Re: Problem solvey.

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you can categorize 6-chunkers, 7-chunkers, and 8-chunkers.

I knew a plumber who used the same names in a very different categorization scheme.


Posted by: Moby Hick | Link to this comment | 09-30-09 8:44 PM
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I dunno, this whole thing sounds cockamamie to me, not just the genetic part. I always heard the "6-8 bits of information" as related to something in isolation, such as random numbers. (E.g. the explanation for why phone numbers were 7 digits long for so many years.)

It seems borderline ludicrous to me to suggest that people are only capable of holding 6-8 bits of any type of information in their brain simultaneously -- how in the name of heaven do the researchers think that most of us get through the day? Imagine sitting at a bar with your best friend, hearing a story about her latest conquest. You* think there won't be more than eight bits of information involved? You think that if she gets ten minutes into the story, you won't circle back and say "But wait--" when she contradicts something she said earlier?

Human memory is a fascinating topic, but I don't think this article is getting at the fascinating-ness.

*Not you, personally, heebie.


Posted by: Witt | Link to this comment | 09-30-09 8:52 PM
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No, I agree, I found that part fairly ludicrous. But I don't doubt that it's the limiting factor in word problems, a lot of times.

What I imagine is that under extremely rigid circumstances, they got robust, stable results.


Posted by: heebie-geebie | Link to this comment | 09-30-09 8:54 PM
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I don't doubt that it's the limiting factor in word problems, a lot of times.

Come to think of it, I probably did worse in philosophy exams out of sheer impatience and annoyance with dumb word problems. I don't know that I was incapable of retaining the information, precisely, but I certainly thought it was stupid and that did not help my willingness to play along with the given structure. (Maybe they weren't word problems in the strict standardized-test sense, but something like that. It was forever ago. I've blocked it out.)

I did think this described a phenomenon I've seen:

Highly field independent people select extremely useful bits from a word problem and from their memory to put on their mental worktable. Field dependent people make very poor choices and get hung up on nonessential parts of the problem.

But again, it's context-dependent. I've known people who were lousy at sifting out the relevant facts from a news article, and astonishingly precise and skilled at listening to a long rambling soap-opera-ish tail and distilling it in to a pointed question or succinct moral.


Posted by: Witt | Link to this comment | 09-30-09 8:58 PM
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Heavens to Betsy: Tale. I don't know where "tail" came from.


Posted by: Witt | Link to this comment | 09-30-09 8:59 PM
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I don't have a particularly good memory, but I've found that I can develop it in the direction of certain skill sets I want to develop. Like, I can memorize poetry, and even long stretches of prose, far faster now, with practice. And I'm better at acquiring languages now. But both of those are evidence that my memorization of tiny pieces of information helps me to learn the rules that might govern later strings of information. But does memorizing poetry help me learn how to memorize strings of random numbers faster? Hell, no. I'd say it doesn't even help me to memorize strings of random words. But neither of those skills seem particularly useful to me.


Posted by: A White Bear | Link to this comment | 09-30-09 8:59 PM
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seems. Heavens to Betsy.


Posted by: A White Bear | Link to this comment | 09-30-09 9:00 PM
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I've never tried to keep track of the number of chunks I can hold, but there is definitely a point where my whole mental edifice collapses and I have to start over. I'm thinking of interpreting statistical results for more complex models or when the codebook was written by an ass (or me in a hurry).


Posted by: Moby Hick | Link to this comment | 09-30-09 9:02 PM
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I had a brute force way of memorizing poetry back when I was memorizing it: I'd get a stanza down line by line and then repeat to myself all of the poem previously memorized up to the most recent stanza and then move to the next and repeat until I was done. Then I'd recite the poem under my breath while waiting for the bus. I always wondered if there were a better way.

I think doing the first poem helped psychologically in terms of showing I could do it, but I didn't feel it got any easier - or that anything else got any easier - afterwards.


Posted by: eb | Link to this comment | 09-30-09 9:06 PM
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3: But I don't doubt that it's the limiting factor in word problems, a lot of times.

Could you give an example of what a word problem is? It seems like a slightly technical thing, a term used in a technical manner for certain types of (mathematical?) problems.


Posted by: parsimon | Link to this comment | 09-30-09 9:09 PM
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What I'm curious is - how could one construct a class that would train students to increase their memory capacity? But in a flexible way? It wouldn't suffice to train them to memorize strings of 8 digits, because that wouldn't translate to another context. How could you actually help students develop these supposedly genetic skills

While I'm not making strong claims for genetic predisposition when it comes to this ability -- although there are certainly genetic aspects to other basic reasoning skills, like subitizing, that are similar -- it seems like you're strongly claiming the opposite, that not only is the genetic explanation wrong, but there is another, correct explanation that we can discuss in this thread. I'm curious what your reasoning for that would be?


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:10 PM
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Could you give an example of what a word problem is?

"Johnny has nine apples. If he gives three apples to Jenny, how many apples does he have left?"


Posted by: teofilo | Link to this comment | 09-30-09 9:10 PM
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For me, the act of writing helps cement something in my mind; I'm lucky that simply taking notes in a class gets it pretty well into my mid-term memory (a few months). If I want to memorize something like poetry or a foreign language, I need to write the words out over and over.


Posted by: Parenthetical | Link to this comment | 09-30-09 9:12 PM
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Memorizing poetry is very different than the memory referenced here.

It means something like this:
Two items have some sort of equation-relationship. It's not quite like the formula we went over in class. You'll have to manipulate the equation so that you can see the parts and how they relate to the version from class. But then, the version from class won't quite be the right version to answer the question. You'll have to understand what the question is asking for, how to represent it mathematically, and how to retrieve it from the question.

Most likely, these are chemistry problems, since the article came from a chemistry professor.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:13 PM
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Whoa, whoa, teo. Could you try it again with just 6 apples?


Posted by: JRoth | Link to this comment | 09-30-09 9:14 PM
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It seems borderline ludicrous to me to suggest that people are only capable of holding 6-8 bits of any type of information in their brain simultaneously -- how in the name of heaven do the researchers think that most of us get through the day? Imagine sitting at a bar with your best friend, hearing a story about her latest conquest. You* think there won't be more than eight bits of information involved? You think that if she gets ten minutes into the story, you won't circle back and say "But wait--" when she contradicts something she said earlier?

Seriously?

You really think that it hasn't occured to the researchers that people are able to process more than six chunks of information of the course of -- for instance -- telling a ten minute story?

You further think that they have devoted neither time nor effort to determining what a discrete "chunk" of information is, and how to represent that in testing?

I mean, come on.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:14 PM
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I guess we know where JRoth falls on the scale.


Posted by: teofilo | Link to this comment | 09-30-09 9:15 PM
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it seems like you're strongly claiming the opposite, that not only is the genetic explanation wrong, but there is another, correct explanation that we can discuss in this thread. I'm curious what your reasoning for that would be?

For almost everything, genetics grants us a range, and then the environment determines where in that range we fall, no? Is there anything (interesting) in this vein that's solely the product of genetics?


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:16 PM
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I have had contact both with work so clever that I can barely understand it, and also with individuals whose capacity for sustained and detailed abstract reasoning is much, much stronger than mine. Trying harder will push the envelope, but I have reconciled myself to not proving the Riemann conjecture or to spinning one clever exactly solvable model after another until I find one relevant to an important and difficult problem.

I don't find these real limitations crippling. Memory exercises my well be worthwhile, and practice with certain types of problems really helps cut down on the blind alleys, but there are definitely limits. Must not be getting the point, this is obvious. Cosma Shalizi's remarks on heritability and stability of IQ cite the original source of the estimate of seven.


Posted by: lw | Link to this comment | 09-30-09 9:17 PM
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10: This vocabulary is suitable for all ages.


Posted by: eb | Link to this comment | 09-30-09 9:18 PM
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12: Johnny is in Jane's bed at the dorm when Jane's roommate walks in. Jane's roommate sees two empty bottles of Boone's Farm Apple wine on the floor. Assume that Johnny drinks 134% of what Jane drinks, that the average human bladder can hold 67% of a wine bottle, that the bladder fills at 8 ml/s, that Johnny and Jane have been drinking at a steady rate starting 25 minutes ago & finishing 5 minutes before Jane's roommate arrived, and that Johnny shares conventional moral standards about nudity and bed wetting. How long will Jane's roommate have to wait to see if Johnny is wearing pants? Show your work.


Posted by: Moby Hick | Link to this comment | 09-30-09 9:18 PM
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12: Really? And we're talking about chunks of information, without knowing what we mean by chunks? Okay, I'll guess there are three chunks of information there. Am I right? Maybe there are two. Depends on how you count them.


Posted by: parsimon | Link to this comment | 09-30-09 9:19 PM
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I don't find these real limitations crippling.

Yes, but our students are disastrously bad at problem solving. For them, it is crippling.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:20 PM
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2: I think that the distinction between "bits" of information as meant in the article and bits in the way you're interpreting is the presence of narrative. The famous memorization device of "placing" words from a list into a room with furniture (or whatever) relies on using a preexisting mental structure to manage large amounts of data. A friend's story is going to fit into a narrative structure that you already fundamentally understand, and so it's easy to keep track of all the moving parts. But in the narrow sense intended by the article, the "bits" can't simply be plugged in, because the subject doesn't have the narrative.

This is part of how we get good at logic puzzles and the like - our brain starts to learn the "narrative" of solving them, so it's no longer keeping track of all these moving parts (Johnny likes blue but hates denim; Joanie hates green but adores souffle; &c.) in isolation.

Or maybe not. I've never studied any of this shit. I was all excited about this thread because the skillset of the architect is only incidentally building materials and the lie; it's primarily and fundamentally problem-solving. But it turns out that all I have to add to the thread is ass-pulled ideas. Humph.


Posted by: JRoth | Link to this comment | 09-30-09 9:21 PM
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18: I guess that's broadly true, but taken as a proof of the claim that people could e.g. do classroom exercises to increase the holding capacity of their working memory it seems to lead to the conclusion that people could also do exercises to cure sickle cell anemia, or grow a thick moustache just by thinking about it the right way.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:21 PM
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22: Um, I assume the researchers knew what they meant by chunks. I have no idea how many chunks are in that problems. But that is what is typically meant by problem-solving at the freshman level.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:22 PM
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Further to 22, and in light of 4's I probably did worse in philosophy exams out of sheer impatience and annoyance with dumb word problems, this has something to do with philosophy? Was Witt talking about logic puzzles?


Posted by: parsimon | Link to this comment | 09-30-09 9:23 PM
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So we're discussing menwha, right?


Posted by: M/tch M/lls | Link to this comment | 09-30-09 9:23 PM
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14: So it's sort of memory of types rather than memory of exact/precise phrasings of problems.

Like moving from

"Johnny has three apples, two rot and he throws them out - how many apples does Johnny have left?"

to

"Emily has four cars, two of them rust and she abandons them in a river - how many cars does Emily have left?"


Posted by: eb | Link to this comment | 09-30-09 9:24 PM
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Oops, pretend the italics in 27 are correct.


Posted by: parsimon | Link to this comment | 09-30-09 9:24 PM
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do classroom exercises to increase the holding capacity of their working memory it seems to lead to the conclusion that people could also do exercises to cure sickle cell anemia, or grow a thick moustache just by thinking about it the right way.

Alright Sfweetie, what the hell are you talking about? Of course you can train your brain. We teach logic and dapper writing skills all the time. That's not saying that you can think your way out of a broken arm.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:25 PM
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So it's sort of memory of types rather than memory of exact/precise phrasings of problems.

Actually, people who are very field dependent will group train problems together and cookie problems together, when hunting for a similar problem that's already been solved to use as a referent.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:27 PM
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16: I don't know, Sifu, but I have seen a lot of truly terrible research in my life, so I'm quite willing to believe that it's possible.

Granted, I think it's more likely that this is a pop summary of somebody's research, and probably one with a political agenda. A lot of the stuff I've read on this type of topic is like that, especially when written for educators. (And some of it is in service to a not-very-hidden racist agenda.) Sweeping claims and global statements are kind of par for the course in those kinds of articles, even when written with the best of intentions.

(And btw, note that your 11 makes some very careful and wise distinctions about genetic predisposition and aspects which anyone who recognizes the brain as an organic organ capable of being damaged ought to be on board with...and is very different from a claim of determinism or hard ceilings.)

In general I think this topic is fascinating and much more is unknown than known. I'm sure there are a lot of people doing sophisticated research that I'm completely ignorant of, and I'm more or less endlessly interested in hearing about it. But one thing I'm definitely not ignorant of is the existence of poorly designed, badly executed, dangerously careless studies. I don't know if this is one of them, but it doesn't look promising.


Posted by: Witt | Link to this comment | 09-30-09 9:27 PM
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31: If I had to guess, I'd say that it's different bits of the brain, which are modifiable in different ways to different extents.


Posted by: JRoth | Link to this comment | 09-30-09 9:28 PM
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14 are 29 are helpful, thanks.

I don't think it's about menwha, M/tch.


Posted by: parsimon | Link to this comment | 09-30-09 9:28 PM
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Everything is about menwha.


Posted by: teofilo | Link to this comment | 09-30-09 9:29 PM
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32: Are cookies and trains linked in ways of which I have been previously unaware?


Posted by: JRoth | Link to this comment | 09-30-09 9:29 PM
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Of course you can train your brain. We teach logic and dapper writing skills all the time. That's not saying that you can think your way out of a broken arm.

Writing skills, for instance, involve the coordination of a vast array of discrete cognitive and motor skills. What you're teaching is how to harness those skills together to solve a high-level problem. When you're talking about doing exercises to increase working memory capacity qua working memory capacity, you're talking about a much more fundamental discrete entity; it's the difference between teaching somebody to be more observant, and teaching somebody to have better vision.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:31 PM
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dapper writing skills

Darn it, where were you when I was in college?


Posted by: Witt | Link to this comment | 09-30-09 9:32 PM
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You think the Memory is an isolated part of the brain like the Eyeball is of the face?


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:32 PM
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32: And that's regardless of whether all those train problems are subtraction (or whatever mathematical concept they have in common) problems? I was thinking of type in this context as the type of math involved when you put it into numbers, not the type of word-object. So if I were grouping, I'd group the two as the tyep "problems involving something being taken away from an initial amount."


Posted by: eb | Link to this comment | 09-30-09 9:33 PM
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Why do you think working memory capacity is immutable?


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:33 PM
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If I recall it correctly (and it was actually a real experiment), one fairly clear demonstration of this phenomenon was giving chess masters and novices boards to memorize. On boards where the pieces had been arranged randomly the masters did no better than novices, whereas on boards that had been arrived at during actual gameplay the masters, with there superior understanding of common structures were much better.


Posted by: Eggplant | Link to this comment | 09-30-09 9:34 PM
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40: The short-term non-contextual buffers that are being talked about here are probably fairly independent.


Posted by: JP Stormcrow | Link to this comment | 09-30-09 9:35 PM
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38 continued: it seems very possible that you could construct pedagogy that would help people solve complex problems with lots of dependencies, but you would be helping those people to develop the kinds of strategies that they -- as per the summary of the summary we're all working with here -- develop later on to deal with complex tasks in the workplace.

From what I gather, the issue is that word problems are specifically designed to not be amenable to the kinds of workarounds people are very adept at developing, and specifically test two pieces of cognitive function that aren't particularly trainable. This seems like a reasonable conclusion to me, but I wouldn't construct the solution in terms of making the untrainable trainable somehow. Possibly this is a semantic difference, but it seems like an important semantic difference.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:35 PM
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41: Right. If the cookie problem involves proportions and you give them an analogous (banned!) train problem using proportions, they'll look back and try to find another train problem, even if it's a distance/rate/time problem. According to one of the articles, at least.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:36 PM
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Possibly this is a semantic difference, but it seems like an important semantic difference.

Wait. Is this about the Palestinians?


Posted by: Moby Hick | Link to this comment | 09-30-09 9:36 PM
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I agree with 38.


Posted by: parsimon | Link to this comment | 09-30-09 9:36 PM
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Just to throw another set of variables into the mix, ages ago I remember reading about a distinction between so-called liquid and crystal intelligence. The argument IIRC was that younger people had more liquid (adaptable, speedy, flexible) intelligence and older people had more crystal (stored, experiential, this-problem-looks-like-that-other-thing) intelligence.

In that case, deciding whether to group the train problem in with the cookie problem, or the subtraction problem in with the other subtraction problem, may be at least as much a function of age and life experience as of any innate intelligence.


Posted by: Witt | Link to this comment | 09-30-09 9:36 PM
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In that case, deciding whether to group the train problem in with the cookie problem, or the subtraction problem in with the other subtraction problem, may be at least as much a function of age and life experience as of any innate intelligence.

It's a function of whether you understand the concepts underlying the problem, and how they apply to the situation.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:40 PM
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40: that's a weird (and banned!) analogy. I would say that "working memory" is (probably) a discrete function of the brain (not in a discrete functional area, necessarily, but a discrete function with its own mechanisms).

42: why do you think it isn't? I have existing (admittedly less-than-conclusive) research on my side.

Incidentally, a reasonably good summary of experimental methods for testing working memory can be found at you-guessed-it.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:40 PM
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What I mean is, it's not innate intelligence and it's not the product of age. A good teacher can get this stuff across to nearly anybody.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:41 PM
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Alright, hell with it, I'm going to bed soon, but before I do I'm just going to talk about problem-solving as I understand it:

A couple current/potential projects, both sprucing up existing, pretty crummy commercial/industrial buildings. The Equipment Co. is in a really nondescript cinderblock building, constructed in 3 campaigns on 3 lots with 3 different wall heights and no consistency in window sizes or symmetry or any of the other things we rely on for making buildings look "good." My job is to - within a tiny budget - figure out some way to make it look good anyway.

The Appliance Co. is in a crumbling old building, once kind of Tudor-ish, with a 1950s storefront that is also crumbling, plus aging and outdated GE and Frigidaire signs. How to make it look good?

