arithmetic. Go figure.

I also want to add: no one should feel ashamed for not being good at math. Fuck the math snobs that act like people are idiots because they can't solve Laplace's Equation at the snap of a finger.
posted by teece at 8:56 AM on May 3, 2007


If the person cannot recognize that you are telling him a joke, in some way, then that person is effectively innumerate. Sure, he might be able to add and subtract, but what good does it do him?

I think I'm still a little too steamed at the article to tell if you're joking. So I'm going to assume you're not and plead "broken sarcasm detector" later if you are.

You see, the jokes you just told have almost no practical value at all, and being able to add and subtract does.

Further, that's the most absurd definition of innumeracy I can imagine. Is all of metafilter illiterate except for languagehat, then? Cause you and I can read, but that motherfucker is one of the only people I can immediately think of who really GETS language.
posted by shmegegge at 8:56 AM on May 3, 2007


(by the way, on that 5th grader episode, was I the only one who went "fucking 1 is also a prime factor of 16!")
posted by shmegegge at 8:58 AM on May 3, 2007 [3 favorites]


1 is not a prime number, shmegegge. 1 and 0 are actually very special numbers. 1 could be a prime number, if someone leaves that exclusion out of the definition. But, by definition, it is not prime. The primes start at 2. (this is a matter of convention, only).
posted by teece at 9:03 AM on May 3, 2007 [1 favorite]


You see, the jokes you just told have almost no practical value at all, and being able to add and subtract does.

Absolutely not true. Both "jokes" that I posed by illustration are examples of how we could manipulate people's perceptions when it comes to political or corporate policies-- ie, "lying through statistics." If you don't understand percentages and proportions, you're going to be liable to be manipulated by those trying to pull one over on you.

Adding and subtracting is a perfectly fine basic skill, but it's not going to do you much good if you don't understand the concept of numbers in general.

Look at it this way-- do you trust an innumerate person to understand casualty trends in Iraq? To understand whether terrorist attacks are increasing or decreasing? To understand whether certain policies or medications are efficacious or not? Because if they can't, then they're going to end up being unable to think for themselves, regardless of whether they can figure out how much change they're owed at the grocery store.
posted by deanc at 9:03 AM on May 3, 2007 [5 favorites]


I've heard a guy on a sports show profess to having no idea which was bigger: the 5/8th inch cleat or the 1/4 inch -- he didn't like algebra, I think he said.

see, now that's a situation I can see someone wanting to talk about, but not because it's evidence of innumeracy so much as laziness. if you had some ability to force that guy to figure it out, he would. and if he had to figure stuff like that out every day he'd be able to do it without thinking. it's not like he can't do math, or doesn't know how. he just doesn't care enough to bother.

If I have to figure out how many frames of video there are in a video that's 3 minutes 27 seconds and 14 frames long at a framerate of 29.97 fps, I can eventually figure it out with a pen and paper. But the most you're going to get out of me if i do it in my head right away is a vague approximation of how many frames there are in a 3 minute 30 second video at 30fps. and it won't be that close. in fact, here's what my brain would do:

"well, 60 seconds a minute, so 60 times 3 is 180 plus 30 equals 210 seconds multiplied by 30 frames a second equals (grind grind grind) something like 6000 plus some, i guess." and that would be my answer. "6000 plus some, I think?" but that's laziness, not innumeracy.
posted by shmegegge at 9:06 AM on May 3, 2007 [1 favorite]


"Half of people are below average!"

You realize this is not definitively true? As in for any categories for which people fall into a non-symmetric bell-curve. Of course you didn't say below average what, but on topic, I'd say this isn't true for math competency being that there's a low bound of mathematically incompetent with a large concentration, and no obvious high bound (chi-squared distribution? Though I'm just guessing without IQ data)

Half of people - 1/2 or 1 (depending on parity) are below median.
posted by kigpig at 9:07 AM on May 3, 2007


A similar thing happens with art I think, where people get the idea early on that they "can't draw", which is true only for people with severe physical disability or something. And these days, not so much for them either - one of the few places I think it can be argued that civilization is making some progress beyond the mere technical.

To be sure, there are great artists and there a people who doodle for fun - but sometimes I think the latter derive more satisfaction from the simple act itself. Everyone is capable of understanding the concept of exponential growth, for example. And that's a concept that yields a bounty of practical and aesthetic experience.

I guess I don't have much to add, just that I agree. Math is one of the most satisfying ways to stretch and improve your cognition and perception, and that experience holds true from the first time you understand the slope of a line to the first time you understand the structure of a differentiable manifold's tangent bundle.

And don't get me started on what we'd gain if everyone knew some simple probability.
posted by freebird at 9:09 AM on May 3, 2007 [2 favorites]


I don't know about you but "impure math" or applied math is boring as hell. I always hated the "real world" questions when learning math. Obviously it's important to understand how all the equations map to real life, but unlike pure mathematics it's not fun at all.

Amen, brother! That's why I quit the math department and became a language major—they kept wanting me to take more calculus when all I wanted to do was play with number theory, topology, and other useless shit. (And don't tell me how those areas can be useful, because that wasn't what I was interested in. Useful = boring.)
posted by languagehat at 9:09 AM on May 3, 2007


I don't personally know anyone who can't add, subtract, divide and multiply

Nice random sample you have there. I happen to know some people who think they can do percentages and think they can do long division on paper because once upon a time they could, but try to get them to work a 17% tip on a check, and they're stumped.

Very many people can't calculate how many square feet of carpet they need to cover a floor (just go to Home Depot and stand around), when the know the room dimensions. They know a problem can be solved with math, but they don't know what "formula" to use.

People don't know what algebra or trig are for, let alone calculus.
posted by Pastabagel at 9:09 AM on May 3, 2007


now that's a situation I can see someone wanting to talk about, but not because it's evidence of innumeracy so much as laziness. if you had some ability to force that guy to figure it out, he would. and if he had to figure stuff like that out every day he'd be able to do it without thinking. it's not like he can't do math, or doesn't know how. he just doesn't care enough to bother.
scmegegge, the fact that people are perfectly happy declaring that they "can't do math" is the reason why people don't bother to figure these things out. It's innumeracy by choice, which is exactly what the original article linked to in the FPP is railing against-- people feel free to choose to be innumerate and not rectify the situation, in part because there's no social stigma against innumeracy.
posted by deanc at 9:10 AM on May 3, 2007


I don't know that shit! Keepin it REAL!
posted by Uther Bentrazor at 9:10 AM on May 3, 2007


You realize this is not definitively true? As in for any categories for which people fall into a non-symmetric bell-curve.

yes, that's why I said that the listener should recognize you are telling a "joke." In fact, it was because I added that statement about "half the people are below average" that I mentioned the "joke" part. A truly pedantic reply would be to demand whether you were talking about the mean average or median average, but the appropriate reply is simply to say, "very funny."
posted by deanc at 9:13 AM on May 3, 2007


'"well, 60 seconds a minute, so 60 times 3 is 180 plus 30 equals 210 seconds multiplied by 30 frames a second equals (grind grind grind) something like 6000 plus some, i guess." and that would be my answer. "6000 plus some, I think?" but that's laziness, not innumeracy.' says shmegegge

It's not laziness, and it's not innumeracy. I'd say that's strong evidence for numeracy and an appreciation that sometimes things aren't worth the effort of doing exactly.
posted by edd at 9:14 AM on May 3, 2007


This thread and the illiterate dean thread are going to collide in a fireball of stupidity that will surely destroy us all.
posted by Pastabagel at 9:17 AM on May 3, 2007 [1 favorite]


A truly pedantic reply would be to demand whether you were talking about the mean average or median average

I always say I am referring to the harmonic mean. Unless it's Tuesday, in that case it's the geometric mean that I mean by average. On Wednesdays, I choose the root mean square. Oh, and on Thursdays I mean the 10% trimmed mean, and on Fridays the 20% trimmed mean. Oh, yeah, and on Saturdays I mean the the mode when I say average. ;-)
posted by teece at 9:17 AM on May 3, 2007


Look at it this way-- do you trust an innumerate person to understand casualty trends in Iraq? To understand whether terrorist attacks are increasing or decreasing? To understand whether certain policies or medications are efficacious or not? Because if they can't, then they're going to end up being unable to think for themselves, regardless of whether they can figure out how much change they're owed at the grocery store.

look at it this way-- no i would not trust an innumerate person to understand the iraq casualty trends because they can't figure out how much change they're owed at the grocery store.

your definition is so bizarre. those jokes aren't evidence of anything. you can sit anyone who knows what a percentage is down and tell them that joke and they'll have an ability to understand it. chances are that they're just not thinking about it. if they don't laugh (and we're ignoring that they're not funny jokes) and you go "wait a second, think about what i just said." they'll go "oooohhh. okay." they'll get it if they think about it. lazy thinking is not innumeracy, nor should it be. the idea that we have to have more than a functional ability to deal with numbers out of some arbitrary definition of "understanding math" is silly. there are plenty of people who don't read harper's or understand why 8 1/2 is a great film. no one who isn't an elitist or a snob calls those people illiterate (or comes up with a new term for film ignorance). this is because literacy is about being able to function in a world dependent on a basic level of reading ability. if you can function in that world, then you're literate, even IF Karl Rove can trick you into believing lies because he's a talented bullshit artist with a knack for twisting words.
posted by shmegegge at 9:18 AM on May 3, 2007 [3 favorites]


shmegegge wrote: But the most you're going to get out of me if i do it in my head right away is a vague approximation of how many frames there are in a 3 minute 30 second video at 30fps. and it won't be that close. in fact, here's what my brain would do:

"well, 60 seconds a minute, so 60 times 3 is 180 plus 30 equals 210 seconds multiplied by 30 frames a second equals (grind grind grind) something like 6000 plus some, i guess." and that would be my answer. "6000 plus some, I think?" but that's laziness, not innumeracy.


