[Link] Why the kids don’t know no algebra
Post by fellow LW reader Razib Khan, who many here probably know from the gnxp site or perhaps from his debate with Eliezer.
A few days ago I stumbled upon a really interesting post. And I’m wondering if my readers are at all familiar with the phenomenon outlined here (it was a total surprise to me), The myth of “they weren’t ever taught….”:
With all this I am not saying conditions which are non-hereditary are irrelevant. What I am saying is that we can’t ignore the shape of the pre-existent landscape before we attempt to reshape it to our own image. Excoriating teachers for having pupils who can’t master mid-level secondary school mathematics is in some cases like excoriating someone for the fact that their irrigation canals from the plains into the mountains are failures. You need to level the mountains before your canals can work (or, barring that design and implement a mechanical system which will move water against the grade). Easier said than done. E. O. Wilson said of Communism, “Great Idea, Wrong Species.” The reaction of Communist regimes to this reality was brutal and shocking. Obviously the modern rejection of unpalatable aspects of human nature are not so grotesque. But they have a human toll nonetheless. I’m skeptical that this generation will pass before we have to acknowledge these realities and calibrate our policies accordingly.
Stage One: I will describe this stage for algebra I teachers, but plug in reading, geometry, writing, science, any subject you choose, with the relevant details. This stage begins when teachers realize that easily half the class adds the numerators and denominators when adding fractions, doesn’t see the difference between 3-5 and 5-3, counts on fingers to add 8 and 6, and looks blank when asked what 7 times 3 is.
Ah, they think. The kids weren’t ever taught fractions and basic math facts! What the hell are these other teachers doing, then, taking a salary for showing the kids movies and playing Math Bingo? Insanity on the public penny. But hey, helping these kids, teaching them properly, is the reason they became teachers in the first place. So they push their schedule back, what, two weeks? Three? And go through fraction operations, reciprocals, negative numbers, the meaning of subtraction, a few properties of equality, and just wallow in the glories of basic arithmetic. Some use manipulatives, others use drills and games to increase engagement, but whatever the method, they’re basking in the glow of knowledge that they are Closing the Gap, that their kids are finally getting the attention that privileged suburban students get by virtue of their summer enrichment and more expensive teachers.
At first, it seems to work. The kids beam and say, “You explain it so much better than my last teacher did!” and the quizzes seem to show real progress. Phew! Now it’s possible to get on to teaching algebra, rather than the material the kids just hadn’t been taught.
But then, a few weeks later, the kids go back to ignoring the difference between 3-5 and 5-3. Furthermore, despite hours of explanation and practice, half the class seems to do no better than toss a coin to make the call on positive or negative slopes. Many students who demonstrated mastery of distributing multiplication over addition are now making a complete hash of the process in multi-step equations. And many students are still counting on their fingers.
The author is involved in education personally, so is posting their own reflections as well as what others report to them. In personal correspondence they explain that this phenomenon is common among children of average intelligence. The lowest quartile presumably would never have been able to master many of these rules in the first place. Some of the information resembles the stuff that a friend of mine experienced when he went in to do tutoring for disadvantaged students in Boston when he was getting his doctorate at MIT. At first my friend was totally taken aback at the level of ignorance (e.g., the inability to see the relationship between 1⁄10 and 10⁄100). Today he works at a major technology firm as a scientist, but continues to be involved in mentoring “at risk” kids. At some point you have to muddle on. He does his best, and does not indulge in the luxury of shock and disappointment. That helps no one.
This matters because American society is notionally obsessed with education. All this isn’t too clear or important to be frank when you aren’t a parent. It’s somewhat in the realm of the abstract. That changes when you become a parent. Suddenly you become immersed in the data of your local schools, and begin to weight various options to optimize your child’s schooling experience. Of course the real differences in school metrics have not only parental relevance, they matter in terms of national policy and attention. Both the political Left and the Right have their own pet solutions. More money, reform teachers’ unions, charter schools, vouchers, etc.
But the biggest problem at the heart of the matter is the fundamental populist drive to ignore human difference. American schools were designed to produce the citizen, and the citizen has the same rights and responsibilities from individual to individual. In some ways the public school system as it emerged in the 19th century was a project by the Protestant establishment to assimilate white ethnics, in particular Catholics (who of course created their own alternative educational system to maintain cultural separation and distinctiveness). In the 21st century the drive to produce H. Americanus seems quaint, rather, we want to citizens of the world with skills and abilities to navigate an information economy.
What American society on a deep philosophical level, no matter the political outlook, detests acknowledging is that a simple and elegant public policy solution can not abolish human difference. Some children are more athletic than others, and some children are more intelligent than others. Starting among conservatives, but now spreading to some liberals, is a rejection of this premise via blaming teachers. The premise is bewitching because it presents tractable problems with solutions on hand. Here is John B. Watson, the father of behaviorism:
Give me a dozen healthy infants, well-formed, and my own specified world to bring them up in and I’ll guarantee to take any one at random and train him to become any type of specialist I might select – doctor, lawyer, artist, merchant-chief and, yes, even beggar-man and thief, regardless of his talents, penchants, tendencies, abilities, vocations, and race of his ancestors. I am going beyond my facts and I admit it, but so have the advocates of the contrary and they have been doing it for many thousands of years
I think if Watson were alive today he’d have to admit he was wrong. Your ancestors are not destiny, but they are probability. If your father plays in the N.B.A., the probability that you will play in the N.B.A. is not high. But the probability is orders of magnitude higher than if you are a random person off the street.
I agree that the “they were never taught” fallacy is common among new teachers- as is the attempt to cover years worth of material in a few short weeks at the beginning the syllabus. I see this all the time with new teachers, and often have to insist that they are taking the wrong approach- students who can’t add fractions aren’t going to acquire it in two weeks.
Where I disagree is the idea that these student can’t learn the material (they just can’t catch up to the material in a few extra weeks of time)- I’ve known a few teachers whose students consistently perform better then their peer group, and retain the information into their next few courses. For one fifth grade teacher we tracked, by highschool his students were moving into advanced math courses at a much higher rate than students who passed through other fifth grade teachers at the same school. The value-added teacher research bares out the facts that good, experienced teachers can produce long-term learning gains in most of their students.
My suspicion is that many grade-school level teachers don’t understand the material they teach (a surprising number of grade school teachers are essentially mathematically illiterate) and can inflict a fair amount of damage to student’s understanding.
The original post seems to say that the students do acquire it in two weeks, they just forget as the class moves on to the next topic. Does that sound right to you?
I will be starting as a high school maths teacher next year. I really really wish I knew how to fix students who arrive in year N and haven’t learned the critical skills they were supposed to have mastered at the end of year N-1. Teachers don’t choose curricula, and curricula are too dense for mainstream students. We already have more than one semester’s worth of material to get through in a semester.
If a bunch of students arrive in my class in February, and the mid year exam is in June, and they don’t know any of the stuff they need for this year, how do I fit all the extra material in? This is not a rhetorical question!
Extra lessons for those who want to do it.
This means extra work for you, but you could try some strategy to reduce the work. For example make a list of Khan Academy videos related to the missing materials, put it on your web page, start your first lesson with a (not graded) background knowledge test, and recommend everyone to watch those videos. You could also make some additional exercises for voluntary homework. -- The general idea is to do something once and reuse it every year.
First, relax and realize you can’t fix everything. That doesn’t mean you shouldn’t try, but you need to set realistic goals or you’ll burn yourself out really quickly. The students really need more lesson time, and more practice time. If the student has resources you can refer them to one of the many tutoring centers designed to address this sort of thing. If they don’t have resources, most attempts at solutions will involve a lot of your personal time, which will already be highly strained as a new teacher.
Ask the other highschool teachers you work with if they can recommend a good tutoring service to refer students to. Also, ask them how they attempt to solve these sort of problems? At one charter school, the math teachers set up an after school program attempting to mimic the structure of the chain tutoring centers (Sylvan learning center, etc). Not something to think about setting up your first year, but if you keep an eye towards the future...