There are various other constraints, but those are the nuts of the problems (note that I've already done a lot of the sifting). The Appliance Co. is actually pretty easy - take out the clutter, pull the whole thing together with a cornice above the storefront height, and use all new materials above (stucco) and below (??) the cornice. Easy peasy. The Equipment Co. is really really hard. Even if we reskinned the whole thing, it's still a mess compositionally. So what I need to do is to think about ways of tying things together or, alternately, acknowledging differences. One way to do this is through almost-literal narrative - part of the building is offices, the remainder is shop space. Use materials and colors to explicate that. Another way would be to impose a narrative - define a line, even if it doesn't correspond to any function, and use that to establish what gets metal panels and what gets paint.

Point being, the pieces of the problem are the "chunks" - where does the sign go, how do we direct visitors to the office door? - and what I'm searching for is the narrative that will tell me how to place the chunks. And my first step is identifying the important chunks, so that I have an idea what I need to fit into the narrative.


Posted by: JRoth | Link to this comment | 09-30-09 9:42 PM
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43 is good, and I believe reinforces my 24.


Posted by: JRoth | Link to this comment | 09-30-09 9:43 PM
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50, 52: I don't think we disagree.


Posted by: Witt | Link to this comment | 09-30-09 9:44 PM
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52: right, but then you're talking about the construction of problems and/or problem solving techniques, rather than the actual brain function (presumably) referenced in the article. Which is fine, and you're absolutely right, you can teach people to do a better job solving conceptual problems with lots of moving parts regardless of how they might score on X cognitive psychology battery, but that's a different thing than what you were describing in the post.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:44 PM
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Incidentally, a reasonably good summary of experimental methods for testing working memory can be found at you-guessed-it.

The Poorman?


Posted by: JRoth | Link to this comment | 09-30-09 9:45 PM
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that's a weird (and banned!) analogy.

I was half-assedly quoting you! You had just said that trying to teach this memory capacity would be like trying to teach someone to have better vision.

why do you think it isn't? I have existing (admittedly less-than-conclusive) research on my side.

Because loosely, two things:
1. They say things are fixed in the brain all the time, and then go back and say "WHOA! We found neurons growing unexpectedly!" Recently they implanted cones in monkey eyes and the adult monkeys learned to see color. WHOA! It just seems like they are always underestimating the capacity of the brain to grow and flex.

2. Good teachers get students to do all sorts of amazing things, and good teachers aren't studied under a microscope to see what happens to the students' neurons. (if that makes sense.) Kids wildly grow in new directions all the time under the right stimulus. It seems like the "good clever teacher" aspect is left out of the laboratory.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:46 PM
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57: you're terrible at learning to click.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:47 PM
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53: Good luck to you on that. We could really use fewer ugly buildings around here.


Posted by: Moby Hick | Link to this comment | 09-30-09 9:47 PM
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Recently they implanted cones in monkey eyes and the adult monkeys learned to see color. WHOA! It just seems like they are always underestimating the capacity of the brain to grow and flex.

That study used gene therapy, which would seem to actually provide support for the idea that color vision is genetically determined.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:48 PM
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56: Yes, 52 was offtrack. Just saying that the misgrouping the train problems together is an easily understood phenomenon.

61: Yes, but the new neurons had to grow. WHOA.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:50 PM
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60: There's another one up in Brighton Heights that is in the process of becoming really nice. If the 2 I described both happen, I'll be very very satisfied.


Posted by: JRoth | Link to this comment | 09-30-09 9:50 PM
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53: Interesting, JRoth, and yes: if one wanted to build something more interesting out of the topic at hand, it would be the building of narratives out of chunks, but of course one has to learn how to decide on what the chunks are or should be.

That's what's odd to me about the way H-G put it in the OP (paraphrasing as she was): the thinker isn't exactly identifying *existing* chunks of information as much as she is creating, or grouping together, the chunks and working with them.

Am I quibbling? Only if the word problem at hand is just how many apples Johnny has left of his 9 after Jenny takes 3.


Posted by: parsimon | Link to this comment | 09-30-09 9:51 PM
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43 is also my recollection. The Pattern-recognition helps explain how masters manage simultaneous games in exhibitions.

It does not explain blindfold simultaneous exhibitions as well.


Posted by: bob mcmanus | Link to this comment | 09-30-09 9:51 PM
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I'm genetically determined where it counts. Laydeez.

Night, all.


Posted by: JRoth | Link to this comment | 09-30-09 9:51 PM
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Reasoning capacity isn't a well-defined phenotype, so direct attempts to answer the question relevant to populations are impossible. The question is not well-posed.

Gary Marcus writes clearly and, where I can judge, accurately about the biology of neural development. Textbook examples usually start with a cognitive deficit that runs in a family, isolate the gene through linkage studies, and then look at orthologs in other organisms; here's an example
This is interesting and solely genetic, but connections to education are completely speculative.

Teaching kids who were trying really hard but just couldn't do it was so frustrating. I liked Sheila Tobias' writing about science education, although I don't know that there's much relevant to cookie problems there.


Posted by: lw | Link to this comment | 09-30-09 9:52 PM
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61: Yes, but the new neurons had to grow. WHOA.

I don't really get your point. Yes, neurons can grow. Yes, the understanding of the brain is vastly incomplete. Making the leap from this to saying "therefore, we can assume that nothing we think we know about the brain is accurate, and assume that brains can change however we want them to!" is what seems to me to be unwarranted.

It's entirely possible -- even likely -- that this isn't what you're doing, or interested in doing. It's just how I read the paragraph I originally quoted of the original post.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:52 PM
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therefore, we can assume that nothing we think we know about the brain is accurate,

How am I throwing away any accumulated knowledge about the brain? Are any of us producing studies saying that the memory capacity is fixed that I'm disregarding? It felt like an unsubstantiated, throwaway line in the article, and if it's not well-documented, maybe there's something to explore there.


Posted by: heebie-geebie | Link to this comment | 09-30-09 9:55 PM
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This would be easier if we could read the article in question, but sure, here's a study that appears to say exactly that.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:57 PM
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Here's another, which has been cited extensively.


Posted by: Sifu Tweety | Link to this comment | 09-30-09 9:58 PM
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63: You should try to see about Greenfield's business district. The last block of Murray is pretty awful.


Posted by: Moby Hick | Link to this comment | 09-30-09 9:59 PM
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The abstract that you just produced says that people have a demonstratable persistent fixed capacity, which is what my article says too. And what I said in the post. It says nothing about whether or not you can be trained to a higher capacity

In my article, it said that this capacity grows at roughly one iten every two years through childhood. What if something could be done to lengthen the time in which this memory grows?


Posted by: heebie-geebie | Link to this comment | 09-30-09 10:00 PM
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I don't feel like opening a goddamn pdf on my already slow-as-balls laptop.


Posted by: heebie-geebie | Link to this comment | 09-30-09 10:00 PM
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Also it's way past my bedtime. Night all.


Posted by: heebie-geebie | Link to this comment | 09-30-09 10:03 PM
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74: Maybe you can train your laptop to be faster?


Posted by: M/tch M/lls | Link to this comment | 09-30-09 10:04 PM
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Some people think working memory can be improved.

Also, I don't know if this was in the original article or just your memory of it, heebie, but the range of typical wm capacity isn't 6-8; it's seven plus or minus two. That's practically a mantra, so if they claimed 6-7 it's a little odd.


Posted by: cynique | Link to this comment | 09-30-09 10:05 PM
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Rereading the OP:

Field independence/dependence refers to how well you are able to make wise choices for those seven chunks of information. Highly field independent people select extremely useful bits from a word problem and from their memory to put on their mental worktable. Field dependent people make very poor choices and get hung up on nonessential parts of the problem.

From this I conclude that in teo's example in 12 ("Johnny has nine apples. If he gives three apples to Jenny, how many apples does he have left?"), there are 5 chunks of information: 9, apples, Johnny, Jenny, 3. The field dependent people get hung up on the apples, or on Johnny and Jenny. Sorry I've been so slow to get this.

I must say that if 7 chunks of information is average or so, people are not sifting information very well, are they?


Posted by: parsimon | Link to this comment | 09-30-09 10:08 PM
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So if I'm understanding things, what heebie's really talking about is whether the capacity of what the cognitive scientists call "working memory" can be increased through training. The relevant wiki article is flagged as "having issues", but if we believe it the gist seems to be that no one's really found smoking gun evidence that it can be yet. And it's worth noting that Miller's working memory studies were back in the 1950s, and people are still talking about this stuff, so we're not just talking about an isolated potentially shitty study here. That doesn't mean the whole literature couldn't be wrong, just that it oughtn't be dismissed out of hand, given that there's so much of it, and presumably at least some of the people writing it were kind of smart. (And what does the literature say, you ask? I dunno.)

These folks (full disclosure: they're sort of in my social circle) have games that aim to improve your working memory through training. Do they? I dunno. (One of the things grad school has taught me is a reluctance to opine even on topics that are closely allied to what I work on, if I haven't done my homework first.)


Posted by: Otto von Bisquick | Link to this comment | 09-30-09 10:11 PM
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Addendum: Oh, but it's not sifting 7 chunks of information, it's holding 7 chunks from potentially hundreds.


Posted by: parsimon | Link to this comment | 09-30-09 10:11 PM
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70: Also, Sifu, I'm pretty sure you're confusing what "fixed capacity" means there. I think that paper is addressing the issue of whether wm capacity is discrete or continuous, not whether wm capacity can change over time in an individual. I can't load the other paper.


Posted by: cynique | Link to this comment | 09-30-09 10:12 PM
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||

I think I solved my windshield wiper problem. But I'm worried its not really locked on as I never felt or heard a click when I slid the blade onto the hook. I ran the wipers with the windshield spray and there didn't seem to be a problem. I only replaced the broken side. Hopefully the difference in brands won't be an issue.

|>


Posted by: eb | Link to this comment | 09-30-09 10:26 PM
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The wiki article on working memory specifies that we're talking about what's held in mind for a brief period of time. It doesn't seem that whatever skills are required to translate word problems into mathematical solutions involves just short-term memory.

Frankly, invoking memory at all here seems to me to be wrong-headed. Memory is a notoriously problematic issue anyway, and not just in the cognitive science realm; there is also, for example, the question of so-called negative memory ("I remember that there was no clown-face-painted mime in my compartment on the train.")

Heebie's talking about parsing, about editing, and editing out, about identifying what's relevant and what's not. Sure, this has to do with memory to some extent, and cognitive function in a hand-wavy sense, but other than that? It can be taught, and I'm not sure what cog sci has to tell us about it.


Posted by: parsimon | Link to this comment | 09-30-09 10:39 PM
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The tests of pure abstract short-term memory ("a baloo is a bear. a younker is a young man. a pillock is a lamp.") always seemed distressingly similar to actual tests of non-nonsensical knowledge. Cramming for one, cramming for the other.


Posted by: Cryptic ned | Link to this comment | 09-30-09 10:54 PM
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What's non-nonsensical knowledge that's purely abstract short-term?

You mean like putting puzzles together? Not doing addition, I assume; that's not short-term memory.


Posted by: parsimon | Link to this comment | 09-30-09 11:05 PM
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83: It was the article that asserted that working memory capacity (in addition to that other thing) is what separates the good solvers from the bad solvers. That's not the first thing that would have occurred to me, either, but I guess we'll have to wait till tomorrow to find out what the dude's argument was. You seldom need to remember more than two or three pieces of information as you go to write them down. Maybe the idea is that when you're first playing around with all the information in your head (way more than 7 +/- 2 items when you count all the concepts laid out by the various words) and using it to decide on a strategy for solving the problem.

I guess I'd want to see something like the performance of some students on a working memory test plotted against their performance on a set of word problems.

It can be taught

So tell heebie how! She's asking for advice.


Posted by: Otto von Bisquick | Link to this comment | 09-30-09 11:14 PM
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Maybe the idea is that these capacity limitations come into play when you're first playing around with all the information in your head (way more than 7 +/- 2 items when you count all the concepts laid out by the various words) and using it to decide on a strategy for solving the problem.


Posted by: Otto von Bisquick | Link to this comment | 09-30-09 11:15 PM
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... This article asserted a stronger version of this: first, that pretty much everyone can hold between 6 and 8 chunks in their head at a time. Second, that this is a fixed amount for each person, and you can categorize 6-chunkers, 7-chunkers, and 8-chunkers. ...

This sounds like bs to me.


Posted by: James B. Shearer | Link to this comment | 09-30-09 11:16 PM
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So tell heebie how! She's asking for advice.

Sadly, I'm not a math teacher. I liked to draw pictures and be demonstrative with them when I taught, but I'd be talking about the mind-body distinction, or the relationship between words and meaning, and I'd be drawing arrows and circles.

I don't know how that kind of thing can help with chunks of information, and how Johnny can be taught to tease out the number 9 from the apples or rusty cars in the word problems. I don't have the appropriate framework at hand to know how to bring students from one to the next in a mathematical context.

It seems a flat-out pedagogical question: there must other math profs out there who have methods!


Posted by: parsimon | Link to this comment | 09-30-09 11:27 PM
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||

Turns out the wiper blade fits much more securely if you spin it 180 degrees from how I originally had it. Thank you, self-doubt, for leading me back down to the parking space.

|>


Posted by: eb | Link to this comment | 09-30-09 11:57 PM
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Working memory studies are one of the standard things undergraduates do. When a friend of mine was doing her intitial psychology undergraduate degree, one of the experiments she had to run was a short term memory test. This isn't, as far as I know, remotely controversial stuff.

Strategies for handling information can be taught, though. For example, books on mental calculation will teach you all kinds of tricks for transforming complex calculations into those that can be done in the head, and a huge part of those tricks is that the transformations reduce the amount of information you need to hold in working memory at any one time.

It's the existence of those types of strategies [which are very effective]* which would cast doubt, for me, on the claim that working memory capacity is the single key factor. Also, in many contexts, what you are doing is shuffling information back and forth between working memory and longer term memory, and that's definitely a skill that can be improved. Indeed, all of those 'improve your memory' books are about training precisely that.

And, of course, as mentioned above, being able to write things down means that you can use pen and paper as a nice adjunct to your memory.

* with a bit of work you can do 'savant' style mental arithmetic tricks.


Posted by: nattarGcM ttaM | Link to this comment | 10- 1-09 12:31 AM
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I can concatenate approximately 43 cubits of goober-related info bites, but only 2 cubits of bleh-related info bites.


Posted by: text | Link to this comment | 10- 1-09 1:38 AM
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Night all!


Posted by: text | Link to this comment | 10- 1-09 2:43 AM
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I actually know (a little) about this kind of thing[*], so I can't resist the urge to chime in even though everyone is asleep and I'm going to do my usual post-and-run-away thing when I go to bed shortly. Apologies.

The notion of a working memory capacity not much larger than 7 +/- 2, and the notion that "chunking" helps, is indeed well-established and not just the product of a shitty study or two. Indeed, it's probably one of the more well-established results in the field, I would say.

The hard issue (and many of the questions people have come up with here) arises when you try to specify exactly what a "chunk" is. My sense of the current state of understanding is that something becomes a chunk once it is overlearned enough to the point that you don't have to process or think about all its little bitty details to manipulate it. [I know that's vague -- it's a hard problem]. So things like digits or letters or familiar words are chunks to native speakers of a language, but not to a kid first learning them. There are famous instances of people increasing their memory capacity by chunking -- for instance, one person was reported to be able to memorise very long lists of numbers by virtue of chunking them into famous racing times (he was a runner) -- but that worked for him because he already had all of these "overlearned" racing times to attach them to.

If you know anything about computer programming, a analogy (which other researchers may or may not agree with, but I find useful) is that when you overlearn something you suddenly create a pointer to it in your head. Thus in order to manipulate it or reason about it or whatever you only need to manipulate the pointer -- you don't need to drag around the entire size of it itself. Under this analogy, people have a working memory capacity of about 7 +/2 "pointers" (or items that take up a similar amount of memory space as a pointer would), but if those pointers each point to some huge mass of data, then it can effectively look like it's quite large. [I am going to emphasise again that this is merely an analogy I find useful; I don't really know how much other people would endorse it].

A lot of the techniques that purport to increase working memory capacity, imho, work by making you create better chunks and teaching you how to chunk more effectively. That said, I don't know enough to say that's true for every technique, and it may be the case that there exists some way to actually increase the 7 +/2 size. If so, I don't know about it, but the list of things I don't know is quite large.

[*] I am a cognitive scientists, have colleagues who study this very issue, and definitely know more than the average layperson, but my specialisation is in a different area.


Posted by: Forza | Link to this comment | 10- 1-09 3:37 AM
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A good night for the band. No gigging, but three of us held the fourth while he puked, and then put him to bed with a wet towel, a dry towel, a bucket and two ibuprofen.


Posted by: k-sky | Link to this comment | 10- 1-09 3:39 AM
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It seems a flat-out pedagogical question: there must other math profs out there who have methods!

Indeed. Or entire fields dedicated to the pedagogy of various subjects, even.


Posted by: Blume | Link to this comment | 10- 1-09 4:58 AM
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the contrast between comments 94 and 95 is pleasing.


Posted by: alameida | Link to this comment | 10- 1-09 5:05 AM
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and teaching somebody to have better vision.

Umm, you can do this up to a point.

There are therapy exercises which work on eye hand coordination or use doubling glasses which can help with strabismus. Patching your dominant eye will force you to use the other one and strengthen it.

Some people even believe that using the right kind of reading glasses can slow the development of near-sightedness.


Posted by: Bostoniangirl | Link to this comment | 10- 1-09 5:09 AM
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re: 98

Yes, however, I think it has limits. I am very left-eye dominant, even though the vision in my right eye is actually fine. I asked my optician about things like patching [which I had done as a kid, too], or other methods to try and reduce the dominance, and he was adamant that in an adult, it's basically too late to do much of any significance.


Posted by: nattarGcM ttaM | Link to this comment | 10- 1-09 5:15 AM
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99: It certainly is better to work on it as a child while you're still developing, but there's work you can do. It depends on how much time you want to invest in it.