(IAAMathProf) That is neither laziness nor innumeracy. It's the opposite of innumeracy. It demonstrates that you understand how to draw out the important aspects of a problem and get an answer with an appropriate degree of accuracy. If the typical college student knew how to do what you just did, people wouldn't be writing exasperated editorials on this topic. Or did you think we were steamed that 50-year-old lawyers didn't remember the antiderivative of the arcsine?
posted by escabeche at 9:21 AM on May 3, 2007 [5 favorites]


It's innumeracy by choice, which is exactly what the original article linked to in the FPP is railing against--

i think i'm in danger of posting too much in here, but let me say this:

i agree that choosing to be ignorant is a bad thing. but innumeracy by choice should be an oxymoron if it isn't already, which is why i'm very specifically saying that I'd like to know what the real technical definition of innumeracy is. if it's your defintion or the one the article seems to be espousing then I'm totally against it as a miserable definition.

if we're not talking about an innumeracy that is comparable to real and actual illiteracy, then let's stop pretending we are. if we're talking about people who say "i can't do math," the way the article describes then we're talking about people who are either exaggerating for the sake of conversation (i do this all the time. "i'm no good at math/music/art/unicycles...") or who simply do not care enough to become better at something they could in actuality do. but that's not innumeracy, that's just not caring. you want to start a movement that we should help kids in our schools and people in our society care more about math? you've got me as a supporter.
posted by shmegegge at 9:24 AM on May 3, 2007


Or did you think we were steamed that 50-year-old lawyers didn't remember the antiderivative of the arcsine?

honestly, i've been wondering. the article is so unbelievably vague about what he's describing that it's driven me to the brink. that said, i'm going to go for a walk or something because i'm running about this thread waving my hands in the air like a crazy person and I think I need to chill. back in a few.
posted by shmegegge at 9:26 AM on May 3, 2007


Vision In Elementary Mathematics or pretty well any other book by W. W. Sawyer brought up a lot of these points 30+ years ago.

He compares mathematics as it's taught today to teaching a deaf child how to play the piano. You could do it by punishing him when he made mistakes and he'd eventually be able to play some pieces but he'd really have no idea what he was doing nor why.

He has tons of other ideas -- like using actual marbles in bags and playing games with them to illustrate algebra -- he has a neat symbol for a bag that becomes an "x" when you omit the top and bottom.

Now I'm wondering why my parents had these lying around the house when I was a pre-10... heh, guess they knew I'd read them!
posted by lupus_yonderboy at 9:26 AM on May 3, 2007


yes, that's why I said that the listener should recognize you are telling a "joke." In fact, it was because I added that statement about "half the people are below average" that I mentioned the "joke" part. A truly pedantic reply would be to demand whether you were talking about the mean average or median average, but the appropriate reply is simply to say, "very funny."

I've heard, quite a few times, someone state this 'joke' as something that's meant to be obvious to make fun of teh stupid people. I know this was their intention because I pointed out the same thing to them, each time, and received the response, well it's almost always true or a simple statement that I was wrong. In fact I've never heard someone use it as a joke of falsehood.

Wasn't sure which joke you were going for. I wonder if they just picked up on something they didn't at all understand and repeated it thinking it would make them sound smart.

It concerns me because although this is a trivial point, such a large concentration of people get duped by statistics, well more than that set of people that can't do basic math, to the detriment of our whole political and social environment.

In fact, I work with engineers and when presented with the bayesian breast cancer problem they get it grossly wrong as in on the opposite side of likely hood. My sample set here isn't huge so hopefully I just have biased observations.
posted by kigpig at 9:31 AM on May 3, 2007


which is why i'm very specifically saying that I'd like to know what the real technical definition of innumeracy is.

Maybe it would be more helpful to think about the topic in terms of degrees of innumeracy, the way that there are degrees of illiteracy from stone, 100% illiteracy to functional, fourth-grade reading level illiteracy. Some people order in restaurants by pointing to pictures in the menu. Others could probably read a simple article in a tabloid-style paper but wouldn't be able to understand, for example, a legal notice they received in the mail or they might struggle with an article in the New York Times.

Does this make sense?
posted by jason's_planet at 9:33 AM on May 3, 2007 [2 favorites]


Effortless facility in mathematics is often associated with a terrible disease-- autism-- after all, and significantly its long shadow; and many of the greatest mathematicians have had notably unattractive personalities: Newton, Gauss, Turing, Goedel, Von Neumann, Ulam, etcetera. Cantor is an interesting exception, but there is that unfortunate insanity....
posted by jamjam at 9:34 AM on May 3, 2007


deanc: "Half of people are below average!"

Depending on your prior, such a fact might well be shocking. There's a big difference between an average and a median. Half of any population falls at or below the median (by definition*). If half are also at or below the average, that is a fact about the distribution of values that is informative - that is, it isn't guaranteed by definition.

Suppose 100 students take a test; 50 students completely bomb it, scoring 0 points out of 100. Another 49 eke out 1 point each. One shining star aces the exam, getting all 100 points. The average score on the exam is 1.49, and 99% of the students fall below the average. The median score is any number between 0 and 1, and exactly half the students fall below it.

shmegegge
is right in pointing out that the article doesn't do a good job of defining innumeracy. He does refer to Paulos' book, which might do a better job (I haven't read it). But I must say that when I was teaching college economics, I often observed resistance to performing very basic calculations that seemed to be something of a different sort than, say, not wanting to work through a short passage of Shakespearean blank verse or write a response paragraph to Stevens' "Sunday Morning". My college students who signed up to take an economics course regularly put in serious effort to avoid doing basic arithmetic. They went to great lengths to cheat, copy, get "tutoring", etc. - often paying money out of pocket to have others help them with arithmetic. Maybe that's not "innumeracy", but it's something. And when people make it a point of pride that they "don't do math", that does seem rather odd. Compare: "I don't do algebra. Algebra is for nerds." with "I've never read a whole book in my life. Books are for nerds."

*In some cases, it may be that more than half of the values are at least as small as the median. But it is always true that at least half are not greater than the median, and at least half are not less than the median.
posted by dilettanti at 9:39 AM on May 3, 2007


It concerns me because although this is a trivial point, such a large concentration of people get duped by statistics, well more than that set of people that can't do basic math, to the detriment of our whole political and social environment.

Which is precisely why I'm so frustrated by schmegegge, right now. He doesn't realize that our whole political and social environment does suffer because people are too lazy to learn math and, more to the point, understand what numbers are all about.
posted by deanc at 9:40 AM on May 3, 2007


I should also note that I doubt precisely 40% of sick days are taken on Mondays and Fridays in part because I would guess that the distribution of sick days is not independently and identically distributed throughout the week. First, you're more likely to call in sick the day after you've called in sick. Next, multi-day sicknesses might fall on the weekend, further skewing the sample. I'd guess, though, that they're pretty closely evenly distributed.

And in retrospect I probably shouldn't have added that "half the people are below average" statement as an example. But I liked it because it's an example of how someone can be easily "shocked" or misled by a statement if they don't bother to think about it to hard or don't even know what to think about.
posted by deanc at 9:46 AM on May 3, 2007


He doesn't realize that our whole political and social environment does suffer because people are too lazy to learn math and, more to the point, understand what numbers are all about.

yes i do. what you don't get is that you haven't shown me why anyone should be called innumerate even if they can do a perfectly functional level of math. because math is important? so is language, and plenty of people are considered literate who i still wouldn't trust to interpret the news coming out of iraq. there have been several interpretations of the term innumerate used in this thread, and they all make sense except yours.
posted by shmegegge at 9:54 AM on May 3, 2007


I would love to be good at math. That would rock. However, as has been previously mentioned, once you fall behind in the school system, you're pretty well screwed. Add Saxon Math in high school and you're super-duper-extra-screwed. And this was in the days before No Child's Behind Left, no less.

I remember reading an article in Newsweek about John Saxon not even having teaching experience or an educational degree the year after I got out of high school. I sent said critical article to my h.s. guidance counselor with what was probably a super-smarmy note.

How badly did our public school fail me, math-wise? My gifted & talented counselor had to fight to get me out of middle-level math junior year. I royally screwed my GPA and any hopes of decent scholarships due only to math, despite studying my ass off and falling asleep on my textbooks, in tears, every night. There's a wide assumption that if you're good at one (verbal-type stuff), you're good at the other. This can be true but isn't always.