Who is “we”?
A school district outside DC. Tthe district was hoping to implement metrics to gauge teacher quality to determine pay under the previous administration. The project was scrapped when the new chancellor of schools came in.
I have heard anecdotally from a number of teacher acquaintances that thick adults consistently start as thick kids. It’s possible that the apparently-thick 5yo will turn out to be a genius, and that the apparently-bright 5yo will turn out to be a doofus, but it’s not the way to bet.
The other problem with educational snake-oil appears to be that it tends to be tested on bright kids—who would learn to read off cereal packets and street signs. So whatever woo you put them through, they’ll do not too badly. The woo then fails when average or thick kids are put through it.
Probably requires overcoming autism/learning disability.
Regression towards the mean, football?, long-term drug use, disease.
Most teachers don’t want to take responsiblity for not turning dumb students into smart students. As a result they are no good source for knowing whether it’s possible to turn dumb students into smart students.
Charles Murray wrote an excellent book title “Real Education” where he explores such issues rather closely and in particular what can be done to improve education systems in light of this information. I found it well written and meticulously researched, I very much recommend it to fellow LWers.
In relation to his book he also did this talk which is a ok overview off his key points.
His argument appears quite solid at first glance, but it has to be decoupled from reactionary politics first. I actually agree with the “core” of even the controversial bits about the need for ethical instruction, etc, but NOT in the way he appears to mean it! Damn, if I had the patience and the time, I’d have put a liberal spin on those same ideas to see how it would look
Except for the bit where he gives an oh-so-fake nod to the happiness and personal development of the “mediocre” students, while stressing that they don’t really matter as individuals. That’s so misanthropic in connotation! (I’m judging by summaries/reviews of the book and bits of the video, not the complete work.)
You should calm down Murray isn’t reactionary he’s just a smart and data conscious moderate conservative thinker. He wants to give poor people enough free money so they can live decently with or without a job. I mean he doesn’t even think democracy is a bad idea! Weak sauce! ;)
We’re on good terms and I know you said this with good intent and I hope you realize I was just citing a relevant well researched book (which I think you really should read before judging) not pushing an agenda. Also remember LessWrong readers are smart, tolerant and sane enough to read material written by people with different politics without risking spontaneous combustion. If they want liberal spin I’m sure they can do it for themselves. And if reading relevant research on stuff can turn them “non-liberal” on that issue… well aren’t you ok with people discovering their informed preferences or changing their ideas about how the world works?
The reason I’m writing out this comment is because what your wrote unfortunately seems a lot like a purely political take. I don’t think that’s cool since we don’t see this sort of stuff for moderately left wing leaning authors, why should we for moderately right wing ones? The reason why I think this isn’t ok is that just by mentioning the guy is blue instead of green you’ve reduced the probability of green people reading him. Especially since you exaggerated his blueness. And you are smart enough to know this.
Remember LessWrong is 3% conservative and ~30% socialist and another ~30% “Liberal”! People say “Wow” when they see someone being socially conservative.
Do we really need majority ideological biases and group feelings reinforced and further privileged?
You’re very correct! And I’m just having a cranky evening, unfortunately. Some days I just seem to take so much issue with people’s tone, to the detriment of addressing their point! And I want to seek out and challenge contrarianism, too… My intellectual behavior is very insecure, I’d say.
Also, when it comes to you personally, I’m very open to the darndest things you link and wouldn’t take much issue if you showed me someone’s endorsement of baby-eating (oops, you did actually propose a policy of baby-eating); I was trying to defuse a perceived bias only for the public’s benefit.
But it’s like I said before—it might be the wisest and most truth-seeking 3% (Vladimir_M alone has more life experience and practical wisdom than many other folks here combined, I’d say), the rest of us might be lagging behind in the race of ideas! I wouldn’t have gotten so worked up if I didn’t fear that might be the case.
It was just a modest proposal!
Ba-dum-tssh!
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http://en.wikipedia.org/wiki/Cultural_hegemony
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Here:
So when you’re off-handedly saying that something is “good sense”, the long Western educational and cultural tradition of left-liberalism, which is undoubtedly the most influential one around, might have something to do with your implicit thought process. It’s not an agency fiction because I’m not suggesting that there’s a cackling university professor somewhere who plotted molding your idea of “good sense” to include a degree of PC-ness, but merely that it’s mostly the memes that don’t go against the intellectual classes’ convictions and preferences which tend to survive, so ideas kind of flow towards an intellectual-dominated consensus.
Again, I’m not even sure that this is a bad thing.
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I see, I see, but how much of that is mere pragmatism and how much is you rationalizing the virtue of politeness, which we’ve been raised with among other such ideology-related memes?
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This seems like basic neurophysiology. Short-term memories and skills dissipate. It takes time to rewire the brain for permanent storage of a given isolated unconnected uninteresting memory. Maybe someone can find the links?
From my tutoring experience, it takes a lot longer than “hours” for rote memorization to take permanent hold. And rote is how math is usually taught, or at least how children with low math aptitude learn it. For an abstract concept like line slope, not related to anything intuitive, it would take about 1000 problems solved by such a student, with spaced repetition over several weeks, before the relevant memory decay rate increases from minutes or hours to months.
In contrast, a person with high aptitude for math will easily fit the new memory into her existing jig saw puzzle of other memories (“oh, this makes perfect sense, given A, B and C!”) and, in effect, has to memorize a lot less random data, so the required amount of repetition is probably an order of magnitude less.
Reading the blog post that this one links to made me immediately think of SRS—isn’t that exactly what it’s design for? Don’t focus on the stuff you just learned, but on the stuff you are about to forget. Maybe we should be doing many-year SRS for our students and doing more cumulative testing and practice. Or maybe I’m still naive and blaming the teachers! I guess I’m just not a cynic.
Agreed. Last I checked (don’t have a reference right now, unfortunately), Khan Academy was experimenting with a SRS-like feature in their system, in order to tackle this very problem. Everyone tends to forget stuff they’re not motivated to use—it’s not at all limited to “problem” students.
IIRC, I was told in
#lesswrongby a KA contractor or employee that they knew of SRS and some were thinking about how to integrate it.Awesome! This makes me more interested in KA as an organization.
Well, I’d be more impressed if they had already integrated it. They (some members) have known of it for probably years at this point, know it’s a big win in review efficiency, and have a review process already coded and running. All the SRS algorithm is really just a sort of exponential for scheduling the next review! It’s not any actual new functionality; my programming intuition is that it should be pretty easy to add, so that they still haven’t rather annoys me. Lost opportunities...
Any information on the stability of learning from the Khan Academy?
Specifically among the children this post deals with—pre-highschool. How many children regularly study with K.A. videos? Does anyone force them to do so, as they are forced to attend school? I expect this is rare, and mostly present with exceptionally able children and/or parents.
Excellent point, this would be very useful information. I second this request.
Education is full of irrationality. You can’t say anything with bad connotations about children, because that’s a big taboo. You can’t say that a child is too stupid to understand something. You can’t say that if a child always refuses to cooperate, it is impossible to teach them. The official hypothesis is that each child is perfect, so if they don’t become Einstein, it’s someone else’s fault, and we should express moral outrage about such loss of a talent. In recent years, the consensus seems to be on blaming the teachers. So it is refreshing to hear an alternative explanation.
But I think that difference in IQ is only part of the story. It explains why some people will always fail. But it does not explain why recently more people fail at school (at least in my country it seems so). Here is an interesting comment from Scott Adams’ blog:
This fits my model that recent bad outputs of school systems are caused by bad inputs. But the causes of the “bad inputs” can be both in biology or in environment. If a child is retarded, that’s bad for the school results. But if parents don’t cooperate in their child’s education (if the child instead of making their homework spends the whole day with Facebook or Counter-Strike), that’s bad too.
Not publicly, but teachers know it, or at least those of my acquaintance.