I improved mine quite a bit as an adult, but I broke my reading glasses and didn't replace them and stopped doing the exercises. (One of them involved having a 2 x 4 lying in a room.) I was 22 at the time.

It required weekly group therapy sessions with prisms and doubling glasses and convergence practicing devices, and you're really supposed to practice about 30 minutes a day. You also have to pay attention to your posture, not look down as you walk and really concentrate on your peripheral vision.

Obviously, I'm never going to have the visual ability of a professional basketball player, but I can take care of my vision and practice my skills. I've lost a lot of my gains, but that's my own fault.

This was my optometrist, and I'm totally bummed, because I was about to make an appointment and found out that she'd died.

She talks about the prevalence of vision problems among low-income children here, and how they are sometimes misdiagnosed with learning disabilities.

And she gives her own story and talks about how myopia develops primarily from strain, but obviously some people are more vulnerable to it than others.


Posted by: Bostoniangirl | Link to this comment | 10- 1-09 5:48 AM
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99: I had to wear an eye-patch over my left eye as a kid. I went to kindergarten with glasses because my right eye is very weak, though I think the pirate phase helped some.


Posted by: Moby Hick | Link to this comment | 10- 1-09 6:30 AM
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(pause)

I have already had an interesting morning. The publisher of the Inquirer was at the train station, so I walked up to him and said "I wish you didn't publish John Yoo."

He said "Excuse me?"

I repeated myself and walked away. He called after me something like "But at least you must like the [unintelligible]!"

(He was there promoting their upcoming Suduku puzzle tournament, so maybe that's what he was referring to.)

I'm glad to have made use of the opportunity, since I suspect that he never read any of the kajillion e-mail complaints I sent.

(play)


Posted by: Witt | Link to this comment | 10- 1-09 6:52 AM
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94: If you know anything about computer programming, a analogy (which other researchers may or may not agree with, but I find useful) is that when you overlearn something you suddenly create a pointer to it in your head. Thus in order to manipulate it or reason about it or whatever you only need to manipulate the pointer -- you don't need to drag around the entire size of it itself. Under this analogy, people have a working memory capacity of about 7 +/2 "pointers" (or items that take up a similar amount of memory space as a pointer would), but if those pointers each point to some huge mass of data, then it can effectively look like it's quite large. [I am going to emphasise again that this is merely an analogy I find useful; I don't really know how much other people would endorse it].

Ah. See, I would see chunk constraints in working memory to be very similar to register limitation in a CPU. And a given CPU can suffer from register starvation (which I cannot find a discussion of online, but 'resource starvation (wiki)' is a similar idea) - which occurs when a given problem needs to keep more distinct numbers at hand than there are registers. So the problem will be forced to dump a register, go to main memory and fetch a different number, and then dump another register and load in a different number from main memory. This is very very very slow, compared to a situation in which a program has enough registers for the problem it is trying to deal with. Slow enough that the program may be abandoned or the system may hang, etc.

Since no one seems to have linked it directly, chunking:

Miller noted that according to this theory, it should be possible to effectively increase short-term memory for low-information-content items by mentally recoding them into a smaller number of high-information-content items. "A man just beginning to learn radio-telegraphic code hears each dit and dah as a separate chunk. Soon he is able to organize these sounds into letters and then he can deal with the letters as chunks. Then the letters organize themselves as words, which are still larger chunks, and he begins to hear whole phrases." Thus, a telegrapher can effectively "remember" several dozen dits and dahs as a single phrase. Naive subjects can only remember about nine binary items, but Miller reports a 1954 experiment in which people were trained to listen to a string of binary digits and (in one case) mentally group them into groups of five, recode each group into a name (e.g "twenty-one" for 10101), and remember the names. With sufficient drill, people found it possible to remember as many as forty binary digits.
Which in turn lead to the paper reference The Magical Number Seven, Plus or Minus Two:
The concept of a limit is illustrated by imagining the patterns on the faces of a dice. It is easy for many people to visualize each of the six faces. Now imagine seven dots, eight dots, nine dots, ten dots, and so on. At some point it becomes impossible to visualize the dots as a single pattern (a process known as subitizing), and one thinks of, say, eight as two groups of four. The upper limit of one's visualization of a number represented as dots is the subitizing limit for that exercise.
Yay. Anyways, a five-chunk memory working with three level tree of information would be limited to 125 bits of information at the ends of the branches, whereas someone with a nine-chunk memory would be able to push three layers to 729 bits. A properly factored problem with less than 125 bits would be easily solvable (well, solvable) by someone constrained by a five-chunk memory; the problem be whether someone ith a nine-chunk memory found the problem trivial.

The constraint is essentially the width of the tree-span at the bottom level.

73: In my article, it said that this capacity grows at roughly one iten every two years through childhood. What if something could be done to lengthen the time in which this memory grows?

That seems unlikely to work; there seem to be clear limits on the time available to brain development, which is why childhood malnutrition has such terrible effects. You would want to push the acquisition of additional chunkwidth if possible. Since that's likely over with by the time they get to you, reducing chunk demand seems like the only alternative.

'Field dependency' seems like an awful garbage can-ey categorization to me.

max
['Misc brains.']


Posted by: max | Link to this comment | 10- 1-09 6:53 AM
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Maybe we should try overfeeding the children with rich, tasty treats.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 7:11 AM
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Speaking of children, I really like the title 'Problem Solvey' because my son is (in what I hope to be the beginning of a life-long capacity for writing brief, meaningful characterizations) telling stories involving characters named "what the character does" + "y". I had to put my foot down about 'slappy' and 'kicky', but 'hidey-seeky' is shows promise.


Posted by: Moby Hick | Link to this comment | 10- 1-09 7:18 AM
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I once knew a commenter called Footy Putty Downy.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 7:19 AM
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My feet used to be downy. Maybe if I bleached my toe-hair?


Posted by: Moby Hick | Link to this comment | 10- 1-09 7:25 AM
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79.2: Otto, any chance you could post a link to the actual games or something that connects somehow to them? I'm all in favor of mocking hipsters, but I'm really very interested in memory exercises, and it's a tad frustrating to have your link go to a site completely unrelated. Unless the exercises involve pictures of hipsters, in which case fuck it - I'd rather be stupid.

94: Thank you. Fascinating stuff.


Posted by: togolosh | Link to this comment | 10- 1-09 7:26 AM
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68: I don't really get your point. Yes, neurons can grow. Yes, the understanding of the brain is vastly incomplete. Making the leap from this to saying "therefore, we can assume that nothing we think we know about the brain is accurate, and assume that brains can change however we want them to!" is what seems to me to be unwarranted.

We've talked about this before in the context of sex-linked cognitive differences. What I think you're missing about the argument is that believing cognitive differences in capacity are genetic and immutable has the potential for being very damaging in outcomes to students who appear to their teachers (on the basis of testing, casual assessment, whatever) to be low in capacity.

That's not a reason to stop doing research on the brain, and it's not a reason to doubt otherwise solid results. It is, however, a reason not to move an iota further down the path of believing that differences in capacity are immutable than actually compelled to by the research. And it is further a reason to think very hard about whether a true belief that differences in capacity are immutable would be pedagogically useful -- unless it's useful, there's no reason to bring it into the classroom (rather than the cognitive science lab) whether or not it's true.

And people really have a hard time not leaping out ahead of their research. I scanned through the articles you linked in 70 and 71 as support for the proposition "that the memory capacity is fixed." They're over my head without spending a lot of attention and looking stuff up, but I don't see either one addressing the issue of whether working memory capacity can change in response to training. That doesn't mean it can, but assuming it can't without really strong direct evidence seems unwarranted.


Posted by: LizardBreath | Link to this comment | 10- 1-09 7:30 AM
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Okay, Diane Bunce is the author, and it appears to be a chapter from a book not listed on her web page. (I'll keep hunting.)

It appears to be chapter 9 from a book, and the chapter is called "Solving Word Problems in Chemistry: Why do Students have difficulties and what can be done to help?"

With the article in front of me, though, I have much better definitions and stats on everything. I do think this is a well-written, solidly informed piece of work.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 7:31 AM
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Oh wait. I was combining articles in my mind. The one with the graph showing the decline in performance when an n-chunker hits a problem with n information load is by Norman Reid, and it's the "Scientific approach to the teaching of chemistry" journal article. I'll hunt now for the text.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 7:35 AM
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And of course, as a bunch of people pointed out above, even if you find a particular cognitive capacity that is immutable in response to training (and 'working memory' easily might be such), assuming that that capacity is the limiting factor in terms of addressing real world problems is also a big leap, and one with the potential for doing a lot of pedagogical damage. In the context of talking about teaching, making that leap without a very strong reason to seems like a really bad idea.

(And what max said about "field dependence". I wouldn't be surprised if 'working memory' were the kind of thing that was immutable. But 'field dependence'? The way they're describing it in the article, it seems like another way of saying 'good judgment'. Bullshit that's a simple, immutable cognitive quality.)


Posted by: LizardBreath | Link to this comment | 10- 1-09 7:37 AM
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Here's the second article.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 7:37 AM
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103: I like the register limitation analogy! Although when people run out of working memory, more often than our systems "hanging", we tend to just drop items. Though of course there is some of both... Anyway, thanks for the links. Miller's paper is still good reading despite being over 50 years old.

108: Thanks for the thanks. I like it when people are interested in my field!

FWIW, I haven't heard of 'field dependency' used in this way before, ever.

Now off to bed.


Posted by: Forza | Link to this comment | 10- 1-09 7:44 AM
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(And after reading the Norman Reid article, it doesn't seem to be subject to the issues I raised in 109. While it offhandedly assumes that 'working memory' and 'field dependence' are immutable, it's about techniques for working around differences between students, and so ensuring that those differences don't turn into a limiting factor for students with weaker working memory and field dependence. So, good stuff.)


Posted by: LizardBreath | Link to this comment | 10- 1-09 7:45 AM
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Turns out the wiper blade fits much more securely if you spin it 180 degrees from how I originally had it.

So is it labeled to indicate the position in which )( originally had it?


Posted by: JRoth | Link to this comment | 10- 1-09 7:49 AM
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No, yeah, I found the article useful and interesting. I was just offhandedly curious about how it was taken as gospel truth that these things are genetically predetermined.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 7:50 AM
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I was just offhandedly curious about how it was taken as gospel truth that these things are genetically predetermined.

Guessing, without actual knowledge, I bet it comes down to unsuccessful short term attempts to train less than five hundred undergraduates, that is, upper-middle-class Americans, to increase their working memory. When that didn't immediately produce results, the assumption was made that it was genetic and immutable, and everybody's been quoting the initial research on it for decades.

I could very easily be wrong about that -- maybe there's much better data than that. But that's what I'd guess.


Posted by: LizardBreath | Link to this comment | 10- 1-09 7:55 AM
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btw, if al is still around: did you feel any tremors associated with the apparently huge quake? I know it's not exactly "near" you, but for how big it was....

Giant earthquakes suck.


Posted by: JRoth | Link to this comment | 10- 1-09 8:01 AM
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I'm kind of struck how much trouble I have staying emotionally chill when I feel like my inability to phrase myself well is preventing me from having a useful conversation.

Last night I got a little worked up because of this. 118 is kind of a relief to read, because it implies that when Sfweetie comes back, LB and her eloquence will be on my side.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 8:09 AM
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118: About something like this negative results aren't going to be very useful. In general, my (unfounded) belief is that we really don't know very much about how to train basic mental abilities, and that once we find some effective strategies things will be much more plastic than once thought.


Posted by: Eggplant | Link to this comment | 10- 1-09 8:17 AM
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118: About something like this negative results aren't going to be very useful. In general, my (unfounded) belief is that we really don't know very much about how to train basic mental abilities, and that once we find some effective strategies things will be much more plastic than once thought.


Posted by: Eggplant | Link to this comment | 10- 1-09 8:17 AM
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For instance, years of research have been unable to produce a method for reliably reducing double-posting.


Posted by: JRoth | Link to this comment | 10- 1-09 8:19 AM
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But there is excellent data on how to produce the phenomenon.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 8:21 AM
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But there is excellent data on how to produce the phenomenon.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 8:21 AM
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121: Yeah, I don't have a strong belief one way or the other about what the real truth is with respect to immutability of basic mental abilities. (I have a very strong belief that actual useful mental functioning is mutable as anything -- I just don't have a strong belief about how far down that mutability goes. Doing word problems successfully? Mutable as all-get-out. Working memory? Who knows?)

But I'm very committed to believing that it's a terrible idea to assume immutability of anything at all about people without really, really solid evidence, of a kind that's very hard to come up with in brain research. That's not cognitive science's fault -- you do the best research you can with the limitations you have -- but it's a huge mistake to put a lot of practical weight on weak data just because it's the best you have, when skepticism is an equally workable attitude.


Posted by: LizardBreath | Link to this comment | 10- 1-09 8:26 AM
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124, 125: But is it repeatable?


Posted by: M/tch M/lls | Link to this comment | 10- 1-09 8:26 AM
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Repetition is key, though.
As for training working memory, the mere existence of so many compensatory strategies might make it hard to train.


Posted by: Eggplant | Link to this comment | 10- 1-09 8:26 AM
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I'm sort of intrigued by this discussion from a litigator's perspective. That is, expert author person wrote X about working memory capacity, etc. Otto and Forza are, so far as I can tell, the only people here with any kind of formal background in this stuff. But most people here are resistant to taking the expert's opinion on its face, in part because it conflicts with our previous understandings of things and in part because it conflicts with our philosophical positions. So I'm kind of intrigued by the type of persuasion needed to convince laypeople of the validity of expert knowledge -- appeal to authority is clearly not going to get you nearly far enough with this crowd, you also need to frame the specialized knowledge in a way that ties it in to understandings already accepted by the "jury".

Probably an obvious enough observation. But I'm intrigued nonetheless.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 8:27 AM
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Trainy train train train.


Posted by: Eggplant | Link to this comment | 10- 1-09 8:28 AM
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129 is a totally interesting take on this thread.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 8:28 AM
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129 is a totally interesting take on this thread.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 8:29 AM
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Too much caffeine, or not enough? You decide.


Posted by: Eggplant | Link to this comment | 10- 1-09 8:29 AM
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The stuff in the post makes total intuitive sense to me, along the lines of Otto's explanation in 94. The nature of a "chunk" is the complexity here.


Posted by: PGD | Link to this comment | 10- 1-09 8:39 AM
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The distinction between Otto and Forza? Less intuitive. (Not giving you a hard time, so much as Forza's either new or doesn't comment much, and I hate to see them lose credit for an interesting, meaty comment.)


Posted by: LizardBreath | Link to this comment | 10- 1-09 8:40 AM
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I had a truly marvelous comment in mind, but 94 and 103 covered it better (and then hours of real work intervened!) so I'll just second the concepts in them. I think the key point is that although there might be ways to expand the number of chunks, the real plasticity and potential practical gain is in teaching strategies to effectively use the existing registers (whatever the number) via mental tools such as pointers, macros, subroutines, encodings, <analogy abuse of the computing concept of your choice here >, or external aids (lists, diagrams, showing your work, what have you) in real problem-solving situations. Chunks may be 6, 7, 8, 9 (or trainable to 12), but the cogent fact is that they are completely inadequate for holding most real problems all at once without the other techniques. Work the exponent, not the mantissa.


Posted by: JP Stormcrow | Link to this comment | 10- 1-09 8:42 AM
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Further to LB's point: Assuming immutability also plays into racist pseudo-science, especially when there are strong environmental and cultural effects that disproportionately affect one sub-population. The Bell Curve is an example of this, IMO.

Also 129 is good. The flipside is expert testimony from "experts" who don't know WTF they are talking about, like the arson investigator who apparently helped to kill an innocent man in Texas.


Posted by: togolosh | Link to this comment | 10- 1-09 8:44 AM
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Assuming immutability also plays into racist pseudo-science,

I agree with this. Especially if what you're measuring correlates really well with what's measured by IQ tests.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 8:46 AM
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134: Yes, for instance, "this is a quadratic" held in the "register" when devising problem solving strategies rather than the individual pieces. The kind of thing that becomes evident when you have students talk the problem back to you.


Posted by: JP Stormcrow | Link to this comment | 10- 1-09 8:47 AM
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138: Yes, there is certainly danger there, but I think as a practical matter, the takeaway is meant to be (or should be), that we all of us special snowflakes have significant hardware/firmware limitations in this regard (instead of accentuating the differences--rather 6≈9 ) and 1) not overwhelm everyone's limited chunking on first presentation (for instance simplified initial problems) and 2) work the chunk optimization strategies.


Posted by: JP Stormcrow | Link to this comment | 10- 1-09 8:54 AM
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129: Of course, there are a lot of ways in which this thread is not like expert witness testimony. For example, we're allowed to actually look at their research. We're allowed to incorporate the comments of people who are actually informed on the matter. If we were on a jury those of us who were informed would be precluded from telling other jurors about our knowledge and precluded from doing any of our own "research." The thing that bothered me the most about my experience of being on a jury was how deeply screwed up the expert witness system is.


Posted by: Unfoggetarian: "Pause endlessly, then go in" (9) | Link to this comment | 10- 1-09 8:56 AM
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But most people here are resistant to taking the expert's opinion on its face, in part because it conflicts with our previous understandings of things and in part because it conflicts with our philosophical positions.

Yes, and also in part because we are (I am) mistrustful of the motivations of people making these assertions. This is alluded to in my 33 and LB's 109.


Posted by: witt | Link to this comment | 10- 1-09 8:56 AM
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129 -- I once met with a jury consultant whose basic message was "your experts matter much less than you think they do." That is, lawyers (at least in complex cases) pay enormous sums for expert testimony and tend to think it's extremely important. But juries tend to very heavily discount expert testimony, partly because they assume (correctly) that expert testimony is bought and paid for, but also (more interestingly) because an expert's testimony is very unlikely to alter the narrative of the case the juror constructs from listening to the fact witnesses or from their own preexisting theories, biases, understandings, etc. And also because experts are often pedantic and confusing.

Another interesting claim was that lawyers at all levels, including judges, tend to give more credence to "scientific" authority than the population as a whole -- more so, even, than other scientists and engineers.


