Probably Not What He Meant, But Alas True

Mr Taranto highlighted a Yglesias post in which Mr Yglesias opines against educational meritocracy. Mr Yglesias is wrong in assuming that “white people” would have problems with Asians getting more places in higher education based on their higher grades and test scores. I offer myself as one white person who sees nothing at all wrong and a lot right with more people with better grades and test scores regardless of the color of their skin getting into the better schools. Furthermore he concludes:

 But rather than dedicating the most resources to the “best” students and then fighting over who’s the best, we should be allocating resources to the people who are mostly likely to benefit from additional instructional resources.

I wholeheartedly agree. We should allocate more of our educational resources to those who are most likely to benefit from additional instructional resources. Who are those people most likely to benefit? We call them the gifted students (at least those gifted students who are also willing to work hard).

35 Responses to Probably Not What He Meant, But Alas True

  1. Mr Yglesias is wrong in assuming that “white people” would have problems…I offer myself as one white person who sees nothing at all wrong

    So your evidence that Mr Yglesias is wrong in citing a scientifically conducted survey is to cite yourself as an ancedotal counter-example? What did I ever do in my previous life to be stuck debating mathematics with an innumerate mathematician?

    Who are those people most likely to benefit? We call them the gifted students (at least those gifted students who are also willing to work hard).

    1. How do we know they are the most likely to benefit? Simply because they have higher scores and grades? The argument seems to be set up here as one where you ‘earn’ a spot by getting grades and high scores. Yet why should spots be allocated like that? For several thousand years China had an intricate system of standardized testing based on mastering Confucian principles to allocate jobs in the civil service (which essentially controlled the entire larger economy beyond the basic farm level)…and there’s not much evidence this method of finding the allegeded ‘best and brightest’ actually worked to China’s benefit.

    2. What is the greatest benefit to them? If college’s value derives from the synergy of classmates and profs (which it must since the actual lectures and texts are available online for a fraction of the cost of tuition), then diversity is needed for students…which means colleges cannot limit themselves to a single admission path.

    3. There are other actors in this drama besides students too. What about the colleges themselves? Do they not have a legitimate interest in their student body?

  2. Boonton,
    Mr Yglesias did not claim a certain percentage of “White people” oppose Asians getting merit access to education. He said “White People”.

    Regarding #1. Do you think Ramanujan might have done more in maths if he had earlier access to some instruction and communication with other mathematicians? Answer, yes or no.

    Regarding #2, “If college’s value derives from the synergy of classmates and profs (which it must since the actual lectures and texts are available online for a fraction of the cost of tuition), then diversity is needed for students” the conclusion does not follow from the premise, or if it does you need to show some more work.

    OK, you are a professor. You are an econometrics researcher. Do you benefit from more from average students from diverse cultural backgrounds or really bright ones irrespective of their backgrounds?

    The problem with the aff action/diversity plug is that you want to judge people by the color of their skin not the content and agility of their intellect. That’s getting the lessons of Mr King exactly backwards. As I remarked, “if I actuall was a racist” the odd thing is, I’d support ACA and Aff action and other liberal programs. Odd that.

  3. Mr Yglesias did not claim a certain percentage of “White people” …

    In discussing social trends, it’s taken as a given that you never get 100% of a population for anything and if you ever did it would be so exceptional that it would be mentioned. Therefore your ancedote of yourself as an alleged ‘white person’ counts for nothing against a well conducted survey.

    Regarding #1. Do you think Ramanujan might have done more in maths if he had earlier access to some instruction and communication with other mathematicians? Answer, yes or no.

    Probably not, his output seems to have been amazing. From roughly his late teens to his death at 32 he produced 3900 results. What would he have done with earlier access? 4200?

    If you had to do history over again, I suspect the best way to have gotten more out of him wouldn’t have been more math education eariler but better public health. If he didn’t have tuberculosis he might not have died at 32 and another few decades would have produced more insights from him. Although that’s a gamble. Look at how many chess masters appear to be geniuses as kids and young adults only to fizzle out in later years.

    Anyway this argues for *NOT* basing *ALL* your admissions based on grades and test scores. Even in a very objective field like mathematics, you can sometimes get people who come in from an entirely non-traditional path. Quite often such people won’t perform all that well but simply being outside the mainstream might be enough for them to serve as the grain of sand works in an oyster.