Yeah, I meant that you can’t say it outside of the school. If you do, a typical reaction is: “If you don’t like children, you are not a good teacher.” Because it is assumed that if you like children, you would never say anything with a negative connotation; and if you don’t like them, you are a psychopath and should be kept far away from them.
So, either the children are perfect, which means that if they don’t get good grades, you are a bad teacher; or you disagree that the children are perfect, which proves that you are a bad teacher. -- The only way to signal that you are a good teacher, is to give best grades to everyone. Some teachers use this strategy, knowingly or not.
Many managers use this strategy during industry performance reviews, as well.
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You know what’s even bigger taboo? Blaming culture and attitudes.
Nor should you be allowed to. (In public, that is—I haven’t yet gone so totalitarian as to propose control of private conversations.) Instead, a neutral language such as “genetically disadvantaged” should be available for accurate and objective use, without any connotations of oppression or uncharitable attitude. Yes, that means that I’m against today’s extreme hypocrisy but for a climate of political correctness, and for some form of censorship!
People who inherited or “won” more intelligence early on should NOT be raised atop the goddamn miserable status heap by the sole “virtue” of said intelligence! This is just one incident of many that convince me that the anti-PC crowd is low-status largely not because they tell inconvenient truths (although the brightest among them sure do), but because they are unwilling to learn basic social skills. And because they have a number of… ethically shaky aspects about their thought.
(Oh boi! I’m so hungry I could eat an octorok and −10 karma!)
What, you never heard of a euphemism treadmill? Choose any “neutral term” you like as a synonym for “stupid”; there’s no kid in the world so “genetically disadvantaged” that they won’t realise what you actually meant to say. You do know that ‘retarded’ was once a perfectly neutral term, right? It literally just means “slower than the others”. It acquired its modern connotations because changing the word doesn’t change the phenomenon and doesn’t change the way people react, either.
It might be a palliative while we’re looking for a real solution. I actually pointed out the root of the problem right there: the godawful connection, overt or implicit, between the raw intellectual power and “General Worth” (incoherent concept, but sadly an emotional given) of a person in society’s eyes. Changing the language is, I think, a necessary but not sufficient part of breaking that habit of thought. When combined with other tactics, linguistic manipulation can be an effective tool, even working for the common good—see “Gay”.
What do you propose as the new measure of worth? I think you’ll find that these things are pretty hardwired.
This is part of why euphemisms are so dangerous—they are often phrases which aren’t accurate. Intelligence is not just genetic. Parasite load at an early age, nutrition, lead exposure, some aspects of parental care can all impact intelligence.
Are they though? This has a lot to do with what one means by status. If anything we have the opposite problem. Look at how many people use “I could never do math” or similar statements as a status raiser.
If you think the “anti-PC crowd” is low status that may say more about who you spend time with than anything else. In much of the US, even in fairly left-wing areas, self-identifying as not PC can be quite effective as a status raiser. People who go out of their way to be “anti-PC” might be low status but that’s more because that often involves high degrees of obnoxiousness, is often a cover for genuine bigotry (e.g.someone claiming that their use of the word “kike” is because of their refusal to be be PC), and are defining themselves as against something else. It is very hard to be high status when one is defined in terms of one’s opposition. But that’s all distinct from being blunt and saying “stupid” when one means some form of “intelligence substantially below the average or the level generally necessary to function in society”.
What is ethically shaky here? That there are genuinely stupid people? That we should acknowledge it? That some of that is genetic?
Exactly. It’s like if someone would decide that the word “green” is offensive, so we need to use “chlorophyll-rich” instead. Problem is, many green things don’t contain chlorophyll at all.
It’s teaching people to immediately jump to a wrong conclusion. And adding a moral connotation that who doesn’t immediately jump to the same conclusion, is an evil person. (And we obviously shouldn’t let evil people teach in schools or speak about education.)
You just shouldn’t say it at all. Unless they really are 100% 0 variance, not one in a million people with their brains will learn it trying their hardest you shouldn’t say this in public because it might damage their chances. Stupid is especially bad because it’s more general than you need to be. If someone has a brain that has some poor cognitive abilities, but others that are normal or good (specifically, I am talking about almost everyone) they shouldn’t be told they are stupid for doing below average in some area because stupid is a general term.. “Stupidness” is often limited to a particular area.
When is it an advantage to the person being talked about to hear that they are fundamentally incapable of doing something over hearing that it is not worth their trying to do it?
Also, stupid and genetically disadvantaged are not synonyms.
What makes you think the anti-PC crowd is low-status? That doesn’t ring a bell. I have no strong belief either way.
also, do you really think this is an accurate reflection of reality? “because they are unwilling to learn basic social skills.” It’s fine if you just wanted to have a go, but X is experiencing negative outcome Y “because they are unwilling to learn” is much more often claimed than is true. It’s just so convenient and just world-ey. Also, “social skills” may in this case actually consist solely of deference to majority opinion.
Where I come from, being overltly PC is low-status. Where I live now, being anti-PC is low status. In both places, unsurprisingly, people think their own attitudes are normal.
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Here’s the comment I posted on gnxp.
Teacher quality does matter.
From the underlying paper (pdf):
Reading this, two comments occur to me immediately:
Is there a simple explanation of how they estimated the “teacher quality” variable? The paper is written in a very complicated and abstruse way, and I don’t have time to wade through it, but surely the basic idea, if valid, should be explicable in a paragraph of plain English.
Even if we take the findings of the paper at face value, the “$100 trillion” estimate is a complete non sequitur. Can the entire effect really be purely because better teachers impart greater wealth-producing skills? Or could it be, at least partly, because they impart advantages in zero-sum signaling and rent-seeking games?
One of the main points of the paper is that typical measures (teacher experience, education, etc.) are not good predictors of quality. The authors spend a lot of time developing a phenomenological model of teacher quality based on comparing student achievement within a school, to reduce the impact of greater variation in populations between schools. From the paper:
This claim is developed in a different paper (linked in the first link I posted), which draws from the paper I linked to discuss teacher quality. Unfortunately, that paper is paywalled, but I have extracted the relevant part, section 4.2, as a pdf (only 2 pages).
They used data comparing performance on math and science tests to economic growth for different countries. They then calculated the improvement in economic growth due to an improvement in student performance from replacing lower-quality teachers with higher-quality teachers. Obviously there is a simplifying assumption of linearity being made for the correlation of test performance and economic growth, and test performance as a measure can fall afoul of Campbell’s Law.
Assuming your summary is correct, it would be an insult for the cargo cults to use them as a metaphor for this sort of “science.”
Honestly I don’t have much commentary to add to this since I agree with Razib’s argument. The comment section is usually worth reading too since he moderates it vigorously. Despite this still being the case with this particular post I found myself rolling my eyes at some of them which is also why I giggled at Gregory Cochran’s comment:
Don’t ever change! (^_^)
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Well, better downvotes than the alternatives. Razib perma-banned me a few days ago.
Update: Razib emailed me saying I am unbanned. When I asked why, he said it was due to this LW thread.
Excellent, +1 to social pressure!
Why? I really like reading both of you and would like to know what caused the conflict.
See my Google+ summary.
(I’m only ~80% sure I was in the right, so I kind of regret bringing it up here: doing so reminds me too much of various malcontents online who get what they deserve but then go around eternally whining about it, making them look even more like prats than the original errors did.)
You didn’t deserve to be banned.
I am very saddened. (Okay, that’s a lie: I’m boiling with anger and I want to publicly beat you both up, evict you from the tribe and rule as alpha.) I expected much more civility from you both.
AFAICT the reason it started escalating is that neither of you made an effort to smooth over small status aggressions. (“Citations are otiose.”) That probably comes from hacker culture that prides itself of being concise and to the point with little regard for social implications, until someone gets told to choke on a bucket of cocks.
He got very angry and very rude over small aggressions, though, and his personal stress is not an excuse. But you were in the wrong as well to keep talking when he told you to shut up, that was provocation.