I'm not proud of my sucky math skills. I can do percentages, I can figure out a lot of basic things if I can draw them and check my process visually. I can do basic arithmatic. But at this point, what can I do? Short of some "things you should know" book that I could study, or going back to school, I'm stuck.
posted by bitter-girl.com at 9:54 AM on May 3, 2007


Part of the problem in current math teaching is that students can get by through rote memory alone. Which is a shame because the enjoyment of math comes through deep understanding rather than through the mechanical exercises. As well, students lose out because mechanical practice can easily be forgotten if there isn't that deep level understanding. My last two years of undergrad calculus and prob/stats faded from memory almost immediately after graduation. I'm trying to get it back now that i have more time but it sure would have been great not to have lost them in the first place.
posted by storybored at 10:20 AM on May 3, 2007


People don't know what algebra or trig are for, let alone calculus. - Pastabagel

Calculus is for everything.

It's not laziness, and it's not innumeracy. I'd say that's strong evidence for numeracy and an appreciation that sometimes things aren't worth the effort of doing exactly. - edd

This is one of the more interesting aspects of Paulos' Innumeracy - he begins by railing against the sort of short-cut business math that is championed by some, but further into the book, he advocates similar types of shortcuts for some types of problems and/or uses.

Jakey's comment makes a related point very succinctly when he says that there is a certain amount of slogging necessary to achieve what the author seems to think is a useful proficiency. That, to me, is the point of Paulos' book. People don't slog, and hence, don't have the chops that Paulos thinks they (we?) need. Paulos follows that up by saying that yes, slogging is the order of the day, but with all of the creativity that man possesses, surely we can come up with some better ways to teach and talk about mathematics?

Too bad you have to be a bit of a math dork to even pick up "Innumeracy." For the more literary minds, I think it's fair to say that Card and Stephenson make points that are, if not the same, then perhaps along the same lines.
posted by rush at 10:23 AM on May 3, 2007


A similar thing happens with art I think, where people get the idea early on that they "can't draw"

Oh yeah. This one drives me crazy and is the reason why I have no interest in teaching art to anyone over the age of five. If you can pick up a pencil, you can draw.

The idea that "drawing" has to be photo-realistic or even perspectively accurate makes my skin crawl. Just make marks that represent what YOU SEE or some form of symbol that stands for an object or idea. That's it! That's drawing! You can do it! Three year olds do it all the time, so can you!

On topic though: I personally know that I used to be just fine at math - I got good grades in Algebra and Geometry in high school, but it has been so long since my brain has accessed that information that it's all dusty and makes me sneeze when I try to drag it out. Then again, the most complicated mathematics I have to do in a day is mixing proportions in coffee beverages and making change, so I don't appear to be hurting much for it.
posted by grapefruitmoon at 10:24 AM on May 3, 2007


bitter-girl, I don't buy that you're somehow inherently bad at it; from your own account, you had bad teaching (which is also defined by lack of availability for reteaching and remediation). Your school failed you.

I say this because six years after holding my husband's hand and reassuring him that no, he was not mentally deficient if he hadn't been given much in the way of math skills, he now does all our bills and taxes and does a bang-up job. Because I walked him through the basic principles of money management/math that he felt insecure about. He was perfectly capable of it all along, as any person of normal intelligence is, but he'd had *years* of crap teaching that both taught him badly and allowed him to graduate without really learning what he needed to because he did ok otherwise.

There's still the myth of left brain/right brain, math/creative, geek/artist out there, and it says a lot more about the faults in our educational system than it does about how people's brains really work. But I remember as a kid being told, all the time, "Oh you must not be a math person...you're such a good writer, I guess that's your talent!" Which helped me not at all. (and probably was also sexist...girls get told this kind of thing a lot).

What did help was my brother drilling me with flash cards on my mulitiplication tables. I still remember them and use that knowledge every day thanks to him.
posted by emjaybee at 10:25 AM on May 3, 2007


this may be, but i know a math dork who has the mandelbrot set tattooed on his back.

Wow, that sounds like it would take forever!
posted by contraption at 10:27 AM on May 3, 2007 [9 favorites]


I'm stuck.

Nah ! Look at me, I tought I sucked.

Now I KNOW I suck, BUT thanks to a she-engineer that ...how to put it without talking about erotic interludes...? Well let say she shagged me into math ...her patience was virtuous, her teaching skills excellent (for me!) and I learned a lot..making me at least arithmetically decent ..and sucking at calculus..but can handle some derivative. She says I just don't have enough practice, but I could do well.

It's all about the teacher AND your real will to learn....try not to be afraid of math, it helps !
posted by elpapacito at 10:30 AM on May 3, 2007


WHUT?
posted by Kwine at 10:43 AM on May 3, 2007


"To put that in perspective, he turned down $500,000 rather than even see the question. Granted, if he had gotten it wrong, he would have lost that amount of money, but the question was really easy (name the only prime factor of 16)"posted by aubin

I've already favorited odin's dream's polite smack down to aubin's comment here - but I can't let it go!

It is a terrible idea to illustrate the average joe's fear of easy math as shown on "Smarter than a 5th grader", if you quite clearly don't understand/can't easily explain the easy rules of "Smarter than a 5th grader".

In aubin's answer, the inessential part of the game is "put in perspective". Hopeless!

(Bad at math myself and very, very grateful to those who are not.)
posted by Jody Tresidder at 10:45 AM on May 3, 2007


Which helped me not at all. (and probably was also sexist...girls get told this kind of thing a lot.

Gee, ya think? ;)

Nooooo, not in the US public school system! Even I caught on early and begged my parents to send me to the all-girl Catholic school -- and we're not even Catholic!

Elpapacito's shag-your-way-into-it isn't gonna work unless my (art degree boyfriend) says yes. And the person's a girl. And he can watch.

So -- any book recommendations? something along the lines of "ok, you can do basic arithmatic, here's the cool math stuff?"
posted by bitter-girl.com at 10:47 AM on May 3, 2007


I'd like to see attention given to Buckminster Fuller's mathematics. It's fun, exciting, practical, endlessly complex, and just plain weird. Great for kids!
posted by No Robots at 10:54 AM on May 3, 2007


shmegegge, your complaints over the definition of innumerate are just a matter of semantics and it's quite a derail. Yes people can get by just fine without knowing how to do advanced math. But in the vast majority of jobs out there, the ability to punch numbers into a calculator and hope is not that useful. The ability to feel whether the answer is correct or to have a hunch about what it should be is crucial in even the simplest calculations. A certain analogue to this is that many illiterate children memorize words and are unable to deal with unfamiliar words. This is no different than someone memorizing the steps on how to use a calculator or even writing it down with a pencil and paper.

I know someone who owns a business that sells carpeting and he had to institute an after work tutoring program for the college graduates he's hired in order to teach them how to calculate the areas of rooms and simple geometry. These are US college graduates. That is a problem.

The point of this article was to point out how easy it is for some people, even the highly educated, to just believe that they are not good at math, give up, and have nobody give them shit for it. If anyone did that with reading or writing there would be rather evident and picked up on quickly. People fall through the cracks in math and without having those years of practice, drilling through problems, developing their own tricks, they'll have an extraordinarily difficult time catching up and in most cases they'll chalk it up to just not being good at math.

Math is just being taught poorly especially in elementary schools. There was a post a while back, I can't find it, that discussed how many elementary school teachers hate math and pass that attitude along to their students. So instead of trying to discuss how to fix this problem let's complain about how people's definitions of innumerate don't jive.
posted by crashlanding at 11:04 AM on May 3, 2007


Sangermaine, i would argue that one could put in quite a bit of effort at math (like, say, two years attempting a degree in chemistry) and then quite comfortably accept themselves for sucking at math. The same goes for people who cannot draw. Plenty of people will NEVER DRAW WELL. Unlike myself.
posted by gorgor_balabala at 11:04 AM on May 3, 2007


Not knowing how to interpret statistics as used by journalists, not being able to calculate the square footage of a room, not being able to figure out approximately how much a 17% tip is: these above mentioned shortcomings would be problematic in living everyday life, but not knowing trig or calculus doesn't mean a thing to me. I don't brag about my mathematical shortcomings, but I don't think worse of someone who doesn't know what a suspended C chord sounds like, either. We all specialize (well, I'm not speaking for the Balinese rice farmer, but...).
posted by kozad at 11:06 AM on May 3, 2007


The reason so many of us suck at math is quite obviously that we don't use it in our everyday lives. We don't need to. Back in graduate school, I knew how to solve partial differential equations, because I was immersed in it -- I needed that skill, that "language" to be able to solve the engineering problems posed. Ten years later, I'm not sure I could tell you what partial differential equations are. I'm not sure I've even done basic calculus even ONCE since then. Trigonometry comes up maybe once a year.

Similarly, how often do you need to, say, multiply 283 * 57 in your head? I sure can't do it, but then I don't need to. The computational tools are readily available. Hell, I have a scientific calculator in my phone. If I needed to know how to multiply big numbers in my head, I would -- or at least I'd be better at it.