    You are an econometrics researcher. Do you benefit from more from average students from diverse cultural backgrounds or really bright ones irrespective of their backgrounds?

    Recall my example of someone casting a soap opera starring 3 brothers and 3 sisters. Does it help if the 6 best actors in the world consist of 4 men and 2 women (assume that even the world’s greatest actor can’t pull off drag as anything other than slapstick).

    I think a monocultural background would produce bad results. So if the more you have a single background, the brighter you need that group to be. So yes technically maybe a class of a single background would work if they were all on the level of Nobel Prize winners. But that’s not usually the choice you get to have. If a monocultural background gives you a 10% edge on ‘brightness’ it very well may not be worth it.

    And now what of the college itself? Does it have no legitimate interest in cultivating an alumni that has a wide geographical and cultural range? Boosting its reputation among more of the culture rather than just a niche? Are the only legitimate interests here the the hypothetical student who has ‘earned’ something and the professor?

  4. Boonton,
    OK. Ramanujan you think would not have benefited.

    Oh, I agree. He should have had better healthcare, better education and all that.

    Look at how many chess masters appear to be geniuses as kids and young adults only to fizzle out in later years.

    Yes, but how many below average intellects who never touch a board at a young age suddenly become chess masters. I suggest failure to reliably locate genius doesn’t mean you never do. But if you want to argue you’ll find genius among those who show no promise you’ll do even worse … or do you have examples where the opposite is truer than the other?

    Let me put the same question a different way. You are the state. You have some grant money. You can give track/field access, sneakers and access to coaching to exacxtly one 12 year old child and two are available, one Mr Boonton and one Usain Bolt. Which would give you more in the way of results, you (and Mr Yglesias) seem to argue that giving Mr Boonton the access is preferred because there are already too many black atheletes on the track we need white boys out there for diversities sake. See. Doesn’t work. But on the other hand, if you give the aid to Mr Bolt you get the world’s best sprinter. Who gains more in ability from the aid if given the chance? I think it is clear that the answer is the gifted gain more from help than those the same measure of talent. The “better” students benefit more than the average/below average from aid.

    Recall my example of someone casting a soap opera starring 3 brothers and 3 sisters. Does it help if the 6 best actors in the world consist of 4 men and 2 women (assume that even the world’s greatest actor can’t pull off drag as anything other than slapstick).

    Recall my response to that.

    Boosting its reputation among more of the culture rather than just a niche?

    You are making the mistaken assumption that one culture/race is academically more fit than others. That, say, a Ramanujan cannot exist because he is not white. This is exactly why you should prefer to promote genius here found, not assume it will be found by race.

    Even in a very objective field like mathematics, you can sometimes get people who come in from an entirely non-traditional path. Quite often such people won’t perform all that well but simply being outside the mainstream might be enough for them to serve as the grain of sand works in an oyster.

    OK. Yes, you in fact sometimes do find someone who has not studied maths for example, who comes over from another field and excels. But … you will find they were likely pretty damn good at the fields they were in before. It’s called “switching majors”.

    You ignore my question (you are economics prof.). Why are the backgrounds important? Why do you think you will end up with one culture if you select on ability or a capacity to learn?

  5. Boonton,

    In discussing social trends, it’s taken as a given that you never get 100% of a population for anything and if you ever did it would be so exceptional that it would be mentioned. Therefore your ancedote of yourself as an alleged ‘white person’ counts for nothing against a well conducted survey.

    Well, the take-away is probably just that people’s first instinct is to give any advantage they can to their children. Odd that. The surprising thing is that this means liberals like yourself wish to judge people by the color of their skin not the content of their character.

  6. Boonton,
    Sorry, that “the surprising thing” doesn’t follow from the prior sentence. The people trying to push policies that advantage themselves is not new.

    The liberal canon on this taken by you and Mr Yglesias is that what we should be doing instead is kinda surprising.

  7. Oh, I agree. He should have had better healthcare, better education and all that.

    No better healthcare. what evidence is there that he needed ‘better education’ or it would have done him any better if he did? Maybe he would have started doing advanced math at 9 yrs old instead of 10? Seems to me if he had died a year or two later rather than starting math a year or two sooner his lifetime output would have been greater.