Yeah, it’s a pity, I have great respect for both Gwern and Razib, and quite appreciate Razib’s heavy-handed approach to moderation, I’m fine with him calling people fucking retards when they deserve it.
Yeah, I’m occasionally guilty of that too. I’m quite impatient with excessive verbiage, even though I should update on the fact that it is actually appreciated in many situations, and not just in high school essays where you are judged by word count.
Quietly removing stupid comments seems to be strictly superior than using slurs. Faster, prunes useless discussions, dissuades trolls, countersignals confidence in your intelligence.
It’s possible to be both polite and concise, but it requires more thought.
False positives happen. I think you will agree that Razib’s attitude on average keeps the comment section pretty readable.
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It is nearly always pointless to debate things with big egos who are in their own domain of power. Your comment nails it:
Why should most students even bother with algebra? Their parents almost certainly don’t use it. It’s more-or-less a hazing ritual. And it’s entirely reasonable to not want to put up with being hazed.
Sure, I’ve got to understand algebra because I program computers. But not very many people do anything like that.
Imagine that instead I were opening a cupcake shop. High school algebra is full of problems like this one: My fixed costs for my cupcake shop are $100,000 per year. My cost of ingredients for a cupcake is $0.30, and I think I can sell 100 cupcakes per day. What do I have to charge per cupcake to have a positive net?
So, the algebra way to do this is to write out an equation, 100000 = 365*100*(c-0.30). Then solve for c. And if I were in this situation and I had been paying attention in high school algebra, I could transform this to c = 100000/(365*100) + 0.30. But if I hadn’t, here’s what I would do: I would say that a cupcake costs around $3, plug $3 into that equation, and immediately see that I’ll be a bit short. So maybe now I have to try $3.25, which will work. Boom, problem solved, no algebra.
Bret Victor calls this process “scrubbing”.
And, of course, there’s basically never a situation where you need a quadratic equation. I guess figuring out areas/volumes, but the scrubbing approach will work just fine there.
Realistically, if I were planning my cupcake shop, I would use a spreadsheet, which unfortunately nobody learns in high school. That’s too bad, because lots more people use spreadsheets than algebra.
It seems like part of the problem is that people don’t really know or agree what mathematical education is for. If we knew for what reasons or purposes we were teaching everyone math, that might help us figure out what math they should learn.
It seems to me like various purposes for math education include:
Teaching students how to work with numerical and geometric quantities — for “real-life” purposes such as making change, planning schedules, and measuring furniture to put in a house;
Teaching problem-solving techniques and mathematical intuition — to improve general problem-solving ability as an intellectual skill;
Teaching techniques of explicit reasoning and methods of logical proof — such as might be applied to analysis of arguments in everyday life; or in law, politics, or other subjects too;
Preparing some students for science, engineering, computing, and other subjects that require particular mathematical techniques (e.g. calculus for physics);
Preparing some students (very few!) to become mathematicians.
More generally, people don’t even agree what education is for. It could be:
preparing people for their future jobs;
preserving the knowledge of humankind, maintaining culture;
improving people mentally, creating better neighbors and citizen.
Generally, all these goals are considered good, but sometimes they are in conflict, if you try to optimize for one of them too much. For example the first rule, in extreme, would require learning only details related to one’s future job, nothing more; but students could learn more details, and have more practice when they finish the school. The second rule, in extreme, would require teaching everyone everything. The third rule requires a value judgement what makes a person good citizen, and in extreme, it would require focusing on those skills and ignoring everything else.
In many discussions about education, one of these ideas is assumed implicitly, and then there is a suggestion how to get closer to this goal… usually at the expense of the remaining goals, which is why other people protest against the suggestion.
When writing out equations using an asterisk as a multiplication symbol prepend it with a backslash like this:
”3 \* 4″. Markdown treats anything between two separate asterisks as italics and backslash is the escape character.
Thanks.
I’m not so sure about that. They way computers are integrating into society it seems likely that the status of people who can’t at least do basic programing will soon be similar to the status of illiterate people ~100 years ago.
I think anyone who finds themselves fully agreeing with this article (in particular the assertion that teachers “can not abolish human difference”) owes it to themselves to read MindSet by Carol Dweck (or at least familiarize themselves with her research; I actually didn’t like the book that much). She argues that in almost all cases, initial differences in intelligence among children can be virtually erased by fostering a “growth” rather than “fixed” mindset (definitions here: http://en.wikipedia.org/wiki/Mindset_(book) )
The basic idea is that while we do have some amount of inborn talent (intelligence say), this is merely a starting point and can (easily) be improved upon. The problem is, we implicitly teach kids the fixed mindset (that their level of talent/intelligence can’t be changed) when they’re young, and as a result they sort themselves neatly into tiers based on their initial level of intelligence, and then stay that way. In this manner teaching the fixed mindset seems to be a self-fulfilling prophecy of sorts—we tell kids they can’t get any smarter than they are, and as a result they don’t even try.
Thus the mindset theory explains the phenomenon of “dumb/smart kids growing up into dumb/smart adults” equally well as assuming that fixed talent actually exists. Moreover, research has shown that adopting the growth mindset causes increases in performance, productivity, grades, etc. - in short, it actually makes people smarter. This works whether you do it subconsciously (ie, priming experiment subjects with growth mindset ideas) or consciously (ie, actually telling people about the mindset concept and pushing them towards a growth mindset). There are a lot of really dramatic results given in the book that can’t be explained at all assuming fixed levels of talent.
Erase the difference, are you sure? I agree that it’s pretty likely that the growth mindset is more beneficial than the fixed mindset, but is there any evidence that the addiitional benefit of the growth mindset doesn’t improve smart kids as much as it improves dumb kids (on average!), leaving a difference still there?
(Your link is broken btw)
I was surprised by that too—is the growth mindset not that helpful for smart children?
I suspect that somehow the message “the other kids will catch up with you” got across, and become a self-fulfilling prophecy. Or the lessons were focused on the parts where the slower kids could catch up, ignoring the parts where the faster kids could get further ahead.
I don’t think many researchers and educators are actually claiming that things like adopting the growth mindset will “close the gap”—that would be a spin added by journalists, etc.
I get somewhat when I read about “closing the gap” as a goal of education; it gives the impression that a policy that improves all children is strictly worse than a policy that improves only stupid children by the same amount.
Well, equality is one of the human values. I think the journalists are adding this spin because readers want to read it; because it is a political topic. Saying that one child leaves the school system smarter than the other child makes people think “that’s unfair”. And being unfair, especially towards children, is a bad thing. So yes, a policy that improves all children is strictly worse at creating a feeling of equality.
(Of course there are other values besides equality, which shouldn’t be sacrificed, unless you want to say things like: “No one should be able to find a cure for cancer, until we all are able to find a cure for cancer… which realistically means: never.” But this is exactly the mindkilling effect of politics: focus on one value and ignore all the others, because our team identifies with this value, and the other value is used in the same way by the other team.)
That’s a good point, I’m not sure that any research shows long-term convergence among students. I may have overstated the point. I guess what I was thinking was that in the long run, all students would improve so much as to make any initial differences unimportant (which may or may not be the case, but it can’t be assumed)
Edit: yeah, I can’t seem to fix the link, the bracket at the end seems to be screwing it up. Anyone know how to fix it?
You need to use escape characters instead of brackets, like this:
http://en.wikipedia.org/wiki/Mindset_%28book%29
Note that when I copy a URL from Firefox’s address bar, the brackets are automatically escaped (I can just paste the result); but when I right-click on a link and select “Copy Link Location”, the brackets aren’t escaped, and I get http://en.wikipedia.org/wiki/Mindset_(book).
Related discussion of Dweck’s findings, from last year.
Any pointers to those bits of her research that you favour?
Even in kindergarten differences in intelligence are so obvious that the children themselves, I suspect, often pick up on them. Some children can do simple Algebra in kindergarten whereas others, despite putting in lots of time and effort, are not even able to figure it out in high school. If we tell the not-so-smart kids that they will be able to catch up if they work hard enough, then what happens when this proves impossible?