Being bad at math is like learning high school Spanish and never speaking it.
posted by LordSludge at 11:07 AM on May 3, 2007


I think we should pause to distinguish between "basic math" and "basic arithmetic." Because if we are harshing on people for their incompetence at "arithmetic," we are harshing on people who are not educated at all in the first place. . . And actually, that is just not nice.
posted by gorgor_balabala at 11:15 AM on May 3, 2007


kozad, there's nothing wrong with that once you get into the real world, specialize, and know what you will or won't need but when people are still in school I don't believe they should be allowed to make that choice, it's too shortsighted. I remember hating chemistry when I took it in high school and my freshman year in college. I dismissed it as "something I'd never need." Now that I'm in grad school I see it all the time and have to work hard to make up for just blowing it off before.

Too many kids are just allowed to blow off math through our educational system and it seriously limits their options and society as a whole, IMO.
posted by crashlanding at 11:17 AM on May 3, 2007


From the introduction to Innumeracy, which I think I'm going to go read again after this thread has left a bitter taste in my mouth:

Part of the reason for this perverse pride in mathematical ignorance is that its consequences are not usually as obvious as are those of other weaknesses. Because of this, and because I firmly believe that people respond better to illustrative particulars than they do to general exposition, this book will examine many real-world examples of innumeracy--stock scams, choice of a spouse, newspaper psychics, diet and medical claims, the risk of terrorism, astrology, sports records, elections, sex discrimination, UFOs, insurance and law, psychoanalysis, parapsychology, lotteries, and drug testing among them.
posted by TypographicalError at 11:18 AM on May 3, 2007


I find a good test for real numeracy is being able to estimate relatively quickly what an answer should look like. In LordSludge's example, I'd have to break out pen and paper to find out what 283*57 is, but I could estimate it to be near 15,000 in my head in about two seconds. (The real answer is 15,211 so I was ~2% off, good enough for me).

The example from a movie I was working through was this to illustrate: It takes one painter 3 hours to paint a house. It takes another painter 5 hours to paint a house. How long does it take for both of them to paint the house?

Because of lack of practice, I didn't immediately know how to solve this. So I estimated. I knew it would be less than 2.5 hours, but more than 1.5 hours, so already I've got it down to a tiny little range.

Now, again because I'm out of practice at middle-school math, I didn't know immediately how to turn those numbers into an answer, so I flipped them all over to see if that made it any easier. I re-wrote the problem into how many houses per hour each painter could paint, making it a rate problem versus a time problem. I got 1/5 and 1/3 obviously. The two together could do 1/5 + 1/3 houses in one hour, which is 3/15 + 5/15, which is 8/15 houses in an hour. Flipping that over again to make it a total-time problem again gives 15/8 or 1 7/15 (~=1.875) which is in line with what I estimated earlier.

Again, this is obviously a trivial problem, and one that you'll likely never run into in the real world. And my strategy is certainly not the quickest way to solve the problem, if you had to do a hundred very similar problems, you'd be far better to arrange it into x*y/x+y and just fill in the blanks.

The problem is that the second way is what (seems) to get taught. Here's a problem. To solve it, put the numbers in this formula. Here's another problem. I'm bored just describing it.

I don't think it's specifically a math thing, this is just the most obvious demonstration at the moment. It's a thinking thing. Kids aren't taught to think, they're taught to pass tests.

*kicks soapbox into fire*
posted by Skorgu at 11:24 AM on May 3, 2007 [5 favorites]


So instead of trying to discuss how to fix this problem let's complain about how people's definitions of innumerate don't jive.

we're here to talk about the article and it's topic. that's what i'm doing with deanc. you're points are important and if you'd like to talk about them then surely i and others will do so with you. there's room for multiple discussions in the thread. several are already going on simultaneously as i type this. one of those discussions is about how vaguely the author of the linked article defines innumeracy. that discussion then went on to discuss the definition of innumeracy, which is the heart of the linked article. that is not a derail. i haven't derailed anything and if you don't like what i'm talking about, then by all means feel free to keep it to yourself.
posted by shmegegge at 11:42 AM on May 3, 2007


"Choice of a spouse"? What is he alluding to, game theory? Seriously: If anyone has read the book, I am curious.
posted by everichon at 11:42 AM on May 3, 2007


Part of the reason for this perverse pride in mathematical ignorance is that its consequences are not usually as obvious as are those of other weaknesses.

And it does not a 'fit' characteristic for sexual selection. Which is morally repugnant on the part of the selectors.

Btw, contrary to the 'get along fine without math' crowd; depends on your definition of get along fine. People for a long time survived and functioned without being able to read. And still can though perhaps not in nearly as many situations. But I doubt anyone would question the limitations it poses.

Something often missed in regards to Math, if one does not understand the concept of differential equations, without regard to whether they can solve them, one cannot be coherently moral. Understanding feedback loops is vital to making any socially conscious decision. I suspect, of course, that far more people understand the notion than those that realize.
posted by kigpig at 11:48 AM on May 3, 2007


crashlanding writes "shmegegge, your complaints over the definition of innumerate are just a matter of semantics and it's quite a derail."

It's not a derail, it's an attempt to rail. 2/3 of the people here are arguing that innumeracy sucks, but all apparently disagreeing about what it means, and 1/3 are saying that the author is making too big a deal, but disagreeing about what innumeracy means. The entire conversation is based on discussing whether or not we agree with a proposition, and yet we don't even agree with what the proposition is. How can trying to determine what we're actually discussing be "a matter of semantics and quite a derail"?

I might as well start a discussion about whether Bob sucks, and then tell someone who says "Bob who? Bob Newhart? Bob Dobbs? All Bobs?" that their question is one of semantics, and a derail.
posted by Bugbread at 11:49 AM on May 3, 2007


The more I think about it, the more utterly bizarre I find the claims that trying to define our terms in a discussion about mathematics is "a matter of semantics and a derail".

Alice: "Do parallel lines ever intersect?"
Bob: "Yes"
Carol: "No"
Dwayne: "Are we talking Euclidean or non-Euclidean geometry?"
Erol: "It doesn't matter if it's Euclidean or non-Euclidean, that's a matter of semantics and a derail! Just answer the question!"
posted by Bugbread at 11:52 AM on May 3, 2007


God, this is just the same rant everyone makes about how other people don't understand or appreciate what they love. Just like I see the ugly fucking sentences people write and wonder why they do not possess a deep, glorious understanding of language that would make their errors painful to them too. The answer is because they don't care. I can't draw 'cause I find it difficult and don't care enough to rectify that. I remember more of number theory than I do of calc and that is because I just didn't care.

I also agree with everything shmegegge has said.
posted by dame at 11:53 AM on May 3, 2007


This article seems to be in context.

http://www.slate.com/id/2152480/
posted by bepe at 11:54 AM on May 3, 2007


Oh and in case there are some mathematicians out there wanting to make math fun again, may I suggest that "games" involving manipulating objects for an hour to understand some "problem" be taken off the table? Having a teacher who knows the answer walk around watching me struggle instead of just explaining it? That put history ahead by thirty points on my subject leader board.
posted by dame at 11:56 AM on May 3, 2007


"Choice of a spouse"? What is he alluding to, game theory? Seriously: If anyone has read the book, I am curious.

Flipping through the book, the only thing I see that even remotely is about choosing a spouse is a classic problem in probability.

Assume there are N suitors for a woman, and they can be ranked linearly. That is, she likes 1 best, 2 next best, and so on, up to N, which she likes least. If these suitors are randomly ordered and presented in sequence, and if she must either accept each one as her final choice or reject him, what should the strategy be to choose the best possible mate?

The answer (which I've never quite been able to work out independently, but have seen quoted several times) is that she should reject the first 37 percent of the suitors, and then afterwards choose a suitor who is better than all the suitors she has seen.

Exercise for the reader: show that such a strategy has an application in real life.
posted by TypographicalError at 11:56 AM on May 3, 2007


Me be bad at math.

I blame the Nixon Administration!
posted by tkchrist at 11:59 AM on May 3, 2007


The point of this article was to point out how easy it is for some people, even the highly educated, to just believe that they are not good at math, give up, and have nobody give them shit for it. If anyone did that with reading or writing there would be rather evident and picked up on quickly.

Have you been to the Internet? And I'm not talking about the cats.
posted by dame at 12:01 PM on May 3, 2007


TypographicalError,

seriously? that's in the book? I kind of want to know how he justifies that method for choosing a spouse, or whether he uses it as a mental exercise exclusively.
posted by shmegegge at 12:04 PM on May 3, 2007


My dad tried tutoring me in math via the Sam Kinison* method. I was actually pretty good at math, but he wanted me to be gooder. He learned math in the old country, and thought that American schools weren't doing a good job of teaching math. He was right about that, but it turns out that yelling and banging a ruler on the desk is not the best way to teach. I am still pretty good at math, very good really by American standards, and pretty average (at best) by Western European standards.



*I'm referring to the Kinison character in the Rodney Dangerfield vehicle Back to School.
posted by Mister_A at 12:10 PM on May 3, 2007


Something often missed in regards to Math, if one does not understand the concept of differential equations, without regard to whether they can solve them, one cannot be coherently moral. Understanding feedback loops is vital to making any socially conscious decision.