    Yes, but how many below average intellects who never touch a board at a young age suddenly become chess masters. I suggest failure to reliably locate genius doesn’t mean you never do.

    Not many, but then what is your purpose here with chess or education for that matter? Are you trying to locate geniuses to stock up an Olympic team? Trying to achieve a cross culture wide literacy? These are different goals.

    Work with chess. What’s the goal here? Are you the cultural minister for the USSR whose job it is to ensure that the USSR is never beaten by the US or anyone else in chess? In that case you really don’t care how many kids take up chess. You only care that your net is structured so you can catch the next Bobby Fisher and let everyone else go.

    Or are you an educational minister operating on the theory that playing chess makes kids better at math and literature? In that case consider a Bobby Fisher. Not the young cute one but the surely older one spouting various paranoid conspiracy theories and exhibiting varying levels of mental illness. Do you want to cultivate him to win all the grand championships and produce cutting edge games? Or would you rather have someone whose less accomplished but better looking, a better speaker, who would have better appeal to kids?

    Note here what’s merit is two radically different things. A Bobby Fisher in the 2nd case might feel he was cheated out of something…after all didn’t he ‘earn’ some spot as national chess spokesperson? Or did he? If the goal is to sell chess to the general public maybe his untreated mental illness, bad personal appearence and bizaar rants indicate that he didn’t ‘earn’ the spot ‘on the merit’.

  8. Sorry, that “the surprising thing” doesn’t follow from the prior sentence. The people trying to push policies that advantage themselves is not new.

    Indeed, ‘surprising’ isn’t quite true. You have embraced the Marxist insight that often what people believe to be a deep philosophical or moral truth is in fact simply a material advantage that they are rationalizing.

  9. It occurs to me that maybe mathematics is an easier way to get this point through. Consider simple linear optimization models. In those models you are trying to achieve some max. level of utility. You can utilize several types of inputs but each input carries a cost and you are constrained by a budget function which limits the total cost you can incur. So your challenge is to find the right mix of inputs that provides you with the most utility (the budget function requires you to come up with some combination…if you had no budget you could achieve infinite utility by adding infinite amounts of each good).

    You’ve presented a case where there’s only one ingredient to a college’s utility….scoring the Superstudent…the John Nash or Ramanujan who will achieve glory and forever associate the school’s name with superstars. Some colleges might put nearly all their resources into this function (Princeton boasts what? a dozen Nobel winners plus?). But for most this will be only one input among others.

    So you’ve presented a case only so far that diversity can be taken too far, that you can use it too much as an ‘ingredient’ to be optimal. But the anti-AA argument requires that it be struck completely from the list of ingredients. Likewise the ‘merit argument’ demands even more…that all ingredients be struck from the list except a handful of very objective metrics like SAT scores or GPAs. But no college has ever simply issued a blanket acceptance of all perfect SAT scores or even all high GPAs. To pull that off you have to make a positive case for it, not simply a negative cases against other possible policies.

  10. We should allocate more of our educational resources to those who are most likely to benefit from additional instructional resources. Who are those people most likely to benefit? We call them the gifted students (at least those gifted students who are also willing to work hard).

    It occurrs to me that this probably does not follow. Ignore the debate about the value of test results for a moment, let’s just say ‘benefit’ means increased test scores.

    Diminishing returns probably means that a given unit of ‘educational resource’ will do more for the non-gifted student than gifted student. In other words someone who got a 500 on the SAT is more likely to see a 50 point bump after a two week tutoring session than a 650 student is likely to achieve a perfect score (I forget if 700 is a perfect SAT score these days or not).

    This goes along with my gym trainer analogy. The pudgy, out of shape kid, will probably get more out of 40 minutes of additional exercise per week than the kid whose trying to make the Olympic team.

  11. Boonton,
    Ok. Sorry for the silence, our company is stretched to the breaking point and I’m on a project in which the customer pushed “go-live” against my and his IT person’s expert advice, bascially because I’m committed elsewhere for the next 3-4 weeks.

    Anyhow, it struck me for a fellow arguing for the benefits of higher education your suggestion that Ramanujan would have not benefited (from education and discussions with other in his field) you have struck essentially used an argument for no higher education aid as an argument for aiding the disadvantaged, i.e., give them a break to get in school because after all school is useless. Not exactly helping your argument.