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Again, from my experience, most can master it, given some 100x the effort and time investment by both teacher and student, compared to those somewhat above average. It took one of my students about 3 years and countless problems to get comfortable with percents (e.g. to calculate sale price). The skill seemed there for a short time after learning, then dissipated after a while, reverting to the old “I don’t understand percents!” mental block.
Whether such an investment is worthwhile is a different story.
No, and it’s child abuse when schools put enormous pressure on low IQ children to learn this kind of stuff.
I mean people who have low aptitude for math, and whose general intelligence (IQ) may well be above average.
For example, were singing mandatory for graduation, I would have had trouble finishing school, because I cannot hold a tune if my life depended on it. Well, as I said, I could have probably learned it with 1000x the time/effort/investment of your average person, but it would be silly to require that.
I’m not sure I buy into this narrative very much. If this were the case, one would expect that one would see similar educational problems in other countries. One could claim that that’s due to different gene pools but if that were the case, one would expect to see schools which have homogeneous populations to be similar to their home countries. But one doesn’t see this. For example, schools with predominantly Irish background don’t have data that looks like Irish schools.
As a matter of anecdote (I’ve done some teaching and a lot of math tutoring), there are a lot of stupid kids out there, but most of the kids I’ve tutored were able to get concepts fine if they were taught well.
Yes, we probably aren’t acknowledging nature enough in many respects. But that doesn’t mean that there aren’t deep problems with our school system that are connected to who the teachers are, what their training is, and what the school environment it. That’s part of why for example there’s strong evidence that smaller classroom size really does help a lot with performance across a wide variety of subjects.
I don’t know if we see this for homogeneous schools or not, but I do know that on things like PISA scores when broken down by ethnicity, American students do reasonably well compared to the countries from which their ancestors came from.
You might want to be careful about posting links to VDARE, lukeprog and some others here consider this crimethink.
One of the many reasons I have been spending less time on LessWrong (sic) recently.
Steve Sailer is not a racist or a bigot. I can’t speak for all of VDARE’s material, but all of Steve’s articles there are ok. Also I’ve seen lots of other posters mention him.
There used to be lots some familiar names here from the old gnxp site. Gregory Cochran and Henry Harpending the dudes with the genetic origin of Jewish intelligence hypothesis did a Q&A here. As long as we stick to the science of the thing and avoid the politics this should be a ok for rationalist to discuss, like we did here. I guess someone might stretch Steve to be inherently political because he advocates limits to immigration, so even when he isn’t directly discussing it he is still persona non grata.… but really? Really?? What if we applied the same sort of standard to Libertarian, Socialist or Liberal writers?
Are we really getting that brain-dead PC? I don’t use that term lightly mind you. Some posters I know have been complaining about the unwelcoming and stifling atmosphere with rules of no politics being selectively employed but I assumed this was just “old forum member thinks it used to be better” syndrome.
(;_;)
Speaking as someone who did upvote the comment because the data was interesting- there are serious issues here. I’ve seen stuff on VDARE which involved very poor presentation or evaluation of data, and the motivation for it was pretty apparent. The signal to noise ratio there is extremely bad, and there’s a lot that’s just out and out racism in the strong sense of thinking that members of minority groups are of less moral value.. The post you set was quite interesting. But frankly, whenever I see something from there I have to doublecheck the data to make sure they aren’t screwing up in some way. For simple matters of signaling, if I were to link there I’d include a note of the form “yes, this website is full of racists but in this case their summary data is pretty accurate.” Steve himself seems to be pretty tonedeaf- I suspect a lot more people would listen to him if he didn’t post stuff on such overtly racist locations.
In the 1990s and early 2000s, he was writing for respectable mainstream conservative papers. The trouble is, once you’ve written too openly about certain topics, you will be ostracised from the respectable media, and these limits of acceptability are getting ever stricter and narrower. And once you’ve been placed under such ostracism, unless you’re willing to restrict yourself to writing for free on your personal blog, you can only write for various disreputable outlets where you’ll have to share the URL or column space with less seemly people.
The fake data usually is the most interesting, in so much as ‘interesting’ is a measure of surprise or confirmation. Also before saying ‘it is pretty accuarete’, the actual accuracy (vs the sources etc, or vs whenever they did the study at all) got to be evaluated. Usually people say ‘pretty accurate’ about stuff like this whenever it simply looks plausible to them.
I’m not sure you saw my point here. Yes VDARE is a politically oriented site, its goal being immigration restriction thus duh some people with racist attitudes are probably writing for it. Selectively applying such standards for the discussion of some policy issues seems like a bad idea. I can see your point if I was citing someone with a very poor reputation who happens to be right, but I don’t at all agree citing someone who is ok when it comes to data and its interpretation, who happens to have written for a magazine that sometimes isn’t ok.
VDARE is (somewhat) crimethink by my standards, much of their stuff not passing my Voigt-Kampf test if you know what I mean, but Sailer is anything but a racist. In fact, all the ethical flaws I might even begin to suspect him of are tied to his epistemic habits (such as thinking that his mainstream targets just Hate Truth), and generally he sounds like quite a decent person.
Amusingly, Razib’s post does not include the word “genetic”. I can’t tell if that was intentional, but in any case, when a trait is highly heritable, that doesn’t mean it’s genetic. One nice example is accent. It’s also a nice example of a trait that a teacher would find really hard to change, unles given huge authority over the kid’s entire life. Maybe basic math aptitude is similar.
ETA: this comment is wrong by the technical definition of heritability, see Vladimir_M’s replies. I should have said something like “has high correlation between parents and children”.
The discussion of accent in that dialog is a neat rhetorical trick, but its main premise is false. If you were to examine the heritability of accent using the standard methods of behavioral genetics, it would turn out to be near zero. (Maybe some confounding factors would yield a small spurious heritability, but there’s no way you’d get a “highly heritable” result.)
Some of the other cited facts are also dubious or exaggerated. For example, while accent of adults is no longer as perfectly plastic as before adolescence, it’s obviously absurd to claim that “nothing that happens after early adolescence makes an impact on it.”
(Also, kids’ accent can be easily influenced if you can just place them into a peer group with the desired accent. No such simple solution exists for traits that are known to be heritable.)
Can you explain in more detail? I don’t know much about heritability, but would be pretty surprised if Shalizi turned out to be wrong on a question of fact.
You can take any of the usual lines of evidence for heritability, and the result will be negative. Unrelated kids growing up in the same linguistic environment end up with the same accent, while related kids, even identical twins, growing up in different linguistic environments end up with completely different accents—with no more similarity between them compared to the other randomly selected kids from these different environments.
In contrast, with IQ, you get dramatically different results. If you discover a lost twin brother who grew up in Hungary, his accent won’t be any more similar to yours than a random Hungarian’s—whereas his IQ test results would be similar to yours with much more than random chance.
(I am ignoring here some minor factors like e.g. speech impediments due to hereditary conditions. But clearly the context is normal linguistic variation.)
When it comes to sheer intellectual ability, I admit that I’m not worthy to sharpen Shalizi’s pencils. Unfortunately, he is not reliable on ideologically charged topics; when discussing these, he will not use his abilities to clarify the matter, but rather to make the best lawyerly case for his favored side. I wish it were otherwise—I’d be delighted to see someone as smart as him try to make sense of these controversial and muddled topics—but that’s the way it is.
Thanks! It looks like you’re right. This is bizarre, Shalizi says accent is “highly heritable”, yet in another post he explains that estimated heritability of accent will be quite low if you measure it properly (see the section “Cultural transmission”). Edited my comment.
Shalizi’s usage seems perfectly reasonable to me. People use the phrase “highly heritable” to refer to the experiments they actually do, not to the theoretically best experiments they could do. Shalizi claims that performing the same experiments with accent would yield a conclusion of “heritable.” (though he backs off of “highly” and is generally evasive about quantity)
AIUI, that’s where people’s accents are generally set, in school from about six to twelve. (You can self-modify afterwards, but that’s where people start.)