Posted by: Robert Halford | Link to this comment | 10- 1-09 9:01 AM
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||

Celebrity news relevant to this blog.

|>


Posted by: JRoth | Link to this comment | 10- 1-09 9:01 AM
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Timberlake has an amazing ass, it's true.


Posted by: Standpipe Bridgeplate | Link to this comment | 10- 1-09 9:05 AM
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Air traffic controllers keep track of ten or more aeroplanes at once. They learn to be able to do this by training. HTFH.

In related news, you certainly can change the physical structures in your brain through training; notoriously, London taxi drivers have enlarged hippocampus structures, with the extent of the hypertrophy proportional to their experience driving a cab.


Posted by: dsquared | Link to this comment | 10- 1-09 9:06 AM
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140: the takeaway is meant to be (or should be), that we all of us special snowflakes have significant hardware/firmware limitations in this regard (instead of accentuating the differences--rather 6≈9 )

Yes, if you're going to use this sort of research in teaching, this seems like a really sensible approach.

142: Yes, and also in part because we are (I am) mistrustful of the motivations of people making these assertions. This is alluded to in my 33 and LB's 109.

I'm actually worried about this sort of oversimplification even when the original oversimplifiers are purely innocent and goodhearted, maybe even more so when they are. If the original research saying "based on our two-week study of 27 Harvard juniors, we think that working memory is immutable" was conducted by someone firmly and publicly committed to the equality of all people who'd never use their research to advocate for cutting educational resources to the 'immutably incapable', and the resulting factoid gets accepted as true by decades worth of fellow researchers with similarly impeccable politics, it gets really hard to clarify the facts when they're finally picked up by someone with bad motives.


Posted by: LizardBreath | Link to this comment | 10- 1-09 9:06 AM
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Looks like it's time to say our catchphrases. Ready, people?


Posted by: Standpipe Bridgeplate | Link to this comment | 10- 1-09 9:07 AM
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That trick never works!


Posted by: Rocket T. Squirrel | Link to this comment | 10- 1-09 9:10 AM
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I'm right!


Posted by: heebie-geebie | Link to this comment | 10- 1-09 9:10 AM
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144.2 is interesting.

Having done some expert witnessing - albeit in front of arbitrators, not jurors - I'll say that, IMO and IME, the key is to use the experts to solidify corners of the argument (a roof of X sq. ft. drains Y gal., requiring a downspout with capacity Z, sized at A"xB" or C" radius), not to outline the shape of the argument (the contractor was an egregious incompetent, as a result of which the house has water problems).

Now, this is a technical matter on the face of it - did the contractor do or not do water-problem-causing things - but I think the point applies more broadly.

All of this is interesting in light of what I've heard, that CSI and similar shows have primed the public to expect more scientific certainty in the courtroom. Are Di's and Robert's experiences lagging, is what I've heard a myth, or are there certain kinds of expertise that are being elevated while the rest remain deprecated?


Posted by: JRoth | Link to this comment | 10- 1-09 9:12 AM
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There's a bit of a Catch-22 with social science, where you can get skepticism from people who are skeptical of science as well as from people who are skeptical that that sort of social science is science.

My impression of social science of this sort (mostly coming from Rhymeswithmaria's experience with some education research) is that there's a strong pressure to measure things that are consistently and accurately measurable so as to get your error bars small enough that people think of it as real science and that this pressure results in measuring things that don't actually match up with the intuitive concepts they're purporting to measure. As a result I have a certain skepticism of social science claims. For example, with this claim my skepticism is whether "immutable" actually means "immutable." My guess would be that it actually means "hard to change" or "hard to change once the person is already in college" because those are concepts that would be much easier to measure.


Posted by: Unfoggetarian: "Pause endlessly, then go in" (9) | Link to this comment | 10- 1-09 9:12 AM
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148: Cock cock cock cock cock.


Posted by: apostropher | Link to this comment | 10- 1-09 9:13 AM
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151 makes sense with my experience. I happily would have traded all the expert medical and safety testimony for 10 seconds of an expert who could tell me "a toilet of design x overflows once in every y flushes, while a more industrial design x' overflows once in every y' flushes." That's something I actually needed an expert for.


Posted by: Unfoggetarian: "Pause endlessly, then go in" (9) | Link to this comment | 10- 1-09 9:16 AM
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Cry, cry, masturbate, cry, cry, cry, masturbate, uh ... I lost track.


Posted by: Bave Dee | Link to this comment | 10- 1-09 9:21 AM
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1 to 154


Posted by: Moby Hick | Link to this comment | 10- 1-09 9:21 AM
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JRoth, the "CSI" thing is allegedly a problem in criminal courtrooms, not my own area. And, as I understand it, the supposed "CSI" issue isn't really trusting scientific evidence per se, but that juries expect that prosecutors and police have billion dollar high tech molecular-DNA-computer-lasers (or something) that can definitively establish guilt. Then, the jury gets disappointed when the state's evidence doesn't look like that.

I also haven't seen any evidence that this is a real problem -- I don't think conviction rates are down significantly anywhere.


Posted by: Robert Halford | Link to this comment | 10- 1-09 9:29 AM
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129 is an interesting take, and helps me think about my reactions reading this thread.

By default I'm more on the "trust the findings as reported", but that's because it matches my experience. My experience is that most of the significant gains that I've made in my ability to do "mental work" as an adult have been based on learning how to approach problems better, and to better understand what mental tools I do and don't have to work with. So my default narrative is, "there are more opportunities for gains by learning better tactics than trying to improve raw firepower" and Heebie's, "Good teachers get students to do all sorts of amazing things" isn't a compelling counter-narrative.

But I also recognize that I am not typical. By the time I got to college I had quite a bit of training in straight mental gymnastics, and not as much in longer-term study skills or mental pacing. So, as a college student, I would not have been someone likely to improve significantly from doing memory exercises. But that doesn't mean that you couldn't help certain segments of the population with some sort of well designed memory exercise.

Which, going back to 129, is just to say that, even though I accept the expert opinions, as presented, it is mostly because they match an existing narrative that I find convincing.


Posted by: NickS | Link to this comment | 10- 1-09 9:32 AM
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Di's and Robert's experiences lagging

Mine almost certainly is. I deal with expert testimony primarily on appeal where the issues gravitate mostly towards: (a) is expert testimony required (in professional liability cases, yes); (b) is the expert qualified (almost always); and (c) was the expert testimony legally sufficient (also almost always -- lawyers and experts know the catch-phrases. Whether the expert should be believed is very, very rarely an issue on appeal. I don't need to care all that much why people do or don't accept expert testimony, but it seems terribly interesting for all of the reasons you guys are listing.

143.1 and 151 suggest, as makes sense to me, that the better persuasive strategy is to sell the jury that your story makes sense and has an appealing outcome based on their pre-conceptions and use the expert to lock that in. Less "You should agree with the experts and rule for me" and more "See! The experts even agree with you that you should rule for me."

So here, maybe the "convincing" narrative (if we want to sell the idea of finite memory capacity) is that all people have this finite capacity of 7 +/- 2, that the difference between 5 and 9 has little practical significance, and that difference in achievement are profoundly affected by facility with different chunking strategies which we can train. "And such-and-such expert agrees!" just helps add that reassurance that we're not just bullshitting the rationale for our own selfish purposes.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 9:37 AM
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Point being, the pieces of the problem are the "chunks" ... and what I'm searching for is the narrative that will tell me how to place the chunks. And my first step is identifying the important chunks, so that I have an idea what I need to fit into the narrative.

Put that way, that sounds like a potentially helpful description of the process involved in writing a mathematical proof.


Posted by: NickS | Link to this comment | 10- 1-09 9:38 AM
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143 matches my experience as a juror. Each side made arguments why we should trust their expert over the other, but we disregarded them both.


Posted by: peep | Link to this comment | 10- 1-09 9:54 AM
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161: And now Robert Blake is a free man.


Posted by: Moby Hick | Link to this comment | 10- 1-09 9:55 AM
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91

Working memory studies are one of the standard things undergraduates do. When a friend of mine was doing her intitial psychology undergraduate degree, one of the experiments she had to run was a short term memory test. This isn't, as far as I know, remotely controversial stuff.

What's uncontroversial? That people have working memory or the stuff I quoted in 88 which claims people can be reliably sorted into 6,7 or 8s?


Posted by: James B. Shearer | Link to this comment | 10- 1-09 9:55 AM
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people can be reliably sorted into 6,7 or 8s?

My understanding is that almost every guy claims to be in this range, but most of them aren't.


Posted by: JRoth | Link to this comment | 10- 1-09 10:00 AM
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109

That's not a reason to stop doing research on the brain, and it's not a reason to doubt otherwise solid results. It is, however, a reason not to move an iota further down the path of believing that differences in capacity are immutable than actually compelled to by the research. And it is further a reason to think very hard about whether a true belief that differences in capacity are immutable would be pedagogically useful -- unless it's useful, there's no reason to bring it into the classroom (rather than the cognitive science lab) whether or not it's true.

If we are using capacity in the broad some kids are naturally brighter than other kids sense of course it is pedagogically useful. Trying to push students faster than they are reasonably capable of going will just induce frustration and hostility, they will tune school out entirely and eventually drop out.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 10:00 AM
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164: I don't want to make anybody feel bad.


Posted by: apostropher | Link to this comment | 10- 1-09 10:01 AM
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161: But if one side had an expert and the other didn't, things would be different. This is why shameless paid liars are so crucial to our adversarial justice system and adversarial journalism system. They balance things out so one side isn't fairly disadvantaged.


Posted by: Cryptic ned | Link to this comment | 10- 1-09 10:02 AM
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165: But knowing that there are immutable differences doesn't get you there. To get to something useful, you'd need to know both that there are immutable differences, and to be able to reliably identify where each student stood on that scale, which is an entirely separate problem.

And even then, not "push[ing] students faster than they are reasonably capable of going" is an oversimplified response -- whatever the immutable differences are, even if they're easily measurable, are going to be susceptible on some level to workarounds and strategies like the strategies in the Reid article heebie linked (describing strategies for teaching people with smaller working memories that make sense whether or not the size of the working memory is immutable.)


Posted by: LizardBreath | Link to this comment | 10- 1-09 10:08 AM
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Trying to push students faster than they are reasonably capable of going

This is the crux of the matter though, James. Of course you don't just want to frustrate kids. But educators who believes these kids are immutably just "less naturally bright" will avoid "pushing" them by teaching them less. Whereas educators who believe the kids aren't grasping the material as well because there's some trainable skill or set of skills that they're lacking are going to focus on getting those kids the help they need to learn the material and succeed just like the "bright" kids. And given the wealth of evidence on the success that dedicated interventions (especially early-interventions) can have on struggling kids, the latter approach seems more sensible (not to mention far more humane).


Posted by: Brock Landers | Link to this comment | 10- 1-09 10:08 AM
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152: Relevant paper. Good stuff, though mostly econ oriented.


Posted by: togolosh | Link to this comment | 10- 1-09 10:14 AM
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167: I'm not sure that is true in this particular case -- the expert testimony seemed so silly. But I can see that neither side would want to take that chance.


Posted by: peep | Link to this comment | 10- 1-09 10:15 AM
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But educators who believes these kids are immutably just "less naturally bright" will avoid "pushing" them by teaching them less.

Why do you hate Waldorf education Brock?

Okay, that's a stretch, but my sense is that Waldorf educators believe that there are brain development reasons why many students can't learn to read at, say, age 5 and so they defer teaching reading until an age at which, they believe, all of the students will be ready for it, in terms of brain development, and not put students in situations in which they will get frustrated.

I don't think most people would describe Waldorf education as giving up on teaching students (though, I'm sure, some people would argue that they don't push the students enough). My point is just that, while I'm sympathetic to the political point that you're making, there's no reason why a teacher that believed that some students are limited by the immutable nature of their brains would necessarily give up on trying to teach higher level skills.


Posted by: NickS | Link to this comment | 10- 1-09 10:22 AM
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103

... So the problem will be forced to dump a register, go to main memory and fetch a different number, and then dump another register and load in a different number from main memory. This is very very very slow, compared to a situation in which a program has enough registers for the problem it is trying to deal with. ...

Just to nitpick, this is why caches were invented.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 10:23 AM
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In one jury trial I participated in (as a juror), the consensus view among us jurors was that the multiple experts put on by both sides were all equally credible, even though they were saying exactly the opposite things. It was frustrating--I'm sure with a few hours in a goddamn medical library I could have figured out who was spinning the research, etc., but being limited to the expert testimony in a field in which I had no experience (nor did any other jurors) just made it impossible to judge. And the expert testimony was literally the entirety of the case: whoever's experts were believed should have won.

We ended up just ruling against the party with the burden of proof. But that was unsatisfying.


Posted by: Brock Landers | Link to this comment | 10- 1-09 10:24 AM
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I don't really disagree with anything in 172, but I also don't understand how or why it's supposed to be in opposition to 169.


Posted by: Brock Landers | Link to this comment | 10- 1-09 10:26 AM
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109

We've talked about this before in the context of sex-linked cognitive differences. What I think you're missing about the argument is that believing cognitive differences in capacity are genetic and immutable has the potential for being very damaging in outcomes to students who appear to their teachers (on the basis of testing, casual assessment, whatever) to be low in capacity.

Of course any fixed false belief can be damaging but I don't see any reason to privilege nuture over nature.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 10:27 AM
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174.last: I'm sure it was more satisfying that ruling against the party whose lawyer had the worst comb-over.


Posted by: Moby Hick | Link to this comment | 10- 1-09 10:29 AM
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I don't really disagree with anything in 172, but I also don't understand how or why it's supposed to be in opposition to 169.

I just thought that 169 was setting up a false dichotomy between educators who either believe in immutable limitations of the brain and don't push their students and other who don't believe in immutable limitations of the brain and do push their students.

I wanted to point out that, while I think that teachers in the first category are doing their students a disservice that there is a category for teachers that believe that both believe that some students have mental limitations that the teacher can't directly change, but still push their students to develop strategies for success (and, presumably, that is the category that HG would fall into even if she did believe that 6-,7-,8-chunkers were fixed categories).


Posted by: NickS | Link to this comment | 10- 1-09 10:31 AM
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176: Because there's good evidence that pre-existing beliefs about the capacities or incapacities of students can turn into self-fulfilling prophecies, making it very ill-advised for teachers to develop such beliefs without extremely strong evidence.


Posted by: LizardBreath | Link to this comment | 10- 1-09 10:33 AM
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169

This is the crux of the matter though, James. Of course you don't just want to frustrate kids. But educators who believes these kids are immutably just "less naturally bright" will avoid "pushing" them by teaching them less. ...

Or they will give them extra attention which is in fact what you advocate.

And if you think everybody is actually equally bright then you could decide the poor performers just aren't trying and yell at them a lot.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 10:33 AM
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179

Because there's good evidence that pre-existing beliefs about the capacities or incapacities of students can turn into self-fulfilling prophecies, making it very ill-advised for teachers to develop such beliefs without extremely strong evidence.

I would like to see the good evidence that teachers who believe some students are naturally brighter than other students perform worse than teachers who believe all students are equally bright.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 10:40 AM
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Ugh, that Waldorf stuff sounds horrible. What do kids do if they start school already knowing how to read and count? Extra handiwork? Are they allowed books? I would have died.


Posted by: Amber | Link to this comment | 10- 1-09 10:43 AM
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181: I'm not following your restatement.

I'm talking about studies showing that if you tell teachers that some of their students are dumber than others going in to the class, the students identified as dumber will do worse academically even if they were chosen randomly to be identified as dumber. I'll go google for them.


Posted by: LizardBreath | Link to this comment | 10- 1-09 10:45 AM
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I'll go google for them.

I haven't seen studies, but according to my mom and all of my high school teachers, he'll learn it better if he looks it up for himself.


Posted by: Moby Hick | Link to this comment | 10- 1-09 10:49 AM
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181: ...all students are equally bright.

Nobody is claiming this. LB is claiming that students don't necessarily manifest their full potential to an equal extent in ways a teacher can clearly see up front, and she is correct.


Posted by: togolosh | Link to this comment | 10- 1-09 10:56 AM
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183: Pygmalion in the Classroom. This is the original study I was thinking of -- while there's been subsequent debate about the magnitude of teacher expectation effects, I don't think there's any significant belief that teacher expectation effects don't exist.


Posted by: LizardBreath | Link to this comment | 10- 1-09 10:56 AM
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I'm talking about studies showing that if you tell teachers that some of their students are dumber than others going in to the class, the students identified as dumber will do worse academically even if they were chosen randomly to be identified as dumber.

I have no idea why I'm channeling JBS here, but isn't this a question of incentives. I would imagine that, for most teachers, their smarter students are responsible for a disproportionate portion of both their personal satisfaction and the praise that they receive.

What would happen if you randomly selected a handful of students and told a teacher, "these students are a little bit dumber than the rest of the class, but your challenge is to get them to do average work. If you can get all of those students to perform at the 40th percentile for their grade or better than you will get top marks in our study of teaching effectiveness."

Again, I get why it's a problem in the real world. But I want to push back against the feeling I get from some of the thread which is, "even if it is true that 6-, 7-, and 8-chunkers are immutable (over some range of inputs), it is a useful fiction to believe that isn't true." That I don't buy. I would have to think that if that's true (and, importantly, if there was a sense of what range of inputs it held true for) that would be useful information for a teacher. I believe that precisely because I think there are or should be a variety of techniques that can be taught to help people solve problems that are above their "level" and that everybody can benefit from learning those techniques.


Posted by: NickS | Link to this comment | 10- 1-09 11:00 AM
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||

When we're covering hard material, I like to call on students in small groups, so that no one student is put on the spot, but every student feels the heat of the class stare to a moderate degree, and is encouraged to participate. (Also it keeps one kid from answering all the questions.)