    Not many, but then what is your purpose here with chess or education for that matter

    No. The point of bringing that up is to show that your pointing out that some young prodigies burn out is irrelevant. While prodigies might burn out, young morons basically never become late blooming geniuses.

    What’s the goal here?

    Apparently the goal of national support for higher education is to make us more competitive and innovative in the global marketplace. Your argument for ignoring the talented and trying to bring up the low side of average is flawed. Innovations and discoveries are more often done by the brilliant. In programming (and maths I’d venture as well as much of the hard sciences and engineering) (reference: Mythical Man Month) the difference in production (lines of working code per day) between an average and excellent programmer can exceed 2 orders of magnitude.

    You have embraced the Marxist insight that often what people believe to be a deep philosophical or moral truth is in fact simply a material advantage that they are rationalizing.

    You call it Marxist, but odd that when you push the notion that people are economically motivated you don’t call it Marxism. But it’s not Marxism to think that parents want what’s best for their children. People noticed that was done way way way before Marx.

    You’ve presented a case where there’s only one ingredient to a college’s utility….scoring the Superstudent…the John Nash or Ramanujan who will achieve glory and forever associate the school’s name with superstars

    No. That is the extreme case to highlight the point that colleges (and society) benefit when we provide our support to those who would use it best.

    Diminishing returns probably means that a given unit of ‘educational resource’ will do more for the non-gifted student than gifted student.

    But this is not about diminishing returns. It’s not about getting 40 minutes of exercise and seeing the fat kid get more from 40 additional minutes where the hyper fit kid who is already working out 6 hours a day pushing that to near 7 might actually be detrimental. The actual comparison is that if you started spending 2 hours on a track a day at age 12 or if Usain Bolt spent just two hours on the track starting at the same age… who would improve them most. You are lying if you say you would, I don’t think you even believe that. Talent is not distributed equally. A person with more potential will gain more from the same resources than those with less. You cannot truly argue that the situation is otherwise. Your diminishing returns argument is not relevant. More potential => same resources => more gain. Giving your resources to those with less potential is counter productive.

    So then the goal for colleges is to identify potential. My argument is that race is not a factor in determining potential. Past performance can be indicative as well as test scores. Grades typically measure perseverance more than ability at the High School level. But along with potential/talent

  12. I only briefly perused Ramanujan’s bio but I’m unclear what education he was lacking. He was given a book on advanced trig at age 10 or so and had it mastered by 12. That’s earlier than most American kids are introduced to the subject. I’m not clear why you think his life and mathematics would have turned out better if he had been given *more* education? Would he have started his work at 9 years old instead of 10?! Seems to me everyone would have gotten more if he avoided an early death at age 32.

    And as far as affirmative action would go, it’s influence would be at the margin. Return to casting the 3 brothers and 3 sisters. If you’re the best male actor in the world, you got the part. If you’re the second best, you got the part. If you’re borderline between the 3rd and 4th best, though, you may get passed over for a woman whose not as good at acting as you but contributes more than you can to the caste by fulfilling its diversity needs. Ramanujans will not have a problem in just about any policy system then.

    Apparently the goal of national support for higher education is to make us more competitive and innovative in the global marketplace.

    And one person is going to do all this innovating? Building a team by spending all your money to hire the world’s best quarterback leaving you with crap for all the other positions may work…but I’m more inclined to think a team of slightly above average players would be more effective as a strategy.

    Your argument for ignoring the talented and trying to bring up the low side of average is flawed.

    Ahhh but as I pointed out above the talented aren’t ignored here. The trouble comes not for the world’s best, but for the merely slightly above average.

    You call it Marxist, but odd that when you push the notion that people are economically motivated you don’t call it Marxism.

    Marx certainly didn’t invent the idea of economic motivation. What he did argue, though, was that dominante cultural beliefs are in fact really simple economic motivations disguised. For example, for centuries people argued about the Divine Right of Kings. A huge amount of ink was wasted by philosophers who felt they had to go to great lengths to either defend royality or dethrone it. Today no one cares. The urgency of the debate back then wasn’t driven by the legitimacy of the question as much as the fact that people’s living depended upon the outcome.

    So then the goal for colleges is to identify potential.