Yeah, the point that genetic != heritable is really important- religion is highly inherited but obviously there’s no gene for being Christian. Some of this inheritance may be due to cultural or socioeconomic effects, but at this point, the data with twin studies seems to suggest that a lot of the heritable differences in intelligence are genuinely genetic.
Interestingly, how seriously people take religion appears to be genetic.
Yeah. Cultural problems are a tricky one. It’s repeatedly shown you can get 15 IQ points from non-genetic differences. So you do need to pay attention to the apparently stupid or shiftless kids so they can in fact be at least some of all they can be. But not neglect the bright ones.
I’ll note here as well: it’s bloody hard work being a teacher.
(Having met the kids in my daughter’s class, her teachers deserve a medal. And they’re pretty nice kids.)
Could you point to this data?
As to your anecdote, how long-term were your tutoring relationships? The post Razib quotes is all about about how everyone fools themselves into thinking that they were much better than the students’ previous teachers. On the other hand, if the students could learn the material once, maybe there is a scenario in which they could retain it. So I wouldn’t be terribly surprised if they did, but how do you assign credit to your having “taught well”? One difference between tutoring and school teaching is that some tutoring is for prerequisites that the student now has to use and has motivation to learn and gets a lot of practice on.
This is what I normally point to although more because they give a lot of good references and are online than because of their own research. Unfortunately, there are a lot of complicating factors here. In particular, suburban schools with generally white students from high income backgrounds are more likely to be in small class room environments, and school districts which try to keep class room sizes small are also very likely doing other things to also improve the learning environment. I can’t point to anyone who has corrected enough for all of those factors for my general satisfaction. I’d describe the data summarized in that link as strong but not conclusive.
Thanks!
How about data on the Irish-Americans you mentioned?
I don’t unfortunately have that off-hand. There was a study a while ago that looked at schools where the students were primarily of different European group descents. Googling for it doesn’t turn up anything (unfortunately the obvious keywords are drowned out by many other articles looking at similar sorts of stuff for blacks and other groups). Glados linked to data below that if anything actually goes against this sort of claim a fair bit, so I’m going to withdraw it until I can find something.
I’m friends with a couple of teachers—some of them are more excited about it than others, and those that are less excited aren’t fooling themselves. I’d guess there’s a large amount of sampling bias here, in that teachers who write about their problems and education policy tend to care more than teachers who don’t. I would guess that that would lead them both to be better teachers AND to be more motivated to convince themselves they were better.
Did you read the original post? Does it match what you observe?
Most of the teachers I know have only been teachers for one year (I just finished my second year of grad school—some friends from undergrad got their credentials and just finished their first year of teaching) and I don’t talk to them about their students very much, so I don’t really have personal experience with longer term effects (or lack thereof).
I haven’t thought much about it because I find the underlying sentiment sort of skeevy (if I give myself time to reflect this effect is often diminished I think) but also because I’m busy and not interested in teaching below university level, at which point selection effects kick in.
Varied, most were in the range of a semester to 2 years.
Yeah, this is obviously a problem. I suspect that in many cases I wasn’t better than the previous teachers in any substantial fashion, but a 1-1 setting will work better than almost any other setting, so even if the teacher is better at teaching, having a tutor will still likely work well.
This is definitely a problem. A lot of the students I tutored were students who were failing classes because they hadn’t mastered basic material from 2 or 3 years ago.
On the other hand, as long as were using anecdotal evidence (which frankly using to this extent makes me uncomfortable) I had one student who was very smart, possibly smarter than I am, and I started tutoring him when he was a junior in highschool and couldn’t do almost any math beyond about 7th grade (had trouble solving any equations more complicated than something like x+8=10). In his case it was very clearly an incredibly poor learning environment (although based on other data, it does seem like the the students were so disruptive that the teachers were spending most of their time just trying to control the students). I tutored him for about 1.5 years and he is he’s now a computer science major at a respected university, and doing quite well. He got an A in linear algebra two semesters ago and is now taking algorithms and some other similar classes. I obviously had some impact but the fact that his general intelligence was very high obviously helped in terms of success and long-term retention.
I can see a lot of mechanisms that would allow tutoring to move faster or go further, but the original post claims that the students do quickly learn the material in the ordinary class, only to quickly forget it. I don’t see any mechanisms for tutoring to lead to better recall. Do you?
There might be. A 1-1 setting makes it easier to see if a student has a superficial understanding that is more likely to be forgotten. But the essential point you raise is definitely a valid one. I’m not aware of any studies that look at retention rates for tutoring.
A smaller classroom contributes to better results, but how exactly?
Does it make easier to explain (to answer every student’s questions and check every student’s mistakes), or does it make easier to maintain discipline (to keep the class quiet and make sure everyone is really doing the exercises)? I think both these effects are helpful, but what proportion do they have in the outcome?
In my opinion, the difficulty of explaining is not that different. It’s not like 2× more students will ask 2× more questions; many questions will be the same. And having more questions asked and answered could help better understanding. There is always a chance another student will come with an unexpected question and make an original mistake, but on the other hand, you can make a Khan Academy video for the whole planet and many people will get it.
The critical part is maintaining the order in the classroom. If there is too much noise, students can’t learn. If you have one disruptive student, that’s bad, but if you have two of them, that’s ten times worse because they will encourage each other. So with a larger classroom there is more noise and a higher chance of disruptive students.
If this analysis is correct, there seems to be an easy fix—just throw the disruptive students out of the classroom, and you can have rather good results with large classrooms too. Unless your population already contains too many disruptive students, in which case pretty much your only chance is to separate the other students in special classrooms and teach only them.
I realize and confess that my sentiments are unusual, that my thinking on this subject is grossly distorted by ideology and therefore not to be trusted, and that I don’t myself know how to set up a learning environment that will actually work for actual children, but I must beg the community’s forgiveness, because I want to say this anyway: I think this ideal of “discipline” causes tremendous harm (which of course I understand is not to say that it doesn’t also have benefits, but those benefits are not the subject of this comment). I consider it a monstrous tragedy that so many millions of people grow up (as I grew up) without any conceptual distinction between learning important things and being enrolled in a school and obeying the commands of the designated “teacher”, with no idea of there being a difference between morality and obedience.
Personally, I’ve mostly recovered from this phenomenon to my satisfaction. I now have an explicit notion that it is morally righteous to learn great ideas and train useful skills, and some experience of the pleasures and satisfactions to be had from these endeavors—which is not to boast that I’m doing well; I would never be so delusionally arrogant as to think that I’m doing well—but I think I’m doing far better than I was before I learned these ideas. It certainly seems so when I contrast myself to my fellow undergraduate students. Last semester at community college, I witnessed a student passionately arguing with an instructor that surely his paper deserved an A- rather than a B+. (I’m given to understand this is not an uncommon occurrence.) I imagine there are many who would take such incidents as evidence that there’s not nearly enough discipline in “our” schools: how insolent of a mere student to argue with an instructor! I, however, draw a different moral. I wanted to cry out to the student: Don’t you see how silly this is? Your work, your creation is already good or already bad, no matter what letter the instructor writes on it afterwards! But perhaps it was I who was being silly. The student, of course, didn’t care about good writing; he just wanted to get into the University of California at Berkeley. That was the highest goal he had been trained to aspire to, from the days when his elementary-school caretakers rewarded him for being quiet and doing what all the other children were doing. Again, I do not claim that I know how society should be organized; any particular reform or revolution I might propose could very well just make things worse. But can I at least say that it’s sad to see entire generations of human minds systematically crippled in this way?---because it’s sad.
[Slightly edited from original version]
We obviously use the word “discipline” to mean different things. For me it’s something like “stop talking loudly while the teacher is trying to explain a difficult concept to your classmates”.