When the material is easy, I'll call on kids individually. Occasionally, it'll totally backfire, and someone will have stage fright, and I'll make the question easier, and easier, until everyone is uncomfortable, and the student will still not be able to muster it. It totally happened today. At one point I was pointing at "3" on the board and saying "So n is..." and she was still shaking her head and saying she couldn't do it. Bleagh. I feel bad when this happens.

|>


Posted by: heebie-geebie | Link to this comment | 10- 1-09 11:06 AM
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186

I suspected that was the study you were thinking of. It took place in the 60s and liberals have been citing it ever since.

It is my understanding the original study had problems and that efforts to replicate it haven't been terribly successful. Although I suppose it would be difficult to get such an experiment through ethics guidelines today.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 11:11 AM
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But I want to push back against the feeling I get from some of the thread which is, "even if it is true that 6-, 7-, and 8-chunkers are immutable (over some range of inputs), it is a useful fiction to believe that isn't true." That I don't buy

I'm not saying that. I'm saying if we don't solidly know that, e.g., working memory is immutable and accurately measurable, we really shouldn't base anything on a what-if, because the possibility of bad consequences is clear.

We get to this point in a lot of these conversations. Digging in my heels hard about not taking some aspect of human inequality as measurable and immutable on the basis of weakly suggestive evidence or pure speculation is really, really, not the same thing as saying that well-established scientific facts shouldn't be stated in public because I don't like their implications.

Treating people as equals isn't a "useful fiction" unless you've got a real fact saying they're not.


Posted by: LizardBreath | Link to this comment | 10- 1-09 11:15 AM
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183

I'm not following your restatement.

There is a difference between believing in general that some kids are bright and some aren't and a belief about a particular kid. It is possible it is beneficial overall to classify kids while being harmful to kids seriously misclassified. Obviously you if believe all kids are the same there is no danger of misclassifying a kid. But there is a danger of failing to do beneficial tailoring of instruction.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 11:18 AM
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I can't tell if this is Nick's position, LB's, both, or neither: that the perception of whether or not their effort will have an impact influences that effort a teacher will put in. (So, a teacher would try harder to teach the 'smart' kids because the 'dumb' kids will never get it anyway. Or, a teacher will try harder to teach the 'dumb' kids because the 'smart' kids already have the intellectual tools they need and won't benefit as much.)


Posted by: Di Kotimy | Link to this comment | 10- 1-09 11:20 AM
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190

Treating people as equals isn't a "useful fiction" unless you've got a real fact saying they're not.

Do you consider differences in IQ to be a real fact?


Posted by: James B. Shearer | Link to this comment | 10- 1-09 11:20 AM
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191: Oh, sure. There's no problem with a teacher believing that some people are brighter than others so long as they're not classifying their students as such on the basis of bad evidence.


Posted by: LizardBreath | Link to this comment | 10- 1-09 11:22 AM
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My understanding was that it is not difficult at all to teach people to perform better at most IQ tests. Like most things a little teaching a practice will go a long way. That's not to say that I don't think there are differences in intelligence between people, but like with many "objective" measures in social science IQ doesn't necessarily measure what it's intended to measure.


Posted by: Unfoggetarian: "Pause endlessly, then go in" (9) | Link to this comment | 10- 1-09 11:25 AM
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193: I think IQ is a fair rough measurement of someone's capacity at the time tested to do academic tasks similar to the ones on the test. That's something real, and something that I could see being useful. I don't think there's strong evidence that differences in IQ accurately reflect differences in immutable academic potential, either within demographic groups or, more strongly, between demographic groups -- or, actually, I think there's fairly good evidence that they don't.


Posted by: LizardBreath | Link to this comment | 10- 1-09 11:27 AM
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195

My understanding was that it is not difficult at all to teach people to perform better at most IQ tests. Like most things a little teaching a practice will go a long way. ...

Does this training reorder how people do or just move everybody's scores up?


Posted by: James B. Shearer | Link to this comment | 10- 1-09 11:29 AM
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You should pick a test subject and make a wager about whether or not you can improve his/her problem solving ability. Please take notes as I'll be writing a musical.


Posted by: Moby Hick | Link to this comment | 10- 1-09 11:32 AM
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Kind of on topic. My wife started teaching 8th and 9th grade science this year. Inherent abilities are laughably not the problem.

She gave a test yesterday, and allowed a "cheat sheet". One side of a standard size piece of notebook paper. She's reminded them of the cheat sheet every day for a week. The test came on the heels of a two day review where she literally waved a copy of the test around and told them to start making their cheat sheet in class, as everything she was covering would be on the test. Also, the cheat sheet is turned in with the test and they could earn up to 5 percent extra test credit just for doing it. She's trying to teach them good habits, so the classes are structured in a way that if they just show up, pay a bit of attention, and actually turn their work in, they'll get a decent grade.

She estimates that less than half the students did a cheat sheet. At least half a dozen kids tried to cheat the cheat sheet by doing notes on both sides. A couple went the extra cheat mile and tried to conceal stacks of notes on their laps and such. In one class, like three kids just outright refused to take the test. As in, wouldn't even put their name on a test and attempt the questions (multiple choice!) despite having sat through two days of review.

Granted, possibly not a representative sample in her classes. It's a low income area, and most of her students are 9th graders. In 9th grade in that school, the options for science are the accelerated program, a bio class that you have to test to get into, and then everyone else. My wife happens to teach the "everyone else" classes, who seem to have a higher than usual showing of the "incorrigible shithead" demographic.


Posted by: gswift | Link to this comment | 10- 1-09 11:33 AM
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Do I get to be Colonel Pickering?


Posted by: LizardBreath | Link to this comment | 10- 1-09 11:34 AM
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193: Do you consider differences in IQ to be a real fact?

I consider differences in the results of individual IQ tests to be a real fact, but that's just because numbers aren't equal unless they are equal, which is a trivial observation. The problem is with the assumption that differences in IQ test results are far more maleable than most people realize. In addition, there are people actively promoting IQ test result differences as reflections of inate and immutable superiority of some groups over others. In other words, it's racial supremacy pseudoscience. The clanging irony of it all is that the same folks heavily promoting this racist pseudoscience about untermenschen are calling their opponents Nazis.


Posted by: togolosh | Link to this comment | 10- 1-09 11:37 AM
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200: Based on the conversation above, I thought you'd be 'enry 'iggns.


Posted by: Moby Hick | Link to this comment | 10- 1-09 11:40 AM
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I'm probably pwned before I even finish typing this, but it's certainly possible to train for IQ tests. I bought some 'test your own IQ' book from a second hand shop when I was a kid and worked my way through the tests, writing down my scores. By about test 4, my IQ was at least 20 points higher than when I started.


Posted by: nattarGcM ttaM | Link to this comment | 10- 1-09 11:41 AM
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202: Yeah, but he's a jerk.


Posted by: LizardBreath | Link to this comment | 10- 1-09 11:43 AM
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We get to this point in a lot of these conversations. Digging in my heels hard about not taking some aspect of human inequality as measurable and immutable on the basis of weakly suggestive evidence or pure speculation is really, really, not the same thing as saying that well-established scientific facts shouldn't be stated in public because I don't like their implications.

I think this is just an example of the difficulty inherent in responding, as I did, to a vague sense of a thread rather than to specific comments. I wasn't particularly responding to you. If anything I was responding, indirectly, to the various back-and-forths with Sifu Tweety at the beginning of the thread.


Posted by: NickS | Link to this comment | 10- 1-09 11:44 AM
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||

http://www.guardian.co.uk/artanddesign/2009/sep/30/photography-willy-rizzo-best-shoot#zoomed-picture

So great. Especially the facial expressions -- both dancers, and the drummer.

More from here:

http://www.guardian.co.uk/artanddesign/gallery/2009/oct/01/willy-rizzo-best-shoot?picture=353673848

>


Posted by: nattarGcM ttaM | Link to this comment | 10- 1-09 11:46 AM
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204: A jerk who can teach. Like that math teacher in that one movie that I don't remember very well.


Posted by: Moby Hick | Link to this comment | 10- 1-09 11:48 AM
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While I personalized it, because I'm sure of what I think but not sure of what other people think, I have the impression that it's pretty common for a position like mine -- skeptical about weakly suggestive research into demographic differences -- to be misinterpreted as "Let's ignore solid research because the implications are ugly." There are probably some people who do want to ignore solid research because they don't like its implications, but I think it's a good rule of thumb to, if you're getting a vague impression that that's going on in a conversation, to work at pinning it down before assuming that it's really what people are saying.


Posted by: LizardBreath | Link to this comment | 10- 1-09 11:50 AM
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And to be clear, I don't think there's anything wrong with responding to a vague sense of what you think people in a thread are assuming, even if you can't pin it down to a quote -- I do stuff like that all the time.

I just think that this particular one is a common misunderstanding.


Posted by: LizardBreath | Link to this comment | 10- 1-09 11:52 AM
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When the material is easy, I'll call on kids individually. Occasionally, it'll totally backfire, and someone will have stage fright, and I'll make the question easier, and easier, until everyone is uncomfortable, and the student will still not be able to muster it. It totally happened today. At one point I was pointing at "3" on the board and saying "So n is..." and she was still shaking her head and saying she couldn't do it. Bleagh. I feel bad when this happens.

This exact thing happened to me in eighth grade (I was the student). In a math class, in fact. The teacher just wouldn't fucking drop it and move on to someone else. Look, I don't know the answer, and everyone's starting to giggle at me--give it up!! The truth was I couldn't see what's she'd written on the board. I needed glasses, but I was too embarrassed to admit it. When she cornered me after class I lied and said I'd been sleeping before she called on me, and so was disoriented and that's why I didn't understand her questions. It was a horrible experience, overall.


Posted by: Brock Landers | Link to this comment | 10- 1-09 12:02 PM
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have the impression that it's pretty common for a position like mine -- skeptical about weakly suggestive research into demographic differences -- to be misinterpreted as "Let's ignore solid research because the implications are ugly." There are probably some people who do want to ignore solid research because they don't like its implications, but I think it's a good rule of thumb to, if you're getting a vague impression that that's going on in a conversation, to work at pinning it down before assuming that it's really what people are saying.

Actually, the most salient comment might be ST's response to the OP in 11.

While I'm not making strong claims for genetic predisposition when it comes to this ability -- although there are certainly genetic aspects to other basic reasoning skills, like subitizing, that are similar -- it seems like you're strongly claiming the opposite, that not only is the genetic explanation wrong, but there is another, correct explanation that we can discuss in this thread. I'm curious what your reasoning for that would be?

Obviously the subsequent conversation has helped pin people's positions down a bit, but I think he was correct to identify in the OP a contrariness with no specific basis. Given heebie's 120, I don't want to put too much weight on that, but I do think 11 was a perfectly reasonable question that wasn't directly responded to (though I may be missing something).


Posted by: NickS | Link to this comment | 10- 1-09 12:03 PM
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OK, the conversation moved on while I was sleeping and talking about motor learning, but I wanted to add a couple more thoughts.

Heebie is right (catchphrase) that the general trend in brain science is that we end up finding that things are more plastic than once thought. However, that does not mean that everything will turn out to be equally plastic. The "making monkeys not color blind" study both shows the remarkable ability of nervous tissue to change, but also suggests that some of it won't do so without extraordinary measures. I seriously doubt you're ever going to get monkeys to grow those cones on their own through some behavioral therapy; you'll probably always have to inject the relevant genes in there.

Along the same lines, bringing up the "London cab driver hippocampi are bigger" study doesn't necessarily tell us much about this working memory issue. "The brain is plastic" isn't all that meaningful of a phrase, as some parts of the brain sure seem to be more plastic than others. The hippocampus is extraordinarily plastic, for example: Neurons there seem to be able to develop new representations of a place after one visit. Visual cortex, meanwhile, seem to change much less easily: Perceptual learning effects (getting better at telling whether two lines are at different orientations) tend to happen over hundreds of trials. There is a "critical period" for visual cortical development after which its plasticity seems to go way down. The initial evidence for this was in the 1970s, and people have been chipping away at ever since, and some adult plasticity has been found, but still no one's figured out how to turn V1 into the hippocampus. [Why am I talking about visual cortex here? 'Cause that's what I know more about. I'm not a working memory guy.]

The folks I know around here (and a lot of the folks I don't know) would love to find ways to make cortex super plastic, because 1. There's a Nature paper in every overturned piece of dogma and (for some of them) 2. There's lots of money to be made. But it really seems that, though there's plasticity just about everywhere, some of it seems to be lot trickier to induce (the girl I know who was talking about reopening the V1 critical period was talking about doing using molecular manipulations, which is not something you want to do willy-nilly to heebie's students), and perhaps more importantly, to change only to an unsatisfying extent (i.e., the difference between statistical and practical significance). Working memory capacity may be one of those things that's harder to change.

I'm a bit rankled to see the WM capacity literature being dismissed as "a few upper middle class undergrads years ago, blithely cited ever since" (though again, I'm not WM guy, though my understanding of the literature could be off). I'm not asking you to have blind faith in cognitive science (I sure don't), but it's my impression that a lot of smart people have been pounding at this stuff for a half century.

And getting back to the practical importance of this, I still find it surprising that variations in WM capacity could explain variations in word problem-solving performance. I'd read heebie's article, but I have to go do stuff.


Posted by: Otto von Bisquick | Link to this comment | 10- 1-09 12:04 PM
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I'm not asking you to have blind faith in cognitive science (I sure don't), but it's my impression that a lot of smart people have been pounding at this stuff for a half century.

If my guess about the basis of belief in the immutability of working memory was wrong, it was wrong -- as I said, I don't actually know anything about the research.


Posted by: LizardBreath | Link to this comment | 10- 1-09 12:10 PM
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Without having read much of the thread, I don't see how the chunking issues involved in being able to recite back lists of numbers have much of anything to do with actual problem solving.


Posted by: essear | Link to this comment | 10- 1-09 12:11 PM
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211: Obviously the subsequent conversation has helped pin people's positions down a bit, but I think he was correct to identify in the OP a contrariness with no specific basis.

I think the original post was pretty clear that her basis was "this seems really unlikely to me". A fair response to that would be something like "No, really, the evidence for this is solid -- here it is." But you really don't need a specific basis for skepticism in the face of weak evidence.


Posted by: LizardBreath | Link to this comment | 10- 1-09 12:14 PM
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re: 214

Pretty much any problem solving ability is going to involve holding information in one's head, and then manipulating it. That applies whether one is engaged in verbal reasoning, some sort of spatial calculation, numerical reasoning, whatever. That's obvious, no?

The reciting lists of numbers is just a way of quantifying that ability.


Posted by: nattarGcM ttaM | Link to this comment | 10- 1-09 12:16 PM
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216: A problem with that, though, is what Pause said way above:

My impression of social science of this sort (mostly coming from Rhymeswithmaria's experience with some education research) is that there's a strong pressure to measure things that are consistently and accurately measurable so as to get your error bars small enough that people think of it as real science and that this pressure results in measuring things that don't actually match up with the intuitive concepts they're purporting to measure.

Ability to recite lists of numbers might match up well with holding information generally in your head and manipulating it, but it's not obvious to me that it would. Might, but might not.


Posted by: LizardBreath | Link to this comment | 10- 1-09 12:23 PM
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213: I perhaps shouldn't be arguing so stridently when I have to use phrases like "it's my impression". I could be wrong . I'll look into this stuff in a couple hours, maybe.

I have the impression that it's pretty common for a position like mine -- skeptical about weakly suggestive research into demographic differences -- to be misinterpreted as "Let's ignore solid research because the implications are ugly."

I don't think you are advocating that we should ignore solid research of this sort, but it does seem like you are biased against believing that any such research could exist. It seems like your strategy is not to say "ugly implications, let's ignore it", but to assume that any discussed research about innateness or immutability is "weakly suggestive evidence or pure speculation", even when you don't know much about the research in question. That's probably true in a lot of cases (I know firsthand how crappy a lot of science is, and I'm in a sort of "hard" science), but when I see you make that assumption about something that's been worked on for decades, I'm going to trust the researchers before I trust your assumptions.

OK, way more out on a limb than I like to be. Gotta go work for reals.


Posted by: Otto von Bisquick | Link to this comment | 10- 1-09 12:25 PM
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re: 217

I think the thrust of the research is that it's a decent but not perfect proxy.


Posted by: nattarGcM ttaM | Link to this comment | 10- 1-09 12:28 PM
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I think the original post was pretty clear that her basis was "this seems really unlikely to me". A fair response to that would be something like "No, really, the evidence for this is solid -- here it is." But you really don't need a specific basis for skepticism in the face of weak evidence.

I guess one reason for my frustration was that this, from the original post, seems like a fascinating result:

Third, that you can accurately calculate the memory load required by a given word problem. There was a graph showing how performance of 6-chunkers plummeted when they hit the problems requiring a load of 7, the 7-chunkers plummeted at 8, and the 8-chunkers plummeted at 9.

Personally I would have been really curious to know more about how they were able to construct problems requiring specific numbers of chunks and what that looked like. I suppose I should go back and read the chapter to which Heebie linked.

My intuition (worth what you pay for it) is just that examining that set of results would have more direct implications for what should be done to counteract that plummeting.


Posted by: NickS | Link to this comment | 10- 1-09 12:28 PM
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One thing that would give me pause with some experiments is that a lot of people have already developed informal strategies for working round chunking and working memory issues. Having a couple of friends who are/were cognitive scientists/psychologists, I was recruited into a few of these undergrad experiments. Sometimes I'd be putting weird little spikes in their bell-curve. Not because I was extra-super-special, but because I already had a couple of acquired tricks.

I presume/hope good experimenters explicitly design around that.


Posted by: nattarGcM ttaM | Link to this comment | 10- 1-09 12:32 PM
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It seems like your strategy is not to say "ugly implications, let's ignore it", but to assume that any discussed research about innateness or immutability is "weakly suggestive evidence or pure speculation", even when you don't know much about the research in question.

Well, yes, I do have a strong bias in that direction, because I've been in a lot of conversations involving gestures toward research that turns out to be really very weak. There might be convincing research that working memory is immutable (and of course, there could be all sorts of fascinating research into working memory that doesn't depend one way or the other on its immutability -- doubting that it's immutable is not equivalent to saying "all research involving working memory is crap."). But I don't know what the basis is for thinking it's immutable, you work in a connected field and you don't know either (offhand -- I'm sure you could look it up faster than I could), and Sifu doesn't know either (or at least the links he gave don't address it).