    OK, so then what’s the obsession with ‘merit’ and whether someone has ‘earned’ a spot in college thru ‘hard work’? If potential is identified by high grades and high test scores, then the goal for colleges can’t be to identify potential (the report card and SAT does that). If those things don’t identify potential, if you can’t really be sure of potential until you send people thru college….well then no one has ‘earned’ a spot by getting good grades and high scores anymore than someone is entitled to a lead role in a movie simply because they graduated from acting school with great grades.

  13. Boonton,

    Diminishing returns probably means that a given unit of ‘educational resource’ will do more for the non-gifted student than gifted student. In other words someone who got a 500 on the SAT is more likely to see a 50 point bump after a two week tutoring session than a 650 student is likely to achieve a perfect score (I forget if 700 is a perfect SAT score these days or not).

    This goes along with my gym trainer analogy. The pudgy, out of shape kid, will probably get more out of 40 minutes of additional exercise per week than the kid whose trying to make the Olympic team.

    No the question. Which kid gets more out of High School. The kid who taking HS ends up with a 500 or the kid who on finishing got 700s. Neither kid would do very well if they didn’t go to school at all, say both spend the four years loafing on a Polynesian Island or taking the test as when they were 13. Say both kids when they take the test at 13 get about close to the same, that is very low. After high school the more gifted kid is getting National Merit Scholarship Offers and the other is considering Jr College. Who got more out of the money spent on education? Diminishing returns is not the point.

  14. No the question. Which kid gets more out of High School. The kid who taking HS ends up with a 500 or the kid who on finishing got 700s

    Why should this be *my* question?

    Actually I didn’t structure the hypothetically correctly. Diminishing returns would mean the kid with 500 might get a 50 point bump after a two week tutoring session. The kid with 650 might only get a 10 point bump.

    Let’s say I’m running a school and I want to have the highest possible *average* score. Then clearing giving the tutoring session (say I only have one to give out), to the 500 point kid would help me accomplish my goal. Likewise if the goal was to decrease average obesity or improve ‘general’ health giving some additional gym to the pudgy kids would accomplish more than giving the pseudo-Olympic team the same additional resources.

    Even if you argue that we should count what the kid is ‘getting’ more you have the problem with diminishing returns. A 650 kid going to 660 is not getting that much more. That’s like giving Ramanujan the book on trig a year earlier. Maybe he would have started doing math a bit sooner, but it’s unlikely that would have made that much of a change in his life story.

  15. Boonton,

    Let’s say I’m running a school and I want to have the highest possible *average* score. Then clearing giving the tutoring session (say I only have one to give out), to the 500 point kid would help me accomplish my goal.

    Ah, that’s one strategy. So here are the two competing strategies for getting the highest average score. Your proposed strategy is to get students with the broadest background diversity, to make sure as many cultures and races are represented and specifically subjugating past scores and measured potential as primary criteria. My proposed strategy is to try to select students with the highest potential.

    Likewise if the goal was to decrease average obesity or improve ‘general’ health giving some additional gym to the pudgy kids would accomplish more than giving the pseudo-Olympic team the same additional resources.

    Again missing the point. Here’s making the point more extreme. We both the same pool to select students. None of our pool of our potential kids has any formal/actual gym/track prior to this. You can take 10 kids. Judging by your strategy, you will pick a variety, 2 are fat, 2 are skinny, 2 are black, 2 are Asian, half are girls. I take 10. I’ll pick the ones who show an interest in athletics, like running and jumping, are active and basically have some testable measure of a aptitude for athletics. We both train them for a year. At the end of the year all 10 take place in a decathlon in a meet. Who wins the meet? Teach me how diminishing returns enters into the question?

    Look at that sentence I wrote. I’m unclear on how you can disagree. “A person with more potential will gain more from the same resources than those with less.” This isn’t about diminishing returns.

    A 650 kid going to 660 is not getting that much more.

    This only is evidence that you are missing the point. Both of your students started High School getting sub 500s on the test. Four years later one has improved his mid 300s to shy of 500. The talented student has gone from probably a little higher, (he might have started higher, say …) mid-400s and four years later to the mid 700s. You do the math. The 650/700 kid improved more in his 4 years at high school than the poor student. Put it another way. You have a poor student and a good student. A high school is putting the same resources (money) into to instruction for both. The good student learns more for the same effort by the school. The gap in their learning and education has grown not shrunk over the 4 years of High School.