As an illustration, here is a quote from my favourite blog about teaching:
Are you familiar with the signaling theory of education? I think that, properly considered, it makes sense of a lot of the things you find so aggravating.
Sort of (if ability is hard to directly observe, but higher-ability people find it easier to obtain credentials, then there could be an equilibrium where one needs a credential in order to be taken seriously, even if the process of obtaining the credential doesn’t actually do anything), but not in any substantive detail. But really (notwithstanding a book I had daydreamed of writing), it’s probably better that I don’t look into it. As I keep telling myself (and keep neglecting to take my own advice), it’s much healthier to just focus on doing good intellectual work, rather than waste any more precious time and emotional energy continuing to feel pointlessly bitter and resentful that “society” (whatever that means) doesn’t care about the sorts of things I consider good work.
(Speaking of healthy working habits, I’m going to try taking out a $20 StickK contract and putting “127.0.0.1 lesswrong.com\n127.0.0.1 news.ycombinator.com\n127.0.0.1 reddit.com″ in my /etc/hosts for 14 days to see if I can remember what it feels like to not be constantly distracted; wish me luck.)
I teach writing at a community college (I began in January), and I agree with this.
I wouldn’t see that student as a sign of poor discipline. If the student was arguing solely about the grade, then like you, I would see it as a waste of time and emotional energy—his and mine.
Incidentally, one of the things I like about the class I’m teaching is that, even before I got there, the syllabus was set up to get students thinking about their purposes in writing the various essays they write, and the purposes the authors of the assigned readings had. Many of my students aren’t getting further than “the purpose is to inform” (argh!) yet, but at least I have an opportunity to teach the difference between instrumental goals and terminal goals.
Fully agreed!
(Meta-discourse note: some time after writing the parent, I worried that I had worded it far too harshly. I usually try to keep most of my comments here very close to being emotionally neutral, on the grounds it’s better to err on the side of being Spock-like than to risk letting my passion tempt me into saying something obviously wrong or harmful (which has happened a few times). But given the karma count and lack of disapproving replies to the parent, perhaps I didn’t actually do so poorly by making an exception this time? Maybe I should even update a little bit in the direction of thinking that it’s okay to express emotion sometimes, as long as you clearly explain what you’re doing? I’m not sure.)
[Edited to add: Actually, I still feel guilty about being non-nice, so I’ve edited out the two instances of cusswords, which, while entertaining, didn’t actually add any substantive content.]
The reason this isn’t implemented is that children are forced to attend school. If they could get out of classes without consequent punishment, not just one or two ‘disruptives’ but many students might opt out. A school doesn’t have anywhere to keep such a group; classes are in large part make-work to occupy students.
On the other hand, if you punished disruptive students but did so outside of class, the habitual disruptives would spend a lot of time in punishment sessions, and would definitely not learn their lessons / pass end of year exams / etc. Schools in the US* prefer to have everyone barely pass exams, to 80% passing with high scores and 20% failing irretrievably. The failing students’ parents have too much political power over the schools.
I’m not from the US, but have seen enough people complaining about US schools on the ‘net. The Israeli public schools I went to in the 90s were the same. Every time teachers tried to set up separate classes for non-disruptive students who could be taught instead of disciplined, the non-eligible students’ parents complained.
I can’t believe I didn’t think of that before. The unwillingness to risk (localized or individual) failure is the strongest guarantee of mediocrity.
It also explains the state of gifted & talented education, incidentally.
Does it? By many metrics the US does better with gifted and talented education than much of the world. For example, the US has some of the highest per a capita rates of Noble Prize winners and Fields Medal winners, more than Britain or France. If anything, the US is doing badly on the average case but is doing a lot better with the very smart students.
Edit: This claim is massively wrong, see Douglas’s remark below.
What is your source for per capita rates?
France has 4x Fields medalists per capita as the US. (and the UK is the geometric mean). (or try wikipedia) For science Nobels, the UK beats the US, which beats France.
Someone a while ago told me this I think and I must have not bothered checking it. Yeah, this is unambiguously wrong as of right now. It is possible that this was true until some point quite a few years ago, but is clearly false today. Thanks for catching me on that.
You shouldn’t reason from Nobel Prize per capita all the way back to gifted & talented education without bringing in many other factors to your regression.
The US is the wealthiest economy in the world with the best elite higher education establishment with some of the largest investments in STEM or R&D in general, with the largest Jewish population outside Israel (which, IIRC, beats the US on per capita measures), and as wedrifid pointed out, for all these factors attracts the best students from across the world. Just off the top of my head.
This means that our G&T programs could easily be underperforming and a simple gross observation of per capita Nobelists not make this instantly obvious. A better approach would be to simply look for experiments, natural or otherwise, on funding for G&T programs and seeing how they do.
Either that or they are doing well at acquiring very smart students (either by immigration or the genetic inheritance from historic immigration patterns.)
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Your disjunction isn’t complete there: it could be something else, like how many questions are asked. We LWers are of course familiar with the testing effect, but not so familiar with Bloom’s 2 Sigma problem. Alas, I cannot seem to find the reference now, but I recall reading that in tutoring, students are asked 2 or 3 orders of magnitude more questions than in ordinary classrooms.
Personally, I think it’s harder to learn arithmetic than to learn algebra once you already know arithmetic. The amount of memorization that you need to do to be able to calculate 247 / 15 is a lot more than the amount of memorization that you have to do to go from being able to calculate 247 / 15 to being able to solve (2X + 3) / 5 = 13.
It looks like the second sentence contradicts the first. Does one of them have a typo?
Yeah, I goofed. Fixed now.
I now agree with both sentences!
Edit: Although it is possible to do arithmetic without memorizing multiplication tables and similar large collections of arithmetic facts (by, say, drawing dots on paper and counting them). See one of my favorite quotes.
Yeah, it’s just much more efficient that way. (Sometimes when I had a bit of trouble recalling the product of, say, 8 7, I found myself doing things like calculating 7 7+7 to find the answer instead.)
Also, a professor I had at college for one of my computer-related courses said that the long division algorithm is one of the most complicated algorithms around and it’s by far more complicated than any of the other algorithms taught in school.
“Some children are more athletic than others, and some children are more intelligent than others. Starting among conservatives, but now spreading to some liberals, is a rejection of this premise via blaming teachers. ”
That some people will be naturally better than others does not mean there are no low hanging fruit that could make people on average much more athletic and/or more intelligent. He doesn’t explicitly claim otherwise but just to spell it out: that humans are not identical does not mean they are reaching anywhere near their potential. Teachers obviously aren’t wholly to blame for any failings but the following possibilites are perfectly compatible: that there is variance among humans, that children are falling far short of their potential, that this is the fault of teachers (or the fault of the people that hire them depending on how you want to look at it.
Or even, depending on how I want to look at it, the fault of the people who trained them.
Of course, looking at it that way only makes sense if I’m willing to ascribe their failure to achieve their (assumed) potential as teachers to the actions, or failures to act, of the folks who trained them.
Which it seems like I ought to be willing to do, if I’m willing to ascribe their students’ failures to achieve their (assumed) potential to the folks who teach them.
Unless you give the kids a pass for being kids.
edit: which I think is inconsistent. There’s no schelling point, but it seems to be the normal attitude.
(nods) I agree that it’s the normal attitude, but I also agree that it’s inconsistent.
True story. Some years back, I was having trouble sleeping and decided I was getting too much light in the mornings. So I measured my bedroom windows, which were all different, odd widths, and went to Lowe’s where they sell nicely opaque vinyl blinds. So I pick out the blinds I want, and go to the cutting machine and press the button to summon store help. The cutting machine turned the blinds, which were cut by a blade which screw clamps to a metal bar marked off like a ruler. There were no detents or slots, so any width could be cut by simply moving the blade to the right measurement. Well, a young woman comes along wearing one of the store vests and I tell her I need blinds cut and show her my measurements. She looks at them and looks me straight in the eyes and tells me, “The machine doesn’t do fractions.”
I almost fell over.