Interesting. Could you elaborate on this?
posted by jason's_planet at 12:20 PM on May 3, 2007


kigpig writes "In fact, I work with engineers and when presented with the bayesian breast cancer problem they get it grossly wrong as in on the opposite side of likely hood."

Woohoo! By various definitions of innumeracy here, I am either very innumerate, or moderately numerate (though it is taboo to discuss which definition we should be using), but I got this one right on the first try! (Well, actually, for some reason I got 7.69% instead of 7.8%, but I'd say that's close enough to count as correct).

dame writes "may I suggest that 'games' involving manipulating objects for an hour to understand some 'problem' be taken off the table? Having a teacher who knows the answer walk around watching me struggle instead of just explaining it? That put history ahead by thirty points on my subject leader board."

Agreed. Or, rather, that teachers realize that not everyone learns the same way. I had teachers (impassioned souls) who tried to get us to understand calculus by visualizing what the curves meant and the like. It worked great for some people. For me, that was the hardest part of calculus, and one that I failed at entirely. Using formulas? No problem. Figuring out which formula to use? Still no problem. Figuring out some sort of complex relationship where different formulas were applied to real life situations in order to get the desired answer? Still no problem. I did quite well in math class. No math major, by any means, but I got a 5 on the Advanced Placement exam, so I wasn't what some/most/a few of us would call "innumerate" either. However, whenever the teacher said "Let's make this a little easier to understand..." and started with an explanation of what the curves meant, or how moving around a curve reflected changes in real life? It was like a blanket was cast over my mind.

Actually, that Bayesian page was like that. "Can you do this mammography problem? Many doctors can't." -> I chug the numbers, get the right answer. "Let's make it easier, with this explanation." -> I find myself incapable of grokking the explanation. I find determining the correct answer far easier than understanding the "simple explanation" which is supposed to lead me to the "difficult" correct answer.
posted by Bugbread at 12:21 PM on May 3, 2007


From the link about Stevinus:

As an engineer, he constructed dykes which are in use to this day.

Dude liked to build lesbians, I guess. And they still just can't get enough.
posted by Mental Wimp at 12:50 PM on May 3, 2007


um...
posted by shmegegge at 12:51 PM on May 3, 2007


if one does not understand the concept of differential equations, without regard to whether they can solve them, one cannot be coherently moral.

Me too: could you explain this (to a moral guy who has forgotten what a differential equation even is even though I'm sure my teenage kid could probably try to explain it to me...)?
posted by kozad at 12:52 PM on May 3, 2007


I don't pretend to know for sure exactly how differential equations correlate, but I don't think he means that you need them to be moral, just to be morally consistent. Like, if you think "X is bad", and "Y is bad", but decreasing X causes an increase in Y, you have to understand their relationships in order to maximize your moral returns. Without understanding it, you may try to crush X, merely resulting in a huge spike of Y, resulting in things being worse off than when you started.

Perhaps a real world example would be one of, I dunno, finding child labour immoral, and finding the allowing of child starvation immoral, and being able to do the math to determine whether it is more beneficial to the children of some country to shut down the child labour factories, which might result in starvation since they lose their income, or to leave the factories running, forcing them to work but putting food on the table.

Just a guess at what he was getting at.
posted by Bugbread at 1:17 PM on May 3, 2007


I didn't get finish in time...bugbread's example is better than my generalizations, but here's the explanation I was writing up:

The diff eq. comment boils down to understanding that the results of an action impact the whole system and thus change how the same action would impact the system the next time. (something called a feedback loop which, when statistical or for all intent and purposes non-discrete, is a differential equation).

For those not familiar, the way it's generally taught in an early calc. course is fox and rabbit populations:
-As the population of foxes grows, they eat more rabbits.
-As they eat more rabbits, there is less food for themselves.
-As there is less food the foxes starve.
-As the foxes starve, there become less foxes to eat the rabbits, and the rabbit population increases.
And so on with an oscillating equilibrium reached.

Understanding this concept is necessary to make an intelligent (something I consider prerequisite to morally consistent, as in, if you don't think through your opinions they aren't really moral regardless if they are coincidentally the best solution) decision on anything where resources are finite.

Again I think most people get the above even if they don't know it's a differential equation.

Furthermore, it follows that as the social climate changes, the politically pragmatic decision can be altered...as in what was a good policy 10 years ago, may not be now. This I see a lot less people being able to grasp.

I'm being generic because this is a lengthy topic and I'm at work and all...
posted by kigpig at 1:23 PM on May 3, 2007


Yeah, bugbread, for some it's just easier to memorize the formulae and the rules for when to use them. Most math nerds like to understand the principles behind the formulae. [Warning: upcoming boastfulness] I remember in graduate school that a classmate was amazed that I didn't memorize formulae, but derived them on the fly from first principles. Up to that point, I had just assumed that's what everyone did. I was shocked that someone pursuing an advanced degree in a mathematical field DIDN'T do that. [Boastfulness off] I guess my mind is just too messy to actually reliably remembers a lot of detailed notation for any length of time.

Also, the right formula gives you exactly the right number on the Bayesian breast cancer example, so you might not be using the right one.
posted by Mental Wimp at 1:30 PM on May 3, 2007


We used differential equations in mechanical engineering to model spring-mass-damper systems* -- a classic case would be one corner of your car's suspension. They let you model the suspension's reaction to bumps and tailor the chassis response to the design specifications, whether sportscar or limosine. Handy stuff! I imagine kids nowadays mostly plug the numbers into computer simulations, something we were just starting with back in my day. ::smacks gums::

Electrical engineers also use them to model electric systems. I have no idea why.

* Hope that applet works; it's blocked for me here at work.
posted by LordSludge at 1:43 PM on May 3, 2007


Electrical engineers also use them to model electric systems. I have no idea why.

The same reason you MEs use them -- the model works. What would a DE class be without the damped harmonica oscillator?
posted by teece at 1:49 PM on May 3, 2007


seriously? that's in the book?

I haven't read the book, but it is a classic problem, often presented in terms of choosing a mate in some sense or another.

You can reformulate it just as well to be about choosing a car or a house or a job offer; the key issue is that you should be choosing against a stream of unordered, quantifiable, and categorically homogenous candidates. For the purposes of the model, it's something you only get one shot at, and it's of sufficient importance and necessity that you are willing to apply a maximizing strategy, because you know you need to pick one and you don't want to make a Hail Mary and get burned.

So a mate fits the bill better than, say, blind bids on your low-stakes auction, from which you might be willing to either take a serious loss or simply not sell at all.
posted by cortex at 1:51 PM on May 3, 2007


Also, I got talked into taking Systems Dynamics in high school (anybody remember STELLA?), and I've never really forgiven the math/compsci coordinator for that.
posted by cortex at 1:52 PM on May 3, 2007


The same reason you MEs use them -- the model works.

Really? I was told it had something to do with magic smoke.
posted by LordSludge at 1:57 PM on May 3, 2007


Mental Wimp writes "Most math nerds like to understand the principles behind the formulae."

My problem isn't necessarily not understanding the principles behind the formulas, but not being able to visualize them. That is, I am more comfortable moving the symbols around in my mind and deriving things than from thinking in concrete terms. I only remember ever deriving one formula with no input, but I did, so I must not be totally incognizant of the reasoning. It's just the visualization aspects that always threw me, and that's what they always used to make things easier to understand.

Mental Wimp writes "Also, the right formula gives you exactly the right number on the Bayesian breast cancer example, so you might not be using the right one."

Yeah, that was bugging me, but it turns out I was reading the question slightly wrong. I was reading that 9.6% of women who took the test had a false positive. That is, 9.6% of 100%. On rereading, I realize it's that 9.6% of women who took the test and didn't have breast cancer had a false positive. That is, 9.6% of 99%. With that adjusted, I got the right answer. So right formula, bad reading of details of question.
posted by Bugbread at 2:04 PM on May 3, 2007


I am not an unintelligent guy, and I understand (and enjoy thinking about) the softer side of math (ie statistics and trends), but I'm functionally unable to do the anything beyond simple Algebra.

I also have two children.

Needless to say, I'm planning to start my rudimentary studies of mathematics shortly.
posted by davejay at 2:23 PM on May 3, 2007


I also have two children.

Well at least there's something you are very good at.
posted by elpapacito at 2:34 PM on May 3, 2007


Well, I got a lot dumber when I had children. Just ask them.
posted by Mental Wimp at 2:38 PM on May 3, 2007 [1 favorite]


I too have met people who take pride in being bad at math. I suspect that there are multiple reasons for this:

1. Fake pride can be a cover for shame. The person may be trying to fend off charges that he's stupid by engaging in bravado. Such behavior might be automatic (unconscious). Maybe it was planned at one point, but after years of repetition it's probably habitual.

2. Very little of what we "learn" in school (at least from what I experienced in my American, public-school experience) involved true mastery of a difficult subject. Yes, we had to read, but no one expected us to read the complete works of Shakespeare. We had to take gym, but no one expected us to compete on an Olympic level or even run a marathon.

Instead of mastery, we were required to complete all sorts of mini-tasks: read this book, write this paper, etc. For me, even much of college and grad school was like this.

But as many have pointed out, math -- beyond the super-basics -- requires mastery. You have to study, really USE your brain, and drill. You have to slowly build an edifice from solid foundations. What else do most people do -- in school -- that is like this? Is such mastery even taught as a positive value?