That doesn't mean that the research saying working memory is immutable is bad. I guessed it's pretty weak, but I'm guessing, based on my pre-existing biases about this kind of thing. If I saw convincing research that I thought proved that working memory was immutable, I'd believe it. I'm still going to stay skeptical until I see that research.


Posted by: LizardBreath | Link to this comment | 10- 1-09 12:35 PM
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220: It's not in the chapter at that level of detail -- all it says is that they used questions for which the information load had been measured.


Posted by: LizardBreath | Link to this comment | 10- 1-09 12:39 PM
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And yes, there are interesting and difficult-to-resolve issues here around appeals to authority and public engagement with science. My cautious nature makes me extremely reluctant to act as a high priest of any sort.


Posted by: Otto von Bisquick | Link to this comment | 10- 1-09 12:48 PM
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What's needed is an experiment where infants are raised in environments where their only companions are varying numbers of chunks.


Posted by: Eggplant | Link to this comment | 10- 1-09 12:55 PM
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My eldest blew chunks frequently, if that would help.


Posted by: LizardBreath | Link to this comment | 10- 1-09 12:56 PM
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I'm still going to stay skeptical until I see that research.

This is more or less my position on a great many things, supplemented by the acknowledgments that (a) I am really never going to be bothered to actually seek out the research, and (b) even if I did, I don't really have the background to competently evaluate or criticize most of these things.


Posted by: | Link to this comment | 10- 1-09 1:03 PM
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227=me


Posted by: Di Kotimy | Link to this comment | 10- 1-09 1:04 PM
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For a change of topic, sort of, this morning I read this good, old-fashioned, bit of working-class outrage, about conditions working for the Royal Mail. It made my morning. It's a great read, well-written, convincing, and passionate.

Relevant to this discussion is his breakdown, after spending the first half of the article talking about all of the staff cutbacks that the Royal Mail had made because mail volume was down, of how the studies and figures being given by the administrators are not correct.

The truth is that the figures aren't down at all. We have proof of this. The Royal Mail have been fiddling the figures. This is how it is being done.
Mail is delivered to the offices in grey boxes. These are a standard size, big enough to carry a few hundred letters. The mail is sorted from these boxes, put into pigeon-holes representing the separate walks, and from there carried over to the frames. This is what is called 'internal sorting' and it is the job of the full-timers, who come into work early to do it. In the past, the volume of mail was estimated by weighing the boxes. These days it is done by averages. There is an estimate for the number of letters that each box contains, decided on by national agreement between the management and the union. That number is 208. This is how the volume of mail passing through each office is worked out: 208 letters per box times the number of boxes. However, within the last year Royal Mail has arbitrarily, and without consultation, reduced the estimate for the number of letters in each box. It was 208: now they say it is 150. This arbitrary reduction more than accounts for the 10 per cent reduction that the Royal Mail claims is happening nationwide.
Doubting the accuracy of these numbers, the union ordered a random manual count to be undertaken over a two-week period in a number of offices across the region. Our office was one of them. On average, those boxes which the Royal Mail claims contain only 150 letters, actually carry 267 items of mail. This, then, explains how the Royal Mail can say that the figures are down, although every postman knows that volume is up. The figures are down all right, but only because they have been manipulated.

Posted by: NickS | Link to this comment | 10- 1-09 1:04 PM
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Well, yeah. I'm competent to evaluate some research, but not much (and competent to point out flaws with much more than I could reliably say that it's good). And my skepticism is biased -- some result that seems both plausible and harmless, I'm not going to devote a lot of energy to doubting, and I'll take even shaky looking research as at least suggestive. The skepticism kicks into high gear for anything that supports the existence of immutable differences between people's capacities, on the other hand, mostly because it's an area where giant errors, in the direction of believing too much in the existence of immutable differences, have been so common, and because those errors have historically been so harmful.


Posted by: LizardBreath | Link to this comment | 10- 1-09 1:09 PM
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230 to 227.


Posted by: LizardBreath | Link to this comment | 10- 1-09 1:09 PM
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Pretty much any problem solving ability is going to involve holding information in one's head, and then manipulating it. That applies whether one is engaged in verbal reasoning, some sort of spatial calculation, numerical reasoning, whatever. That's obvious, no?

But there's "memorize as much as you can of this list of phone numbers and recite it back to me fifteen minutes later", and there's "keep in mind these relevant and contextually-situated facts", and the latter is what matters. The "chunking" studies I'm aware of are more like the former. But, as I said, I haven't read much of the thread, and I probably won't due to severe time constraints in the next two days, so I'll shut up now.


Posted by: essear | Link to this comment | 10- 1-09 1:15 PM
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What I want to know is whether better chunking skills can qualify a six-chunker to date Ogged.


Posted by: Not Prince Hamlet | Link to this comment | 10- 1-09 1:16 PM
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116: It may have been but the directions didn't have the greatest diagrams. I think I'd have gotten it on the first try had I not absentmindedly moved the adapter before installing it on the arm without first paying attention to its original orientation.


Posted by: eb | Link to this comment | 10- 1-09 1:23 PM
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Somewhat less flippantly, keeping teachers and ed school professors as far away from brain research as possible seems like a good idea. Trying to teach teachers about neuroscience research is a hell of a lot more likely to give them a sciencey peg to hang their prejudices from than to improve their pedagogy.


Posted by: Not Prince Hamlet | Link to this comment | 10- 1-09 1:38 PM
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235: Dude, as an ed school drop out (well, I got the degree, not the teaching certificate), the tiny little bit of neuroscience research I was exposed to* was the nearest thing to interesting and useful I encountered**. The teachers who will be looking for a peg to hang their prejudices from will find one no matter what you teach. The ones who don't have prejudices that they need a peg for may actually get something out of actual brain sciencey stuff.

* Actually, from a text I bought for a class I ended up having to drop due to a schedule conflict.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 1:51 PM
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236: For the musical:

Ed school drop out, Go off to law school


Posted by: Moby Hick | Link to this comment | 10- 1-09 1:54 PM
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236: What might they get out of it?


Posted by: Not Prince Hamlet | Link to this comment | 10- 1-09 1:56 PM
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To do a quick 180, I don't think that's always true. The article Heebie's talking about and linked above seems like a neurosciency sort of thing that could be really useful: the idea is that, immutable or not, people do in practice differ in working memory capacity, and you can design tests and study materials that vary significantly in how much working memory capacity they require, without affecting the actual rigor of the class, or the amount of information you're expecting the students to learn. And so designing your materials to be accessible to low-WMC students is going to make them learn better without doing any harm to the high-WMC students.

If that's true, it's really useful, and it's not about sorting the students into the smart and dumb ones. I could see research along those lines being very helpful for teachers.


Posted by: LizardBreath | Link to this comment | 10- 1-09 1:57 PM
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239 to 235, but it's a partial answer to 238.


Posted by: LizardBreath | Link to this comment | 10- 1-09 1:58 PM
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the idea is that, immutable or not, people do in practice differ in working memory capacity, and you can design tests and study materials that vary significantly in how much working memory capacity they require, without affecting the actual rigor of the class, or the amount of information you're expecting the students to learn. And so designing your materials to be accessible to low-WMC students is going to make them learn better without doing any harm to the high-WMC students.

Thanks for that summary. I had read the article and was going to write something to that effect when I had a moment, but that's a good summary.

I think it's important to say, contrary to some of the worries in this thread, that the original article isn't about how low WMC cripples some students but about how a well designed course can minimize the importance of different WMC between students, and can do so without sacrificing rigor or instructional value.


Posted by: NickS | Link to this comment | 10- 1-09 2:02 PM
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233: Can she open doors?


Posted by: togolosh | Link to this comment | 10- 1-09 2:04 PM
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||

There was a great anecdote -- I think from A White Bear -- about working in a tea shop and having to sell women tea that solved imaginary health problems. Can anyone please find it for me? I am suddenly overtaken with curiousity.

|>


Posted by: k-sky | Link to this comment | 10- 1-09 2:11 PM
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233: Can she open doors?

Heteronormativist.


Posted by: NickS | Link to this comment | 10- 1-09 2:12 PM
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Maybe, but it would still surprise the hell out of me if neuroscience research was producing results that (a) translate easily to the classroom, and (b) haven't already been stumbled on in by teachers or ed school types.


Posted by: Not Prince Hamlet | Link to this comment | 10- 1-09 2:13 PM
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192

I can't tell if this is Nick's position, LB's, both, or neither: that the perception of whether or not their effort will have an impact influences that effort a teacher will put in. (So, a teacher would try harder to teach the 'smart' kids because the 'dumb' kids will never get it anyway. Or, a teacher will try harder to teach the 'dumb' kids because the 'smart' kids already have the intellectual tools they need and won't benefit as much.)

This gets to the purpose of public education. Is it to teach everybody the basic skills that are needed to function well as adults or is it to identify and sort out the brightest students? The first dictates spending more effort on the dumb kids, the second more effort on the smart kids. Of course in practice it is a mixture but it seems like, especially in the higher grades, the second dominates to the point that schools seem actively hostile to teaching anything of practical value. As seen in dropping driver's ed for example.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 2:14 PM
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199

Granted, possibly not a representative sample in her classes. It's a low income area, and most of her students are 9th graders. In 9th grade in that school, the options for science are the accelerated program, a bio class that you have to test to get into, and then everyone else. My wife happens to teach the "everyone else" classes, who seem to have a higher than usual showing of the "incorrigible shithead" demographic.

Or maybe the incorrigible ones are the people in authority who force students to repeatedly fail to learn material which is difficult to impossible for them and of no practical value even if they should manage to succeed.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 2:20 PM
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Is it to teach everybody the basic skills that are needed to function well as adults or is it to identify and sort out the brightest students?

Actually, in my shiny happy world, the purpose is to help all children maximize their individual potential.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 2:20 PM
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243: Somehow I thought that was on her blog rather than here. Which I don't think is accessible anymore.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 2:22 PM
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222

That doesn't mean that the research saying working memory is immutable is bad. I guessed it's pretty weak, but I'm guessing, based on my pre-existing biases about this kind of thing. If I saw convincing research that I thought proved that working memory was immutable, I'd believe it. I'm still going to stay skeptical until I see that research.

I also doubt the idea of a fixed and discrete working memory (of the 6,7,8 type in the post) because it is contrary to my subjective experience. I have on occasion had to enter long lists of numbers into a computer. I would do this by putting a few of them into my working memory and them typing them in. My subjective experience was this was like carrying in bags of groceries from a car. The more bags you tried to carry at once the fewer trips needed but the more likely you were to drop something. I did not get the feeling there was some fixed number of positions I was filling.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 2:29 PM
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... And so designing your materials to be accessible to low-WMC students is going to make them learn better without doing any harm to the high-WMC students.

This sounds like teaching people to type with one hand which is certainly going to limit the performance of people with two hands.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 2:32 PM
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[I have had to wander off twice during composition.]

114: 103: I like the register limitation analogy! Although when people run out of working memory, more often than our systems "hanging", we tend to just drop items. Though of course there is some of both... Anyway, thanks for the links. Miller's paper is still good reading despite being over 50 years old.

Oops. Four hours of sleep here. I assumed you already knew all that - I was aiming that at everyone else. Sorry. But you're welcome anyways!

As for drops - well, the problem with using register starved CPUs as the example is the tendency to try and refactor the psuedo-code on the fly. ('Wait, I need to find a fucked up, non-functional way of doing this? Oh, shit. Well, I could.... no. I could... no. Fuck.') (And also, temporary drops do occur.)

112: (And what max said about "field dependence". I wouldn't be surprised if 'working memory' were the kind of thing that was immutable. But 'field dependence'? The way they're describing it in the article, it seems like another way of saying 'good judgment'. Bullshit that's a simple, immutable cognitive quality.)

Here we go:

According to Bonham (1987), Herman Witkin's Filed Independence-Dependence is the most widely known cognitive style, perhaps owing to the extent of its research. The theory has been continually revised for over 30 years. Current theory places field independence within the framework of psychological differentiation. Field independent persons epend more on self and seem readily to learn material that has a social context. Field independent students appear to be more adept to the usntructured classroom than their field dependent counterparts. Field independence appears to result in a greater development of cognitive restructuring skills.
The more field dependent person is reliant on external referents as a result of their amount of differentiation of self from non-self. Dependent learners rely more on the teacher and peer support. By this theory, the independent student tends to be more analytical and attends less to peer pressure or teacher direction.
The Embeded Figures Test (EFT) is designed to measure disembedding, a restructuring skill, which results from the use of style. According to Bonham (1987), the EFT was adapted from Gottschaldt's figures by adding colored patterns to increase complexity. Each complex figure included an embedded simple figure, which the subject is to identify as quickly as possible; there are 24 figures in the EFT. The group version (GEFT), is a paper-and-pencil instrument which requires students to attempt to discern simple geometric figures from more complicated patterns. Students find eight hidden figures by tracing over them.
Casey (1993), citing Witkin (1976), reports reasonably high validity data (-.82 for male undergraduates, -.63 for female graduates) with Spearman-Brown and Tyron's variance coefficients of .89 to .95. Bonham (1987) notes a number of problems that seems to exist in relation to theory and isntrument including gender bias; sex differences were first reported then discounted. Instrumentation is questionable: the epception-of-the-upright equipment is now said to measure style while the EFT and GEFT insruments are said to measure ability. Critics note that the instruments are a measure of either general intellegence or some specific ability. It is not always clear what version is being used or why, nor how readers should interpret outdated literature (Bonham, 1987). Bonham sees two particular problems associated with the new model: the nature of hierarchies and use of a bipolar dimension that is really two dimensional.
Meanwhile the first Google link for field dependence has a long list of qualities that sounds suspiciously grabbag, or possibly 'introvert v. extrovert', etc. Autistic Analyst Assholes vs. Superficial Social Slatterns. (I'm a slattern AND an asshole! Go me!)

147: If the original research saying "based on our two-week study of 27 Harvard juniors, we think that working memory is immutable" was conducted by someone firmly and publicly committed to the equality of all people who'd never use their research to advocate for cutting educational resources to the 'immutably incapable', and the resulting factoid gets accepted as true by decades worth of fellow researchers with similarly impeccable politics, it gets really hard to clarify the facts when they're finally picked up by someone with bad motives.

There are going to be limitations of this particular lowlevel type. No one can access all the data in their basic storage at the same time, at the same speed. Consider how you recall something from long ago that you haven't thought about in a long time. As a comparison, I know, for a fact, that if I hit you in the head just the right way, just above your left ear, I can knock out your ability to deal with vowels, permanently. Hitting an area just behind that will take out your consonants (and not your vowels) and taking out an area a little bit further to the rear will render you totally aphasic. The chunking thing is not as solidly dramatically illustrated, but the research seems close to rock solid, given that I know such a thing has to exist in the first place. If it's amenable to change after someone has spent 20 years on earth being pushed to excel at it, I don't see how, or at least not without immense effort. On the other hand, the capability must grow with the brain. On the other other hand, it seems likely to be about a fairly minor issue of better throughput by not overloading people.

The skepticism kicks into high gear for anything that supports the existence of immutable differences between people's capacities, on the other hand, mostly because it's an area where giant errors, in the direction of believing too much in the existence of immutable differences, have been so common, and because those errors have historically been so harmful.

In the endless ideological debate between perfect plasticity and immutable genetic determinancy, I actually tend (ideologically and mostly practically) to the plasticity side. But the plasticity vs. determinancy debate often seems to be taking place about 150 years ago and ignores everything that's been learned since. (The phrase 'the greater sins of the right' is also applicable here.) And now I should write some useful conclusion here, but I have none.

max
['Not trying to beat up on you, LB; you're doing most of the talking.']


Posted by: max | Link to this comment | 10- 1-09 2:32 PM
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Ack, I'm only up to 125 on this thread and it is killing my productivity.

Is this the bottom line: the 7+/-2 barrier is real, but there are so many ways around it that it is not even worth trying to punch through it.

I'm probably a six- or even a five-chunker. I get around it by having a shitload of different narratives to impose on different things and being really good at chunking. One of my problems communicating with students is that they seem to have so few frames of reference and find it so hard to switch between them. I have this converstation with students a lot

Student: Is that like X?
Me: Well, no, not really. I think you are just picking up on accidental feature Y.

Also, I am fundamentally an analogical thinker. The analogy ban was an effort to silence me and my kind.


Posted by: rob helpy-chalk | Link to this comment | 10- 1-09 2:36 PM
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251: No, it's like saying that if you teach the whole class good lifting technique, the strong and weak kids alike will be able to lift more than they could with poor lifting technique. The strong kids will still outlift the weak, but everyone gets stronger and fewer people get hurt by bad form.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 2:46 PM
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Um, 254 also to voice my solidarity with 253.last.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 2:47 PM
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If it's amenable to change after someone has spent 20 years on earth being pushed to excel at it, I don't see how, or at least not without immense effort.

This all sounds reasonable to me. I'm just really, really tetchy about literally making that last jump from "Seems to be very hard to change in practice" to "We know that it's genetic and immutable" without very powerful evidence. Because once you start saying "Quality X is genetic and immutable" and "Quality X is importantly related to general academic capacity" it's really easy for someone else to argue "General academic capacity is genetic and immutable and so we should test for X, and write off the dummies on that basis."

Now, if there really is very strong evidence that X is genuinely immutable, then tell the truth about it and let the chips fall where they may. But without that, what's the harm with sticking with "In practice, X seems to be very stable in people over 12," or whatever the data actually establishes.


Posted by: LizardBreath | Link to this comment | 10- 1-09 2:48 PM
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252: Meanwhile the first Google link for field dependence has a long list of qualities that sounds suspiciously grabbag, or possibly 'introvert v. extrovert', etc.

Tell me about it. More formally: indeed. While I enjoy personality tests as much as the next person, the lists provided there are .. can I just say "meh"?