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I think something very important to remember here is that different people learn differently. Genetics have a lot to do with that, and my (admittedly extremely limited) understanding is that US schools in general cater to different learning styles extremely poorly. Another thing to consider is raising. The most recent evidence suggests that how one is raised has an extremely significant effect on all aspects of mental ability—I think that that is likely to be far more important than anything which happens in school.
Weren’t learning styles type ideas mostly debunked or rather turned out to be something for which very little evidence existed?
I would very much like citation since your most recent evidence conflicts with most of the other evidence I am aware of! From what I know early childhood interventions produce effects but these are temporary gains that mostly wear off over time, having very little to no effect on adult performance.
Having done some research, I find that you are correct, at least as regards to parenting and genetics. My ‘cached’ opinion was based on misleading information absorbed for what I though was good reason, but, on reflection, was just blindly following authority. Retracted.
Citing any key material you looked up might be useful for other people. Awesome job on actually checking out the literature yourself a bit and updating!
Rationalist hugs for you (if you want them)!
(^_^)
You’re adorable.
I’m not sure how to take that.
As encouragement :)
I don’t know. But the converse is that there’s one style that’s optimal for nearly everybody. Yet many different styles are used in practice around the world. Which style is supposed to be best?
ETA: retracted, my bad. I thought you were talking about “teaching styles” not “learning styles”.
Actually, teaching styles is more what I meant. Perhaps a better phrasing would have been different people respond to learning differently, though that still doesn’t sound right. For this, I have only anecdotal evidence, albeit quite strong. I’ve seen it, both in people I’ve tried to teach things to, and in people I’ve learned alongside.
I find the reactions to this topic in this thread very interesting, given that the (currently) second-most-upvoted article on the site contains this passage:
I’ve seen a lot of claims about different learning styles mattering, but I’ve never seen any actual studies that backed up that this was a substantial issue. Do you have evidence for this?
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I want to support the idea of learning styles for two reasons. First, it seems unlikely to me to think that everyone learns the same way—even that the majority of people learn the same way. Secondly, we know specific ways in which people understand and handle such basic operations as counting fundamentally differently (see this Feynman passage “It’s as Simple as One, Two, Three...” for an amusing anecdote about this). My prior says that learning styles are very likely.
If studies are saying that ‘learning styles’ don’t matter, then I would say that the problem is that we haven’t figured out what the real learning styles are and how to target those, not that there are no learning styles. The ones teachers talked about during school struck me as naive—but I bet there are some real ones out there.
“Who are you going to believe, me or your lying eyes?”
It seems to me you are hypothetically placing anecdotes over data here. Any reason why?
Re: original post: I agree that many many kids are overeducated given their hardware.
I think my above post gives those reasons. I have a large prior against this and don’t think that studies that investigate popular learning styles are showing that there are no learning styles but rather that the learning styles educators currently use are not good.
I will be completely clear here: I have read none of the studies on the subject and what you are saying is a very valid criticism. I am not making a full argument here—I have no such argument. But I’m going to defy the data for now and wait until someone explains why people who hear numbers and people who see numbers best learn to count, add, etc. the same way.
Right, I was just wondering where your large prior comes from? (What magical place DO Bayesian priors come from?).
I will try to make this very explicit since I seem to be failing to communicate since I thought my last two posts stated the entirety of my view. Two points:
1.) There is a large variance in the human population. There are people who experience numbers in extremely different ways from others. There are people who experience the senses in very different ways than others. In order for me to believe that these differences play no part in the learning process, I will want to see some arguments as to why, theoretically, they don’t matter as well as some experimental evidence that they don’t. This is the primary cause for my large (not insurmountable) priors.
2.) The current studies are, to the best of my understanding which is rather limited, directed at testing the learning strategies that we have hypothesized so far. These learning strategies strike me as fairly petty and overly hopeful—“if I just say this him, he’ll understand and if I just have her read this, she’ll understand.” I accept that these styles are not genuine styles. But I don’t see reason to go beyond this to say that there are no useful differences in styles.
If you want to convince me, tell me why my intuition in number 1 is wrong or show me a study that has managed to go beyond the existing spattering of fad learning styles and has systematically shown that the existence of any learning styles is very unlikely. Preferably both. I am genuinely interested in hearing counter-points to this position, but am growing tired of restating my position. I hope this time has clarified exactly what I think.
Go Bayes! So if you just make your priors big enough, you never have to change your mind.
Americans obsessed with education? Well I guess that’s true in a way, Americans do seem obsessed with the notion that everything is school or teacher’s fault (or liberals fault for not understanding ‘genetic differences’, if you ask the thinly veiled racists), and are rather unwilling to blame the cultural attitudes or the lack of motivation among those born into privilege of earning for the unskilled labour 10x the typical market price (which lets you easily buy top-of-the-line made in china shit like ipods while doing something entirely unskilled). Or to blame this very attitude of “i am basically perfect and it’s someone else’s fault”.
note: the worst thing is that the abovementioned lack of motivation is rather rational. It’s nowhere near as worth your time to put work into your study as it was worth my time (in terms of the pay with vs without this initial investment).
This part is exactly the same in Slovakia. In many discussions it seems like the parents no longer exist or have absolutely no influence on their children. Anything bad happens—why don’t teachers do something about it?
A personal anecdote: When I was a teacher in a private school, a mother of my student asked me to do something to make her daughter not spend whole days with computer on social networks at home. I didn’t even know what to answer, because our models of reality were so obviously incompatible. In my model, teachers have epsilon influence on what students do at home, while the parents are there and can apply the rewards and punishments. (For example, how about simply turning off the computer of your 15 years old daughter?) Her model probably did not contain this, and instead acribed some magical powers to me. -- This was an extreme case, but many people are probably doing less extreme version of this.
So while some specific details of this might be an “Americal obsession”, there is definitely a general trend beyond USA.
From a selfish cost:benefit analysis—the more advanced civilization, the more is there to learn, but you have a higher quality of life even if you learn nothing. So depending on one’s priorities, ignoring education could be a rational choice. Maybe when you are an average person, it does not make much sense to learn, because an average educated person will not make so much money anyway. It makes more sense to learn if the ability to learn is your competitive advantage.
From a society point of view—educated people are a positive externality to a society they live in. Most of the benefit of your education does not end in your pockets, but improves the lives of people around you, whether in positive sense (you invent or produce something they can use, you are a smart employee they can employ cheaply) or just in negative sense (you avoid some stupid choices which would have negative effects on people around you).
So this disbalance suggests that for an average person, learning is not as useful for you personally as the society tells you. And the average people can notice it.
Yep, that’s a good point.
My point was more on the disparity. For me, being qualified boosts my pay from the typical wage of Eastern Europe to good qualified labourer wage of the richest country, if I am actually good. For those born with more privilege in the today’s world, the non-educated pay is several times larger but the ceiling is the same (and is much more reachable without having to actually put work into studying).
But is society capable of having a point of view and promoting it? I don’t think that is working.
And that is the attitude towards education issue.The necessity of actual motivation and work is ignored. There is that vague belief in the ideal self that is held back by something which you can easily fix by attending some sort of ritual self improvement, and a plenty of people offering (scientology, nxivm, etc), and at the much grander scale, the ineffective higher education which sells tokens of endorsement in forms of increasingly meaningless diplomas.
The cultural attitude is vaguely anti-intellectual (The young physicists are people into star trek and videogames, wanting to but entirely unable to date a woman several steps below them on the social ladder, is the premise of a popular comedy show, for instance. This is very ridiculous). And that is, to some extent, a phenomena in all developed countries. It’s not even so much that it is anti-intellectual as, well, who would want to be mr. Bean? What do you get if the science characters are the stock mr Bean of comedies? Humans are social creatures, and being laughed at is something most humans instinctively avoid. It’s bad enough that the education takes time and there are more and more shinier distractions everywhere; it’s bad enough that if you want to study you would have to not go to parties as much as the other kids; but to add to it the low status on the laughing ladder?