So Math is the first thing most people try and fail at. They plug away at it, doing as little as possible (which is generally what's asked of them), until they pass the required courses. Then, when they attempt more complex math -- and discover that it requires mastery -- they fail.

They may not even realize that they COULD succeed if they just tried harder (drills, etc.) They may not realize this, because having never mastered anything before, they may feel that if they can't achieve the goal via simple-to-digest tasks, it's utterly impossible. They are simply Not Good At Math, as if most of the people who are good at math just glanced at a textbook and got it instantly. (I think many people really believe that math geeks are like this: they're freaks of nature who came out of the womb with a complete understanding of Calculus.)

So Math is many people's first real failing -- and it's an especially hurtful failing for those people who are academically "gifted", who pride themselves at being smart and doing well in school. Doing well in school mostly involves handing your homework in on time, being polite to teachers and learning various social and procedural rules. But many people mistake doing well in school with being smart. "How can I, a smart person, be failing at math? It must be something wrong with math!"

People need some way of dealing with the hurt of this failing. So they generally deal by proclaiming, "I'm not a math person!" As if it's 100$ genetic. They don't want to say, "I'm not willing to put in the time and energy to master something." Some of them may really believe that they're genetically unable to get math (again, because they've never had the experience of mastering anything).

3. What kind of person DOES master math? Someone willing to spend a large amount of time -- when they're young -- doing drills and taxing their mind. At this same age, most kids spend the bulk of their energy socializing. So there's a high likelihood that the math-geek will be less adept than them socially. He'll be a nerd. People will equate his nerdiness with his mathematical ability, and they'll scorn both. "I suck at math" = "I'm not a nerd."


I spent years as an adult educator, mostly teaching people how to program. Over and over, I ran into "I just don't get that computer stuff," "I'm not a computer person," etc. 90% of the time, the people who said this were people who had been coasting for decades. They really thought that they were "bad at computers," but what they were really bad at was learning. In fact, they hasn't been asked to learn anything new in years. Some of them had "challenging" jobs. Jobs that I couldn't do unless I studied for years (lawyers, etc.). But they'd done their studying years ago, learned what they needed to learn, and then stopped learning. And their job didn't require any additional learning -- except the occasional small procedure, much like the small procedures they had to tackle back when they were in school. Do the homework. Call the client.

There's a horrible pattern that many people get into. At least I think it's horrible. Go to school, get a job, and then coast until retirement. All spare time is spent socializing or watching TV. How many people do you know that say, "Wow, I haven't mastered anything lately. I should get to work!"

By the way, I suck at math. I suck at it, because me teachers were terrible and I wasn't willing to do the work I needed to do on my own (which is what I would have had to do, since they wouldn't have helped me). I suck at math, because I didn't work to master it. It's nothing to be proud of, but I don't much care about pride or shame. I'd love to understand one of the most profound human achievements. I'm working on it.
posted by grumblebee at 2:50 PM on May 3, 2007 [5 favorites]


What kind of person DOES master math? Someone willing to spend a large amount of time -- when they're young -- doing drills and taxing their mind. At this same age, most kids spend the bulk of their energy socializing.

You don't have to do it when you're young (I did it all in my late 20s, and was good enough to get a B.Sci in math). I got by in Algebra (it was easy for me, but I did not study nor did I do homework, so I didn't do great). I failed trig./math anal. in high school because I refused to study.

But I was able to catch up in college, with a little bit of work (it was easier for me, as I've always had a natural aptitude -- it was the dedication to studying that I needed work on).

dame, I hear ya, but I think there is a point to defining innumeracy. It is important not to be a dickhead math snob, as some are, but I think society in general could go a long way toward being better at math. Of course, we could go a long way toward being better writers, too. I once got Soviet-volunteered as an unofficial editor of prose at a large corporation (in spite of being the lowest pay grade there, I was the only one who could turn out at least partially decent English). Man, many college graduates have got themselves some atrocious writing skills. I don't mean bad editing skills, I mean prose that made you want to break a shovel over their head.
posted by teece at 3:05 PM on May 3, 2007


I agree with a lot of what you said, grumblebee, so this isn't an attempt to counter your comment, but just a few minor footnotes of disagreement:

For some people, constant drill isn't necessary. I never liked math, but never hated it. I was horrible at visualizing anything mathematical, but I understood explanations pretty much immediately, and with an example or two of practical applications, could apply a new formula to a real-world situation even when it wasn't made explicit that a certain formula should be used for it. So, yes, for most people, math requires lots of drilling and hard work, but that isn't a universal constant.

Second, regarding math geeks: all the math geeks I've ever met, by which I mean not just geeks who are good at math, but geeks who are geeks about math, have been amazingly instinctual, seriously "look at the book and immediately grok it" types. I mean, math was easy for me to understand when explained, but it sure as hell wasn't instinctual. But look at Mental Wimp: he didn't memorize formulas, he derived them on his own. So there are people like that. But I totally agree when you talk about "most people who are good at math". In my high school classes, there were lots of people who were good at math, but no "math geeks". Nobody who got a hard-on from math. And all these "good at math" people were good because of hard work, or at least moderate work, not from natural instinct. The only math geeks I knew were in Uni, and though they were instinctual types, they were far fewer in number than the people who were good at math because they used and practiced it.

Last, regarding adult learning:

I don't think it's horrible that people grow up and stop mastering new things. There are three reasons to learn something: 1) it will be useful, 2) it is fun to learn, or 3) it isn't fun to learn, but it's fun to know. I, for example, learned Japanese (and now translate), but I never enjoyed studying Japanese. The studying part sucked. It was the knowing part that was good.

So, as an adult, if you have a career, and a subject isn't going to help your career, nor will it help outside of your career, reason 1 is out. What's left is enjoying the work, or enjoying the results. If someone doesn't have an interest that they enjoy studying, or an interest whose end enjoyment is greater than the suffering of studying, then there's no reason that they should try to master something.

Sure, that may not match my own preferences. Sure, I may enjoy learning stuff as an adult. But I certainly don't find it horrible if Bob doesn't, any more than I find it horrible that homosexuals and straight women don't enjoy having sex with women, even though I think sex with women is a fun activity. They've got their interests, I have mine. Same with someone who doesn't enjoy mastering things for fun; they're not interested, I am, and there's nothing wrong with them for not enjoying what I enjoy.
posted by Bugbread at 3:17 PM on May 3, 2007


As for the "is it good/is it bad" question, we may all disagree about the definition of innumeracy, but I think we can all agree:

There are a lot of people out there who are proud of being bad at math. Not just folks who admit they're bad, but who find pride in it. That pride is not a good thing.
posted by Bugbread at 3:20 PM on May 3, 2007 [1 favorite]


I don't think it's horrible that people grow up and stop mastering new things.

Your points are well taken, bugbread. And I tried to make it clear that it was just my feeling -- totally subjective -- that it's horrible people stop learning.

But it's a really strong (almost primal) feeling. I feel it in the same way that some people feel it's horrible that many people don't appreciate classical music, gourmet food, or beautiful art. The Beatles suck and "King Lear" is a boring play. I have a gut reaction that I can't shake. I hate living in a world where people feel this way. I fear that I can't connect to such people.

We're born with a love of learning. Love may be the wrong word. Maybe appetite is better. I suspect that in a natural state, this craving would never die. School, work, peer pressure and the drudgery of life kills it for many people.

In any case, I'd add to your numbered list of reasons to learn: 4) because, like sex or laughing at a joke, it's natural. It's what one does -- if one isn't damaged. School -- for many of us -- is the biggest damager. It teaches us that learning is about reward, punishment, forcing, posing and "what you can get away with."
posted by grumblebee at 5:20 PM on May 3, 2007


Just as an aside and for reference, the problem that TypographicalError brought up and that cortex also referred to is clasically known as the secretary problem. I believe the 37% (i.e., 1/e) solution only applies to the case where you're trying to maximize your chance of picking the very best out of the 100 secretaries/mates/whatever, and that the optimal strategy when you're willing to distinguish between, say, second and third-best is somewhat different.

But I guess this thread isn't about the details of math problems, is it.
posted by sappidus at 5:20 PM on May 3, 2007


Eh, I can add, subtract, multiply and divide. Anything beyond that, I'll use a computer or find a nerd.
posted by jonmc at 5:25 PM on May 3, 2007


The only thing that matters is being able to count your beers, jonmc....
posted by rhizome23 at 7:26 PM on May 3, 2007


Flipping through the book, the only thing I see [is X.]
[...]
The answer (which I've never quite been able to work out independently, but have seen quoted several times) is [Y].
posted by TypographicalError


seriously? [X=Y]'s in the book?
posted by shmegegge


Perhaps it isn't "innumeracy" as an ill-defined concept that's so worrying and/or offensive. Perhaps it's the Telephone-esque means of communication employed by the intellectually complacent?
posted by unregistered_animagus at 7:28 PM on May 3, 2007


Then I ask them to subtract one number from another for me, using a pen and a piece of paper I hand them: say -2and7/8ths minus 1and3/17ths.