Posted by: parsimon | Link to this comment | 10- 1-09 2:48 PM
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Actually, in my shiny happy world, the purpose is to help all children maximize their individual potential.

Lots of kids aren't born to be academic types and don't flourish in a system design for and by academic types.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 2:49 PM
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253: Is this the bottom line: the 7+/-2 barrier is real, but there are so many ways around it that it is not even worth trying to punch through it.

I believe so, yes. That's the bottom line. In light of it, it's not particularly worth getting worked up about whether the 7 +/- 2 experimental findings are genetically hard-wired.


Posted by: parsimon | Link to this comment | 10- 1-09 2:53 PM
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a long list of qualities that sounds suspiciously grabbag, or possibly 'introvert v. extrovert', etc. Autistic Analyst Assholes vs. Superficial Social Slatterns. (I'm a slattern AND an asshole! Go me!)

I just liked that bit enough to want to quote it (you know, as an Autistic Analyst Asshole).


Posted by: NickS | Link to this comment | 10- 1-09 2:53 PM
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254

No, it's like saying that if you teach the whole class good lifting technique, the strong and weak kids alike will be able to lift more than they could with poor lifting technique. The strong kids will still outlift the weak, but everyone gets stronger and fewer people get hurt by bad form.

This makes sense for things like strength that can be trained but not for things like the number of hands you have that can't. The premise of the post is that some mental qualities are discrete and immutable (like the number of hands you have). I actually doubt this but if true teaching to the lowest number will handicap the more capable students.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 2:56 PM
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Lots of kids aren't born to be academic types and don't flourish in a system design for and by academic types.

Albert Einstein, for example. I'm not advocating on behalf of the current design of the educational system. I'm all for radical rethinking of these things.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 3:12 PM
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I actually doubt this but if true teaching to the lowest number will handicap the more capable students.

Well... the claim made in the linked article is that whether the materials are high or low-WMC doesn't have any effect on the rigor of the class. I have to admit that I kind of doubt that myself -- that you can look at materials, figure out what level of WMC they require, and adjust that without affecting the amount of information conveyed. If the claim is true, and it seems possible, just surprising, then designing low-WMC materials isn't a handicap for the more capable students, it's removing a handicap from the students that are less capable at a task that's irrelevant to what they're trying to learn.

To pull out a banned analogy: say the capacity was the ability to screen out background noise, rather than WMC. If you've got a jackhammer running in the back of the classroom, the students more capable of ignoring the noise are going to do better than the less capable students. But it wouldn't make sense to think of removing the jackhammer as handicapping the more capable students -- ability to ignore loud noises isn't something a chemistry class should be testing you for.


Posted by: LizardBreath | Link to this comment | 10- 1-09 3:13 PM
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(I should say that it seems surprising that it would work at all -- that you can look at an academic problem more complex than memorizing numbers and quantify how much working memory it requires, and redesign it to require less and so to be more accessible to people with lower WMC. If it does work in practice, though, and without sacrificing rigor, it'd be the pedagogical equivalent of finding money -- all upside, no downside.)


Posted by: LizardBreath | Link to this comment | 10- 1-09 3:22 PM
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I actually doubt this but if true teaching to the lowest number will handicap the more capable students.

The point is that capability in memory shouldn't be limiting in maths, because maths isn't about short term memory. So it isn't handicapping the more capable, because they are more capable at something ideally unrelated which should be removed from the matter.


Posted by: Keir | Link to this comment | 10- 1-09 3:24 PM
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the claim made in the linked article is that whether the materials are high or low-WMC doesn't have any effect on the rigor of the class. I have to admit that I kind of doubt that myself

This sounded fishy to me, too. I parsed it as that you can ask incredibly detailed questions about chemistry, just one detail at a time.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 3:33 PM
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By the way, heebie, I was curious whether you agreed with my comment 160? Useful might have been overstating, but it seemed like a reasonable comparison.


Posted by: NickS | Link to this comment | 10- 1-09 3:37 PM
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I'd agree with 160. But not if you meant that it's a helpful way to teach someone how to think about proofs. It's a good notion in hindsight, if you already understand what it means to prove something.

Teaching kids how to write proofs is ridiculously hard. I desperately want us to start teaching a class solely dedicated to proof-writing, where you don't attempt to cover any meaningful amount of material.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 3:41 PM
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... If the claim is true, and it seems possible, just surprising, ...

True, but I am not willing to proceed on the basis of a possible but unexpected claim without some strong evidence in support which I have not seen.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 3:41 PM
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I desperately want us to start teaching a class solely dedicated to proof-writing, where you don't attempt to cover any meaningful amount of material.

I believe you are talking about my PHLY Logic 171.


Posted by: rob helpy-chalk | Link to this comment | 10- 1-09 3:45 PM
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The thing is, curriculum design isn't science, it's craft. I'm not a teacher, so I'm not proceeding on the basis of this at all. But if I had something walking me through how to design low-WMC tests and study materials, and if in my professional judgment the resulting tests and study materials weren't less rigorous than I would have come up with if I weren't worrying about WMC (and if the whole process weren't prohibitively more work than I would have been doing anyway) why not give it a shot and see if it seemed to have a beneficial effect on the next class?

Professional judgment seems like a good enough safeguard against loss of rigor -- other than that, what's the possible harm?


Posted by: LizardBreath | Link to this comment | 10- 1-09 3:46 PM
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270: Am I making it up, or did you and I have an off-blog conversation about this once?


Posted by: heebie-geebie | Link to this comment | 10- 1-09 3:48 PM
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268: Teaching kids how to write proofs is ridiculously hard.

Heh. I hated the epsilon-delta proofs in calc, which was probably as close as I ever got to a real proof (if you don't count messing around with similar triangles in 9th grade geometry). I alternated between sullenly muttering "This is all perfectly obvious and a waste of time" and a sneaking belief that I was on some very deep level missing the point.


Posted by: LizardBreath | Link to this comment | 10- 1-09 3:49 PM
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265

The point is that capability in memory shouldn't be limiting in maths, because maths isn't about short term memory. So it isn't handicapping the more capable, because they are more capable at something ideally unrelated which should be removed from the matter.

The claim was you have to able to hold enough of a problem in memory at once to identify and isolate the key features. Which seems plausible to me. There are probably work arounds and multipass stategies but I doubt it is actually unrelated.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 3:49 PM
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172: Basically. I asked you what you thought students who weren't going to have any other math classes should get out of their one math class. The one class in question was, in fact, PHLY 171 Logic.


Posted by: rob helpy-chalk | Link to this comment | 10- 1-09 3:51 PM
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271

Professional judgment seems like a good enough safeguard against loss of rigor -- other than that, what's the possible harm?

The same harm as teaching two-handed people to type with one hand. You are training the more capable students in an awkward and inefficient (for them) way of solving problems. They will still be able to do the work but in a slow and inefficient way. And there may be more advanced tasks which can't be performed with one hand tied behind your back.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 3:55 PM
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The claim was you have to able to hold enough of a problem in memory at once to identify and isolate the key features. Which seems plausible to me. There are probably work arounds and multipass stategies but I doubt it is actually unrelated.

But it really is: there are two things here, memory & mathy, right? And if you don't have the memory, you can't do the mathy at present. But if you have the memory, you can do the mathy in a way that doesn't seem to relate to the memory in any interesting way. (Better memory doesn't mean you're mathy better when you're working within your memory ability.) But in a maths class, we don't care about the memory, just the mathy, so if we can play down or eliminate the role of the memory, this will be good.

Further, it may handicap certain students, who may appear to be currently more capable, but they mightn't be the most mathy capable, so as far as a maths class is concerned, it isn't handicapping the most capable exactly.

(Mathy means maths-like-thing-or-possibly-even-maths that maths teachers seem interested in.)


Posted by: Keir | Link to this comment | 10- 1-09 3:58 PM
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I think IQ is a fair rough measurement of someone's capacity at the time tested to do academic tasks similar to the ones on the test. ...

So you don't think the general stability of IQ in adults over time is established?


Posted by: James B. Shearer | Link to this comment | 10- 1-09 3:59 PM
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The same harm as teaching two-handed people to type with one hand. You are training the more capable students in an awkward and inefficient (for them) way of solving problems. They will still be able to do the work but in a slow and inefficient way. And there may be more advanced tasks which can't be performed with one hand tied behind your back.

You're assuming that it does affect rigor -- that the altered materials are awkward and inefficient. As I said above, this seems like a strong possibility to me, but also like the sort of thing a competent teacher would spot in the process of designing the materials, and at that point you'd have to think about whether the tradeoff was worth it. But if there's no tradeoff -- the memory issue really is irrelevant to the math skills, in the same way that ignoring a jackhammer would be -- there's really no tradeoff.


Posted by: LizardBreath | Link to this comment | 10- 1-09 4:02 PM
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The issue of what skill level to teach to is such a hard one. If I have a nice bell curve distribution, I feel comfortable teaching to the middle, with occasional asides to the two tails of the curve. When the class starts getting stratified--a bimodal distribution with a distinct bump at the low end and another at the high end--I get really flummoxed. I need to work on better solutions to that problem.

In a similar vein, Molly reports that Caroline's first grade class includes fluent readers (like our little Marie Curie Jane Goodall E.O. Wilson) and kids who cannot recognize three letter words. That must be a hard room to teach.


Posted by: rob helpy-chalk | Link to this comment | 10- 1-09 4:04 PM
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For third grade, I switched from a Montessori school into this horrible private school. On the first day, we sat in a circle and recited the alphabet. Then we reviewed what sound each letter makes. I was beyond horrified.


Posted by: heebie-geebie | Link to this comment | 10- 1-09 4:09 PM
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278: I don't think it's established in children, certainly. "General", even applied to adults, is doing a fair amount of work there -- I have the impression (although I haven't looked at research) that IQ is fairly stable for most adults in the US. On the other hand, I don't know what research has been done on, e.g., measuring IQ stability for someone who made up a substantial educational deficit as an adult -- and I'd expect to find that IQ would at least sometimes change significantly under circumstances like that.


Posted by: LizardBreath | Link to this comment | 10- 1-09 4:11 PM
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277

But it really is: there are two things here, memory & mathy, right? And if you don't have the memory, you can't do the mathy at present. But if you have the memory, you can do the mathy in a way that doesn't seem to relate to the memory in any interesting way. (Better memory doesn't mean you're mathy better when you're working within your memory ability.) But in a maths class, we don't care about the memory, just the mathy, so if we can play down or eliminate the role of the memory, this will be good.

This isn't right. Mathematical problem solving ability involves at least two things. The ability to calculate and the ability to figure out what to calculate. It is the second part that is usually the difficulty (especially with calculators to do the arithmetic).

Consider a word problem. Alice has 2 apples, Bob has 3 apples, Carl has 4 apples, Diane has 5 apples, how many apples do the girls have? If you want to do this problem in one pass you have to hold a bunch of things in memory because you don't know what is important until the end of the problem. In this case the problem can be rewritten to be easier by putting the end first (or by taking two passes) but this may not always be the case.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 4:12 PM
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I desperately want us to start teaching a class solely dedicated to proof-writing,

Yes, yes, oh god, yes.

And yes, Intro to Logic is a big part of it. It should be mandatory in high school. The number of people in this country who can't reason their way past an undstributed middle, or who think ad hominems are powerful, is appalling.

On even numbered days I think it's all about epistemology. The people who think that the only way to justify knowledge is faith (mostly, faith in fair and balanced authorities), or who think that it's all just a matter or opinion and mine's as good as yours ...

This whole business of nature vs nurture and chunks is fascinating, but doesn't seem of much current practical use. Finding better ways to teach people to think effectively - whether that means choosing better chunks, or having better narratives to apply to those chunks, or more analytical tools, I dunno - that would really improve the world.


Posted by: Michael H Schneider | Link to this comment | 10- 1-09 4:15 PM
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282

I don't think it's established in children, certainly ...

That's because it isn't. Or at least the underlying quality can't currently be reliably tested for in very young children. I think it is pretty stable in older children but said adults to avoid specifying a cutoff.

... "General", even applied to adults, is doing a fair amount of work there -- I have the impression (although I haven't looked at research) that IQ is fairly stable for most adults in the US. ...

By general I meant there is a high but not perfect correlation and that there will be exceptional cases involving brain injuries and the like. But "fairly stable for most" conveys the same thing.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 4:21 PM
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what sound each letter makes

Gah! (Not at you, HG.) Letters don't make sounds. They represent sounds. Sometimes.


Posted by: md 20/400 | Link to this comment | 10- 1-09 4:25 PM
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My point is that most adults don't have substantial changes in their environments of the kind that you might expect to affect IQ, like returning to school after dropping out young. I figure my IQ probably hasn't changed much since I've been an adult -- I've had a pretty stable level of intellectual stimulation all along.

It'd be interesting to do IQ research on well educated UMC people after long prison sentences, and see if IQs drop under those circumstances.


Posted by: LizardBreath | Link to this comment | 10- 1-09 4:27 PM
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I'm still going to stay skeptical until I see that research.

This is more or less my position on a great many things, supplemented by the acknowledgments that (a) I am really never going to be bothered to actually seek out the research, and (b) even if I did, I don't really have the background to competently evaluate or criticize most of these things.

And this is why we still have evolution "skeptics".


Posted by: F | Link to this comment | 10- 1-09 4:29 PM
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Consider a word problem. Alice has 2 apples, Bob has 3 apples, Carl has 4 apples, Diane has 5 apples, how many apples do the girls have? If you want to do this problem in one pass you have to hold a bunch of things in memory because you don't know what is important until the end of the problem. In this case the problem can be rewritten to be easier by putting the end first (or by taking two passes) but this may not always be the case.

Isn't just a maths problem though; suppose that some people are unable to tell that Alice is a girl's name and answer 5, are they bad mathematicians? Not really. So rewriting the problem to eliminate that issue would make it a better maths problem.

The ability to figure out what to calculate is actually two things: mathematical working out what to calculate, and non-mathematical. (Let us suppose that we see `colony of insects' and we write down y=e^x, because we know that insect populations only ever turn up in problems where we must differentiate e; are we doing maths? Well, not really.) I think that the memory thing is not mathy.


Posted by: Keir | Link to this comment | 10- 1-09 4:37 PM
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My subjective experience was this was like carrying in bags of groceries from a car. The more bags you tried to carry at once the fewer trips needed but the more likely you were to drop something.

If you look at the graphs linked to in 111 you see that the dropoff is not immediate, but rather sigmoidal, occuring over a range of approximately 2 chunks. I.e. 6-chunkers are not 6-chunkers, but 5-7 chunkers, and 7-chunkers are 6-8 chunkers, with a greater probability of failure with each additional chunk. Just as you describe.


Posted by: F | Link to this comment | 10- 1-09 4:38 PM
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Assume the second paragraph of 288 is also in italics.


Posted by: F | Link to this comment | 10- 1-09 4:39 PM
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Not because I was extra-super-special, but because I already had a couple of acquired tricks.

I'm pretty crappy at certain types of attention shifting exercises, but I scored better than I should have, because I went through and marked all of one symbol and then went back to do the others--even though you were supposed to shift between them. I still didn't do well, but my score would have been worse if I hadn't done that. I didn't think that I was "cheating." I'd learned that lesson in trigonometry. I had a teacher who liked to play with our calculator abilities by switching between sin in degrees and radians. You should have gone through and done all the degree ones first and then the radian ones. Otherwise you were too likely to click the wrong button and would waste time switching back and forth.


Posted by: Bostoniangirl | Link to this comment | 10- 1-09 4:45 PM
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260: I just liked that bit enough to want to quote it (you know, as an Autistic Analyst Asshole).

Thank you. I almost went with 'Dicks vs. Pussies' ('Rah Rah Rah! Sis Boom Bah! Goooo Dicks!' 'Booo! Yay Pussies!') Also, I would like to add here that all students are MADE OF MEAT! But the alliteration attack attracted as a... as a... oh, fuck it.

277: But it really is: there are two things here, memory & mathy, right? And if you don't have the memory, you can't do the mathy at present. But if you have the memory, you can do the mathy in a way that doesn't seem to relate to the memory in any interesting way.

I will break cover here, briefly, and say that when I was attended the institutional learning facility for triple 9 type, we would be assigned grade/classwide logic problems, quite possibly in an attempt to drive up chunk space. (At any rate, it was supposed to practice problem solving skills.) They were thorny and hairy and nasty and I was best or near-best at them in the whole grade, in spite of the fact that I was in the lowest math group there. (Probably due to my having gone to schools that were far more minority-dominated than the Nice White Kid schools.) (And the math groupings were also a form of deliberately designed social experiment, since he liked to do that.)

So the whole chunk thing isn't really math-specific or even memory-specific. It's not about how many balls you have {hums Rule Brittania}, or how well you keep track of them when they're in their boxes, or even how well organized they are when they are in their storage boxes, it's how many you balls can juggle and keep in the air at any one given moment, without dropping any. Which is apparently between five and nine, with very young children and cognitively disabled adults probably having fewer than five slots.

256: Now, if there really is very strong evidence that X is genuinely immutable, then tell the truth about it and let the chips fall where they may. But without that, what's the harm with sticking with "In practice, X seems to be very stable in people over 12," or whatever the data actually establishes.

None. Since that's about what it appears to be.

282: I have the impression (although I haven't looked at research) that IQ is fairly stable for most adults in the US.

Actually, it appears to go up until the age of 29-30, peaks and starts falling. Crystal intelligence (which Witt referred to somewhere back there) keeps rising - speed-related stuff falls. (IQ tests have a speed component, which means they has an implicit reaction time component, which also means the capability measurement can be subject to lots of spurious effects.) In theory then, IQ is supposed to relate to how rapidly one can learn. That would be the actual 'mental whateverness' part.

So! We can draw a large envelope. One the right-hand side, the lower limit of base (genetic?) abilities, which involves lots of processing subsystems that seem to be 'automatic', and on the left-hand side we've got the ability to adapt to complex external stimuli non-randomly in virtually all cases, and at the bottom we have the young who are busy building actual brain structure and and at the top the old/very old who are running just to stay in place. There's a hell of a lot of maneuvering room inside that structure. Also, the interior of that envelope appears to be bumpy and generally irregularly unsmooth. Which could be translated as, 'Damned if I know.'