Easy! -2 7/8 - 1 3/17 is very nearly -2 14/16 - 1 3/16, or -4 1/16. This differs from the correct result by only 0.27%.
posted by ryanrs at 7:44 PM on May 3, 2007


School -- for many of us -- is the biggest damager.

Can we talk about really bad teachers? I had a university prof who came into class and copied out a textbook. Thanks for the inspiration, man. :-(

We've talked about the pernicious belief by students that the ability to do math is inbred. The same belief is even more harmful when it's the teacher who subscribes to this theory. In that case, he or she separates and labels those who "can" and those who "can't".

Finally there are the teaching materials. How about more math textbooks that make math interesting and excite curiosity in the student? I don't think for example that i've ever seen a mathbook incorporating some of Martin Gardner's delectable mathematical recreations for example...
posted by storybored at 7:54 PM on May 3, 2007


Perhaps it isn't "innumeracy" as an ill-defined concept that's so worrying and/or offensive. Perhaps it's the Telephone-esque means of communication employed by the intellectually complacent?

Oh hey, thanks for pointing out my intellectual complacency. Otherwise I'd have thought it was just an innocent mistake.
posted by shmegegge at 7:56 PM on May 3, 2007


teece wrote: 1 is not a prime number, shmegegge. 1 and 0 are actually very special numbers. 1 could be a prime number, if someone leaves that exclusion out of the definition. But, by definition, it is not prime. The primes start at 2. (this is a matter of convention, only).

No! One must not be prime, otherwise prime factorizations would not be unique. That would break The Fundamental Theorem of Arithmetic. Those conventions are there for a reason, man!
posted by ryanrs at 8:08 PM on May 3, 2007


I wouldn't say it's a matter of pride. I've been addled by a learning disorder in mathematics since I was young, and it's hard to explain to those who can't conceive of an inability for algebra or calculating areas. It's like not being able to see the color red. If you've never seen it, you cannot possibly understand it, and I just don't have the capacity. I'm 30-something and back in school, fighting to make progress against a system that insists that I pass Algebra before I advance in classes. It's maddening. I don't have the neurological capacity to "get it," it's as if that part of my brain just didn't exist, and there's very little room in academic for realization without mastery of numbers. I hope at some point, for the next generation of LD-addled learners, our ideas of cognitive structures will take in to account those who are forced to live with differences beyond our control.
posted by moonbird at 9:30 PM on May 3, 2007


I think that the biggest fuckup is the American education system. Caveat: I fucking hate math and need a calculator to do anything. Like add up the money in my drawer at the end of my shift.

Of course, my dad (the mechanical engineer) and my mom (an accountant) tried to help me. Every night they attempted to help, ended in tears. Or my dad just shoving himself away from the table in frustration that I DIDN'T GET IT.

Teachers didn't understand. They thought that I just 'wasn't trying'.

Fuck American schools. Fuck them in the ear with the algebraic equations.

I rocked Honors Physics though, much to the amusement of the professor. He didn't care if you did the math right (for the most part) as long as you understood the concept and what was *supposed* to happen.
posted by sperose at 9:38 PM on May 3, 2007


We're born with a love of learning. Love may be the wrong word. Maybe appetite is better. I suspect that in a natural state, this craving would never die. posted by grumblebee

With respect, I think that's starry-eyed bullshit.

I think we're born with a love of surviving - and an appetite for same.

A love of learning has to be acquired.

I suspect our natural state is splashing around in mud puddles and that love for learning doesn't come until we see its advantages - then we start to "fly"!

I am more with bugbread that the great, lazy self-delusion for the mud puddlers is that some folk just "love" studying. I think we love where it gets us and I do so wish (like you grumblebee) that everyone got those advantages quickly.

Because - being a snotty, bookish sort - I think it's so much more fun.
posted by Jody Tresidder at 6:25 AM on May 4, 2007


Jody Tresidder writes "I suspect our natural state is splashing around in mud puddles and that love for learning doesn't come until we see its advantages - then we start to 'fly'!"

Well, I don't think we're naturally born with a "love" of learning, but we're definitely born with a natural propensity to learn. I say this because my kid is 1 year old, and is learning a lot, despite the fact that he has no need to learn. He's going to get fed whether he tries to learn to pick up his spoon or not, and he's going to get a kiss whether or not he learns what the word "kiss" means. And yet, despite having no need to learn either thing, he's learning them.

I don't think he's learning it because he loves learning, but I don't think it's just for survival either. It's just a natural thing, like picking one's nose: one doesn't do it out of love, nor as a means of survival. One just does it.
posted by Bugbread at 7:50 AM on May 4, 2007


Learnin' things never taught me nothin'
posted by jonmc at 8:11 AM on May 4, 2007


Bugbread,
Congrats on your one-year-old - that's such a brilliant age.

However, you wrote: I say this because my kid is 1 year old, and is learning a lot, despite the fact that he has no need to learn. He's going to get fed whether he tries to learn to pick up his spoon or not, and he's going to get a kiss whether or not he learns what the word "kiss" means. And yet, despite having no need to learn either thing, he's learning them.

Of course he has "no need to learn" in one sense, because you're there, anticipating his needs - and being reminded - with a great, lusty, survival-motivated natural "yell" when his needs aren't met!

I'm not suggesting you find a "control" one-year-old and see what happens, though!

But once he gets a bit older, I think you'll understand the lazy lure of mud puddling for kids - and the importance of rewarding learning so that young bugbread gets the knack nice and early for self-motivated improvement!
posted by Jody Tresidder at 9:31 AM on May 4, 2007


first post!
posted by YoBananaBoy at 10:06 AM on May 4, 2007 [1 favorite]


*thud*
posted by LordSludge at 11:22 AM on May 4, 2007


They may not even realize that they COULD succeed if they just tried harder (drills, etc.) They may not realize this, because having never mastered anything before, they may feel that if they can't achieve the goal via simple-to-digest tasks, it's utterly impossible.

Oh, that's just bullshit. Go back to my high school and find the math textbooks I cried myself to sleep on every night. I worked my ass off, to no avail. I, too, had shitty teachers who couldn't even get the answers to problems right, something we called them on when the same problem -- with answer -- was written out in the back of the book.

By contrast, I learned German, French, Latin and Chinese in high school. Well. I'm fluent in German and can read French even now at a decent level. Went on to study Czech and Russian in college. Tell me foreign languages don't involve drilling and being able to break down learning into smaller tasks, such as vocab acquisition.

A friend who was diagnosed with dyscalculia has a lot of math "symptoms" similar to mine, so I really wonder sometimes if it's not me, but an actual disability. I do know I put the work in, so the "try harder" method isn't really an end-all solution. And as I've said, I'd love to have a better understanding of math...
posted by bitter-girl.com at 6:50 AM on May 5, 2007


I didn't mean to make light of your hard work, bitter-girl.com. Your experiences sounds deeply horrible and frustrating. Please note that I was never talking about ALL students. Sadly, my evidence is anecdotal, but it is based on 15 years as a student and about the same number of years as a teacher, both of children (2 - 10-year-olds) and adults. There are a few who, like you, mastered difficult subjects in high school yet tried and failed to master math. But -- in my experience -- those people are few and far between.

Let me be crystal clear that I'm NOT talking about laziness. Many people who failed at mastery are hard workers -- and they may even have worked hard at math. That describes me. I spent hours doing math homework, but I never mastered it. I worked hard, but I worked in the wrong way. I don't blame myself (or the millions of others like me), because no one showed me the right way (not to say that there's just one right way.) Like you, I had terrible teachers. I also had terrible textbooks.

I spent the last five years teaching programming. I found that -- with myself and most people -- it's not enough just to drill. It's not even enough to explain (to put the drills in context) and drill. Math (and some other subjects, like programming) are different from foreign languages in this way. One really can master languages through drilling, context and continual usages. But, for most of us, that won't cut it with math.

And I guess I'm mincing words here, but when I said many people have never really mastered anything, I meant the sort of mastery that I'm discussing here (that necessitates going beyond drills). So foreign languages don't count. Please note that I'm not belittling your achievements. I'm just struggling with words. You clearly "mastered" German (etc.) and you clearly did this through hard work. I need another word for a different kind of mastery, but I don't have that word.

For me, and for may of my students, such mastery comes through the following steps (and minimum):

1. drills.

2. daily usage.

3. large-scale projects.

4. lectures, books, etc. that put the above points in a contextual, intellectual framework.

5. an "apprenticeship" in which you gradually learn good habits that more experienced programmers have honed over the years. It's not enough to memorize these. They need to become a part of you. It's not enough just to read about them and "get" them. It's necessitates a whole, permanent shift in your thinking.

6. a relationship with complex ideas that your form in (at least) three ways. In other words, you need to hear a lecture about a concept, read a book about the same concept, and watch a training video about the same concept. The need for this step varies from person-to-person. "Three ways" is a ballpark estimate. Some people need six. A very few need one.

For most of us, re-reading the same book three times (or even reading three different books) won't work. The concept needs to enter your brain in (at least) three completely different ways, each way utilizing different metaphorical frameworks, examples and senses (hearing, reading, seeing...) Needless to say, all these sources need to be good. A bad lecture or a poorly-written book don't count.

I'm not sure why this works. My theory is that -- in addition to the drill aspect -- it signal a social part of our brain that "you're hearing the same idea from three different 'people.' This means it must be important. So you'd better remember it.

Did this EVER happen in your math education? Did you read a ( good) book about adding fractions, hear a (good) lecture about adding fractions and watch a (good) video about multiplying fractions?

By the way, I've also found that there must be a time-lag between these steps. It doesn't work, for most people, to -- back-to-back -- read the book, listen to the lecture and then watch the video. My guess is the brain needs time to process each one, move on to something else, and then move back. The "moving back" part, I think, is what says "oh, we're re-visiting this. It must be important."

7. a large amount of time is needed. I'm not talking about a school year. I'm talking more on the magnitude of ten years. There have been some studies that suggest ten years are needed for the sort of mastery I'm discussing. (But you can master multiple things during that ten-year period.)

I can think of three things I've mastered on this level: teaching, computer programming and directing (theatre). I feel I have mastered them, because I feel totally confident doing them, and because other people react to me as one does to a master craftsman. In both these cases, it took me at least ten years to get where I am. I did plenty of useful work one, two, five, etc. years into the process, but if I'm honest with myself, it wasn't until I'd after a decade that I felt that the subjects had become a part of me and that I wasn't playing secret catchup or struggling to understand basic concepts.

(To me, aside from objective markers in a particular field, like speed measurements for a marathon runner, mastery has most to do with confidence. I don't expect a master mathematician no know ALL of math. I expect him to be confident about his strong mathematical ability, and I expect him to feel at ease about extending his knowledge -- via reference books, etc. -- when the need arises.)

THIS is what I meant by mastery, and this is why I say that many people confuse innate ineptness with lack of mastery. They assume they're naturally bad at math, and maybe they are, but my thesis is that they can't really make this claim because they haven't attempted mastery via the steps I've outlined above. (Or other -- similarly rigorous -- methods.)

If they understood this, they would have to say, "I'm bad at math. It may be because I'm unwilling to devote ten years of my life to mastering it." That doesn't mean they're bad people. I'm bad at gourmet cooking. I'm sure I could become really good at it, but I'm not interested enough in it to devote the time that I know I'd have to put into it. Some disciplines are complex enough that they need that sort of commitment.

It's not necessary that everyone makes such a commitment, but I think it would be great if people understood that they COULD master hard subjects if they DID make a commitment. It took me years to understand this, but now that I do -- now that I know I have the ABILITY to master things -- I actually feel good about my POTENTIAL to master gourmet cooking. I won't do it, but it's nice -- and a confidence boost -- to know that I could.

I DO want to master math, and I intend to do it. I started thinking about doing this a couple of years ago, and I got a bit too busy to start on it. I'm 41 now. I look forward to mastery in my mid 50s. Cool.
posted by grumblebee at 11:03 AM on May 5, 2007


Nice post, grumblebee. I agree with your definition of this slippery concept of mastery. Ten years is about right for a minimal committment.

My first experience of mastery was with software too. Fresh out of university i thought i was a hot shot programmer. I got a rude awakening. I thought you just had to make the code work. I was lucky enough to work with a group of masters. They had discussions and questions on issues i hadn't even begun to think about. And slowly, through practice and guidance it started to sink in. It took about nine years to get to the level where i was within grasp of mastery. (To this day, I'm not sure, I got there completely).

Mastery seems to be a combination of structured knowledge, technical prowess, intuitive global understanding, and attitude.

The sad thing is that there are many who do spend ten years in software but do not achieve anything close to mastery. You get a weird vibe when you talk to them. i.e. that they're using the words but the "grammar" is wrong.
posted by storybored at 2:23 PM on May 6, 2007


A good story about math ability and teaching: John Mighton is a playwright who had big problems learning math. Classified as a math dummy, he discovered it was the teaching methods that were at fault. He then went on to get his Ph.D in mathematics, to write an inspiring book, The Myth of Ability and to found a non-profit math tutoring program for kids called JUMP.

The program has proved so successful an entire class of Grade 3 students, including so-called slow learners, scored over 90% on a Grade 6 math test.

See an example of their free tutoring materials.
posted by storybored at 2:37 PM on May 6, 2007


I agree with your definition of this slippery concept of mastery. Ten years is about right for a minimal commitment.

I wonder when you came up with this definition? Did someone explain it to you early on, or did you discover it once you'd already mastered something, as a way of explaining what happened to you by accident (which isn't to imply that you didn't do hard work).

That's what happened to me. I didn't understand master. I just happened to master something. I worked really hard for years, and then one day I suddenly started feeling the confidence that mastery brings. THEN, looking back, I realized what had happened.

The horrible thing is that I also realized how easily it might not have happened, had my life taken a different path. I just got lucky. And I'm SO glad that I did get lucky, because this luck made me realize that I'm CAPABLE of mastery, which makes me strive to master new things.

If I hadn't lucked into this fact, I'd probably never master anything. I'd work hard at something for what would seem to me like a reasonably amount of time (a couple of months? a couple of years?) and then assume that I was incapable of ever mastering it.

It's such a colossal crime that we're not taught about mastery. Back when trades were learned through an apprenticeship system, people understood this. But for the most part, such knowledge has been lost.
posted by grumblebee at 10:14 AM on May 7, 2007


I wonder when you came up with this definition? Did someone explain it to you early on, or did you discover it once you'd already mastered something....I just happened to master something. I worked really hard for years, and then one day I suddenly started feeling the confidence that mastery brings. THEN, looking back, I realized what had happened.

Grumblebee, that was exactly my experience! My low-level mastery came about without my planning or knowing about it. Kinda scary like you said, because if i had left the field earlier i would never have gotten it, and missed a (the most?) valuable lesson in life.

Trying to understand more about mastery after the fact led me to The Seven Stages of Software Expertise. Unfortunately, it doesn't explicitly talk about time frames which is a crucial omission. Then there is the more recent research and the concept of deliberate practice: "'The ten-year rule represents a very rough estimate, and most researchers regard it as a minimum, not an average.' In many fields (music, literature) elite performers need 20 or 30 years' experience before hitting their zenith."

I agree they should teach this in schools. It is the ultimate enabler, and especially important now in this age of short attention spans.

I noticed you mentioned mastery of theatre directing as well. By coincidence, i had my first (co-written) play produced last year. I've been writing for two years now and I've got a long way to go :-). I'm having a lot more trouble with the process of mastering writing. When I was in software, the deadlines ensured I had to keep at it. The feedback from master co-workers made sure I stayed on the right path. Now as a writer I have neither! Argh!
posted by storybored at 11:41 AM on May 7, 2007


I'm a professional writer (in the sense that I've had books and articles published), but, like you, I don't list writing under my "mastered" skills. I love writing, I'm reasonably good at it, but it's not second nature to me, the way, say, directing is. I may even be a better writer than I am a director. That's for others to judge. But I don't feel the same confidence when I write that I feel when I direct.

I've been wondering why this is, and I think I know. For me, it's less about time than time well spent. As a director, I've had always gotten such instant, clear feedback about how I'm doing -- from the actors and the audience. I've had a harder time getting this feedback as a writer, even though I've been writing seriously for well over ten years.

When you're trying to master programming, you have a great feedback mechanism called functionality. You have to keep refining until it works. As we know, "it works" isn't enough to make a bad programmer good. It can work and still be ugly and unmaintainable. But there are further benchmarks one can apply if one wishes. There are books on programming that will quickly make you blush as you read them and think about your own shoddy code. There are also senior programmers who demand that you refine, comment and optimize. In the real world, this doesn't always happen, but at least there are mechanisms in place.

When I was in school, I noticed that my peers were always getting writing advice from teachers. Yet I never got any. I did often get remarks that my papers were well written, and it felt good to hear that, but it didn't help me improve. Teachers and friends kept telling me I was a good writer, but I knew that when I compared myself to the writers I really admired, I was a rank amateur. It's not that I need to be John Updike, but I would like to be able to swim more easily in words.

I discovered that, in standard American schooling, if you reach the level of competency, that's all anyone expects of you. Teachers expend so much energy helping the remedial students, they don't have time to help the ones who are generally getting by. Worse, I suspect they don't know how.

To be fair, I'm the same way. I could easily critique a beginning writer and help him improve, but if Margaret Atwood wanted my help, I wouldn't know where to begin. While I'm sure there are ways she could improve, I don't have the skill set to see them. On the other hand, I'm not passing myself off as a writing teacher.

So I think this is another stumbling block to mastery. In many educational systems, it's not even a goal. The goal is basic competency, and both teachers and students feel blessed if they even reach that point. I can't deny that we'd be living in a better world if more people were at least competent writers. But shooting for just that seems like an awfully impoverished goal.
posted by grumblebee at 12:11 PM on May 7, 2007


By the way, there ARE ways to master writing. You need a teacher or self-teaching method that picks your writing apart on the word, sentence and phrase level. You need someone to point out any stylistic quirks (that hinder communication or expression), and someone to compel you to break lazy habits (that you might not even know you have). This post helped me immensely.
posted by grumblebee at 12:17 PM on May 7, 2007


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