248: Actually, in my shiny happy world, the purpose is to help all children maximize their individual potential.

I heartily endorse this, BTW.

max
['I am dropping my balls here, bigtime. Sleep. Sleeeeep!']


Posted by: max | Link to this comment | 10- 1-09 5:02 PM
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when I was attended the institutional learning facility for triple 9 type,

Fascinatingly mysterious.


Posted by: LizardBreath | Link to this comment | 10- 1-09 5:19 PM
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my sense is that Waldorf educators believe that there are brain development reasons why many students can't learn to read at, say, age 5 and so they defer teaching reading until an age at which, they believe, all of the students will be ready for it, in terms of brain development, and not put students in situations in which they will get frustrated. [...] [T]here's no reason why a teacher that believed that some students are limited by the immutable nature of their brains would necessarily give up on trying to teach higher level skills.

But there is a vast difference between acknowledging the impact of developmental stages for a very young child and "immutable." There are vigorous arguments in the early childhood ed field about when children are developmentally ready for this or that, and the consequences of pushing them or not. (I am biased towards the not-pushing, if you have to oversimplify.) But for a teacher to think "Oh, he's not ready yet, wait a few months," is monumentally different from "He can't do it; he's dumb."

I'm probably touchier than most on this topic because I've spent a fair bit of time in places where adults had tremendous power to permanently alter the lives of teenagers by making such judgments, and in fact often did so on the basis of overtly racist beliefs about their capacities.

Hurting people by having low expectations for them is a widespread and severe problem in the U.S. Letting a five-year-old hang out with some enriching and useful materials and narrate stories to himself until he's ready for more focused reading instruction is, IMO, not.

Fascinatingly mysterious.

max is a William Sleator novel.


Posted by: Witt | Link to this comment | 10- 1-09 5:52 PM
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And this is why we still have evolution "skeptics".

Exactly right. I was going to toss out climate change as an example when I first made that comment. I believe in climate change and evolution, but if I think really hard about that I have to admit that I am doing so on faith, not because I actually have a competent understanding of the underlying science sufficient to make an independent assessment. I mean, I tend to think of people who question climate change or evolution as idiots. But truthfully, I'm doing the same thing they are -- relying on sources I trust. For the most part with only vague memory of what those original sources were. I'm just lucky enough to be right.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 6:01 PM
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290

If you look at the graphs linked to in 111 you see that the dropoff is not immediate, but rather sigmoidal, occuring over a range of approximately 2 chunks. I.e. 6-chunkers are not 6-chunkers, but 5-7 chunkers, and 7-chunkers are 6-8 chunkers, with a greater probability of failure with each additional chunk. Just as you describe.

The actual paper .

These graphs do not justify or explain why working memory should be considered a discrete rather than a continuous quantity. You can talk about A,B and C students but ability is continuous.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 6:04 PM
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max is a William Sleator novel.

Hey! I used to love William Sleator novels when I was a kid. I have been trying to remember for ages now what books it was I read as a kid that, upon googling, appear to be The House of Stairs and Among the Dolls. I want to get these for Rory -- and then she'll probably hate them and think I must have been a big weirdo as a kid.


Posted by: Di Kotimy | Link to this comment | 10- 1-09 6:06 PM
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William Sleator is super awesome best!


Posted by: redfoxtailshrub | Link to this comment | 10- 1-09 6:11 PM
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289

Isn't just a maths problem though; suppose that some people are unable to tell that Alice is a girl's name and answer 5, are they bad mathematicians? Not really. So rewriting the problem to eliminate that issue would make it a better maths problem.

Word problems usually assume some general background knowledge. And this makes sense because a mathematician who is unable to connect mathematics with the real world is pretty useless.

In this case we could rewrite the problem to add Alice is a girl, Bob is a boy, Carl is a boy and Diane is a girl. But this would favor people who already knew this. If we change Alice to Alpha, Bob to Beta, Carl to Gamma and Diane to Delta then the problem becomes substantially harder.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 6:17 PM
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296

Exactly right. I was going to toss out climate change as an example when I first made that comment. I believe in climate change and evolution, but if I think really hard about that I have to admit that I am doing so on faith, not because I actually have a competent understanding of the underlying science sufficient to make an independent assessment. I mean, I tend to think of people who question climate change or evolution as idiots. But truthfully, I'm doing the same thing they are -- relying on sources I trust. For the most part with only vague memory of what those original sources were. I'm just lucky enough to be right.

Some of the people who question are idiots (or at least blinded by ideology) in that they say not that there are doubts (there are doubts about everything) but that the theories are nonsense and that there is no chance they are correct which is ridiculous.

The ideals behind evolution and global warming are really pretty simple. For global warming that a thicker blanket will keep you warmer, for evolution that selective breeding works.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 6:28 PM
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And this makes sense because a mathematician who is unable to connect mathematics with the real world is pretty useless.

The world of numbers and their relations is the realist thing there is.


Posted by: Irked Platonist | Link to this comment | 10- 1-09 6:44 PM
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Shorter 302: A is A.


Posted by: Not Prince Hamlet | Link to this comment | 10- 1-09 7:03 PM
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Thinking more about the issue of the immutability (or not) of working memory (not the question of education, which I hesitate to weigh in on, or the question of field dependence, which sounds dubious but I don't know much about)... maybe the Flynn effect can give us another clue.

The Flynn effect is the well-established but mysterious empirical phenomenon in which average IQ has increased substantially over the past few generations (to the point that the tests have been renormed so often that an average schoolchild in the year 1900 would have scored about 70 on today's test). Moreover it has occurred mainly in developed countries (and starts as countries start to develop) and is probably not mainly related to nutrition (since it continues well after everyone has adequate nutrition). The Flynn effect suggests that a fair amount of IQ must be due to environmental factors, because genes don't change that fast over such a large population.

The interesting thing for working memory is when you look at what subscales of IQ have changed over time. Digit Span and backwards Digit Span (which are the purest measures of working memory) have changed very little relative to performance on subtests like Raven's matrices (which is supposed to measure something more like "figuring out how to solve abstract puzzles") and Similarities (which measures competence in classifying in an abstract way, which I see as arguably reflecting cultural knowledge as much as anything, though others might disagree).

Whatever has caused the changes in IQ, it's probably not simple short interventions, but rather reflective of wholescale changes in the way our society forces people to habitually think. And -- the point -- whatever those changes are, even they haven't led to an increase in working memory capacity. (And that's even between generations; the plasticity of any given individual is probably less). Which, again, is not to say that working memory is necessarily immutable, or that the correct pedagogical thing to do is to assume that it is. But that's pretty darn intractable if even the Flynn effect doesn't touch it.

That said, I have a fair amount of sympathy for the people who worry that in practice, the effect of that would be to entrench differences and make it harder for people who have somewhat low WM to achieve to their potential. So these discussions make me kind of nervous.


Posted by: Forza | Link to this comment | 10- 1-09 7:45 PM
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That said, I have a fair amount of sympathy for the people who worry that in practice, the effect of that would be to entrench differences and make it harder for people who have somewhat low WM to achieve to their potential. So these discussions make me kind of nervous.

How would steering people out of areas in which they are at a disadvantage hurt them?


Posted by: James B. Shearer | Link to this comment | 10- 1-09 8:01 PM
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293: It's not about how many balls you have {hums Rule Brittania}, or how well you keep track of them when they're in their boxes, or even how well organized they are when they are in their storage boxes, it's how many you balls can juggle and keep in the air at any one given moment, without dropping any. Which is apparently between five and nine, with very young children and cognitively disabled adults probably having fewer than five slots.

Christ, I must be cognitively disabled (or effectively childlike), for I do not like having to keep too many balls in the air at once.*

*But yes, I know the balls of which Max speaks here are informational chunks held and managed at one time, not projects on the to-do list.


Posted by: parsimon | Link to this comment | 10- 1-09 8:05 PM
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I know the balls of which Max speaks

Can one ever really know the balls of another?


Posted by: apostropher | Link to this comment | 10- 1-09 8:20 PM
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305: Suppose WM capacity is truly immutable, and truly is the major thing that affects your ability to do whatever is the relevant problem you care about, call it Problem X or Field X. (I don't necessarily believe this, but for the sake of argument...) I can still think of two potential problems with thereby encouraging people with low WM to avoid Field X.

(a) Our ability to measure WM may still not be perfect - at the very least, any measure will be confounded with more temporary or mutable things like motivation, concentration, effort... not to mention reliance on other "tricks" like chunking or other cognitive skills. So discouraging people on account of their observed WM runs the risk of discouraging people who could actually potentially contribute to Field X.

(b) What if having people who can contribute to Field X is so helpful that it's worth even drawing people who won't be the best at it into it? (And it's worth it for them, because the renumeration / societal "blessings" of being even a rather crap Field X-er are better than that of even being a good Other Field-er?)

I kinda doubt (b) is the case for most fields, but it certainly seems logically possible that it could be. And (a) is definitely a realistic fear. And this is even if you make the assumptions that I started with for the sake of argument, which, again, I don't think you necessarily can.


Posted by: Forza | Link to this comment | 10- 1-09 8:25 PM
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307: One can only try.


Posted by: parsimon | Link to this comment | 10- 1-09 8:31 PM
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Another way to solve problems.


Posted by: Not Prince Hamlet | Link to this comment | 10- 1-09 8:38 PM
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310 is great. I like the Ig Nobels. These especially:

Economics: The directors, executives, and auditors of four Icelandic banks "for demonstrating that tiny banks can be rapidly transformed into huge banks, and vice versa, and for demonstrating that similar things can be done to an entire national economy."
Literature: Ireland's police service, for writing more than 50 traffic tickets to one Prawo Jazdy. (As it turned out, whenever the Irish cops pulled over a motorist with a Polish driver's license, they mistakenly recorded the Polish word for driver's license, "Prawo Jazdy," as the driver's name.)
Biology: Fumiaki Taguchi, Song Guofu, and Zhang Guanglei, of the Kitasato University Graduate School of Medical Sciences, "for demonstrating that kitchen refuse can be reduced more than 90 percent in mass by using bacteria extracted from the feces of giant pandas." (Paper: "Microbial Treatment of Kitchen Refuse With Enzyme-Producing Thermophilic Bacteria From Giant Panda Feces," abstracted in the Journal of Bioscience and Bioengineering, Vol. 92, No. 6, 2001.)

Posted by: Witt | Link to this comment | 10- 1-09 8:50 PM
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308

Our ability to measure WM may still not be perfect - at the very least, any measure will be confounded with more temporary or mutable things like motivation, concentration, effort... not to mention reliance on other "tricks" like chunking or other cognitive skills. So discouraging people on account of their observed WM runs the risk of discouraging people who could actually potentially contribute to Field X.

But this is just saying you can never do any steering or sorting because you might make a mistake. But this makes no sense. The tests just have to be good enough to improve things on average. If you don't steer someone out of X you risk having them fail when they could have made a real contribution elsewhere.


Posted by: James B. Shearer | Link to this comment | 10- 1-09 8:54 PM
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And this makes sense because a mathematician who is unable to connect mathematics with the real world is pretty useless.

Eh, I doubt that this is at all true in any useful way. If you talk to mathematicians, they don't really care about the real world & maybe you get useful stuff out of them, but really, the reason mathematicians study primes is because they are there & isn't that cool?

And maybe it turns out that primes are really handy for cryptography, but that wasn't the motivating factor for a long time.

(Or, yay formalism.)


Posted by: Keir | Link to this comment | 10- 1-09 10:22 PM
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Isn't math supposed to be unreasonably effective?


Posted by: eb | Link to this comment | 10- 2-09 1:03 AM
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313: GH Hardy, "A Mathematician's Apology".

"If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and less mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean...is not the position of an ordinary applied mathematician in some ways a little pathetic? If he wants to be useful, he must work in a humdrum way, and he cannot give full play to his fancy even when he wishes to rise to the heights. 'Imaginary' universes are so much more beautiful than this stupidly constructed 'real' one; and most of the finest
products of an applied mathematician's fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts."

http://www.math.ualberta.ca/~mss/misc/A%20Mathematician%27s%20Apology.pdf


Posted by: ajay | Link to this comment | 10- 2-09 7:59 AM
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And, of course, the killer line, "No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems very unlikely that anyone will do so for many years." This written in November 1940...


Posted by: ajay | Link to this comment | 10- 2-09 8:02 AM
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315: Hardy is a fun read, but in the final analysis, sort of a total dick in a nerdy way.


Posted by: JP Stormcrow | Link to this comment | 10- 2-09 8:08 AM
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I truly think that being a mathematician is the job where you will be faced with the fewest possible ethical dilemmas. I can't think of another job that doesn't intersect at least some decision.


Posted by: heebie-geebie | Link to this comment | 10- 2-09 8:49 AM
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I think he's right. Number theory is beautiful, and facets have found recent application in cryptography, but it's been very distant from anything applied other than that. The quantum physics relevant to nuclear weapons is nonrelativistic. Hardy's number theory book is great.


Posted by: lw | Link to this comment | 10- 2-09 8:54 AM
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318

I truly think that being a mathematician is the job where you will be faced with the fewest possible ethical dilemmas. I can't think of another job that doesn't intersect at least some decision.

I don't see how being an academic mathematician is much different from any other academic job. You make lots of decisions about how to treat your students and colleagues and what to work on.


Posted by: James B. Shearer | Link to this comment | 10- 2-09 8:59 AM
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I truly think that being a mathematician is the job where you will be faced with the fewest possible ethical dilemmas. I can't think of another job that doesn't intersect at least some decision.

Wasn't G.H. Hardy ever faced with the decision of whether to pass a student from Calc 2 who couldn't find the intercept of a line?


Posted by: Cryptic ned | Link to this comment | 10- 2-09 9:00 AM
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Number theory is beautiful, and facets have found recent application in cryptography, but it's been very distant from anything applied other than that.

Well, "being the foundation of modern cryptography" is a fairly big 'that' to be other than.

The quantum physics relevant to nuclear weapons is nonrelativistic.

I'm not even sure that you necessarily need quantum physics to build a nuclear weapon. Atomic physics, yes.

Using relativity in warfare had to wait for (IIRC) the launch of the GPS satellites.


Posted by: ajay | Link to this comment | 10- 2-09 9:01 AM
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Dammit, pwned by James B. Shearer yet again.


Posted by: Cryptic ned | Link to this comment | 10- 2-09 9:03 AM
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||

I see the IMF is concern trolling the UK:

http://www.guardian.co.uk/politics/2009/oct/01/nhs-debt-imf-britain

>


Posted by: nattarGcM ttaM | Link to this comment | 10- 2-09 9:11 AM
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I think it's worth noting in this thread that this Forza character really oughta comment more often. I am very much enjoying the contribution.


Posted by: Di Kotimy | Link to this comment | 10- 2-09 9:18 AM
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What's the IMF doing saying anything about the UK? I am embarrassingly confused about what exactly the IMF does, but I thought it dished out foreign aid on the condition that recipient governments comply with deeply flawed economic ideologies -- in the absence of the foreign aid, which I don't believe the UK is a recipient of, why would the IMF be issuing statements?


Posted by: LizardBreath | Link to this comment | 10- 2-09 9:20 AM
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It's ideological bullshit, as far as I can tell. The UK has one of the lowest health-care expenditures per capita of any first world nation. The IMF should be shutting the fuck up, basically.


Posted by: nattarGcM ttaM | Link to this comment | 10- 2-09 9:27 AM
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I don't see how being an academic mathematician is much different from any other academic job. You make lots of decisions about how to treat your students and colleagues and what to work on.

I mean a pure mathematician. Teaching is fraught.


Posted by: heebie-geebie | Link to this comment | 10- 2-09 9:27 AM
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A pure mathematician, not teaching and not working on any practical problem would face all sorts of ethical dilemas, like who to rob for grocery money.


Posted by: Moby Hick | Link to this comment | 10- 2-09 9:31 AM
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The IMF should indeed be shutting the fuck up about the NHS. But it issues economic reports on everybody, even the U.S. (I have a friend who works there, and when I ask him to explain what the IMF does he says "maintain the balance of payments," but it seems to do a lot more and a lot less than that these days. I will raise this NHS thing with him next time I see him, because it's obviously, as ttaM says, ideological bullshit.)


Posted by: Bave Dee | Link to this comment | 10- 2-09 9:32 AM
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329: Duh. The IMF.


Posted by: heebie-geebie | Link to this comment | 10- 2-09 9:36 AM
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331: It occurs to me that just robbing the grocery store is a simpler solution. Don't make me write the proof.


Posted by: Moby Hick | Link to this comment | 10- 2-09 9:37 AM
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Isn't Shearer an applied mathematician? They're like that.


Posted by: Walt Someguy | Link to this comment | 10- 2-09 9:38 AM
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329: what, there's no such thing as a research fellowship nowadays?


Posted by: ajay | Link to this comment | 10- 2-09 9:41 AM
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334: A "research fellowship" is just the euphemism universities use because if they post an ad asking for subjects to be locked-up for twelve months and given an experimental medication, the subjects are going to demand better reading material.


Posted by: Moby Hick | Link to this comment | 10- 2-09 9:54 AM
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Good line I remember from a New Scientist article on the physics of black holes:

"Now, what would I experience if I jumped into a black hole - or, as we say in academia, pushed a graduate student in?"


Posted by: ajay | Link to this comment | 10- 2-09 10:14 AM
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A rat would be able to write a more complete report of the experience, but we don't have that kind of money in the budget.


Posted by: Moby Hick | Link to this comment | 10- 2-09 10:16 AM
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||

Cross-posted in Di's thread.

Is there anybody with access to Wiley Science journals who would be willing to e-mail me the pdf of an article.

If, yes, please let me know with an e-mail to the linked address.

|.


Posted by: Bostoniangirl | Link to this comment | 10- 2-09 12:36 PM
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