    That’s like giving Ramanujan the book on trig a year earlier

    Which was not proposed by anyone. I suggested getting Ramanujan into a modern maths collegiate environment in his early development. That’s a far cry from start his autodidact path a year sooner.

  16. We both the same pool to select students. None of our pool of our potential kids has any formal/actual gym/track prior to this. You can take 10 kids. Judging by your strategy

    This works if my goal is to have the highest team average. YOu’re right. An NFL team picks its players by selecting those it thinks have the potential to improve the team’s average performance by the greatest amount.

    But what if your goal is to improve the health of society in general? In that case cherry picking your team will let you have the best team but will not let you make the most contribution towards that goal. Many colleges fancy themselves not as isolated islands but as playing a role over the whole ocean.

    “A person with more potential will gain more from the same resources than those with less.” This isn’t about diminishing returns.

    Again depends upon how you define potential. The kid with a 650 on the SAT will only gain 10 points with the 2 week tutoring class while the kid with 500 will gain 50 points. Using your analysis then that only makes sense if we consider the lower test score to indicate *greater* potential. Which is fine IMO but will be counter-intuitive to most people. You can’t use that as your system while at the same time using a ‘rights/fairness’ metric (people with higher scores or better grades have ‘earned’ some spot) without becoming incoherent.

    This only is evidence that you are missing the point. Both of your students started High School getting sub 500s on the test. Four years later one has improved his mid 300s to shy of 500.

    But potential is set in the future, not the past. The question isn’t which kid improved more during high school, but which kid will improve more upon being given the 2 week tutoring session. We’ve already given out the high school resource so we’re talking now about who gets this slot in the tutoring program. In terms of physics consider a plane at 30,000 feet and a hot air balloon at 300 feet. Clearly the planet has more potential energy to fall. Yet imagine the balloon lands on a platform 50 feet high and the plane lands on a runway and is sent to a hanger where mechanics jack it up 5 feet high. while the plane started out with much more potential energy, it now has spent most of that leaving its account smaller than the humble balloon.

    Which was not proposed by anyone. I suggested getting Ramanujan into a modern maths collegiate environment in his early development. That’s a far cry from start his autodidact path a year sooner.

    Correct me if I’m wrong but he was doing high level high school math at around 12 and at 17 was doing the work that a senior college math major might be expected to do. So HS to college is usually 8 years and he leaped it in 5. That would seem to indicate he did better as an autodidact than if he had followed the traditional path but had been allowed in school at an earlier age.

  17. Boonton,

    Correct me if I’m wrong but he was doing high level high school math at around 12 and at 17 was doing the work that a senior college math major might be expected to do. So HS to college is usually 8 years and he leaped it in 5. That would seem to indicate he did better as an autodidact than if he had followed the traditional path but had been allowed in school at an earlier age.

    And … what the eff does this have to do with my suggestion? I never suggested he be given an opportunity to follow the “traditional path” so I’m unclear on what you base your remark.

    The question isn’t which kid improved more during high school, but which kid will improve more upon being given the 2 week tutoring session.

    So, let’s see. Two kids. Both went through high school. One learned much more than the other. You tutor them for two weeks, yet you expect the kid who shows less ability to learn to learn more than the other. I guess that’s liberal logic for you. The rest of the planet however, more logically, expects rightfully that the better learner can learn more in two weeks.

    Using your analysis then that only makes sense if we consider the lower test score to indicate *greater* potential

    That is the result of your analysis not mine. You are the one thinking the poor learner has more potential.

    We’ve already given out the high school resource so we’re talking now about who gets this slot in the tutoring program.

    I think I covered this. But let’s try again. You have two weeks. You teach a poor learner and a fast learning. Which will learn more in two weeks? Hmmm? You argue the poor learner will pick up more. Bzzzzzzzt. Wrong answer!

    But what if your goal is to improve the health of society in general?

    Then putting your resources into teaching those with the greatest potential to learn maximizes those resources and benefits society in general the most.

  18. Boonton,
    Let’s take an extreme example for your tutoring thing … you have a relatively famous high school (grad?) recently in the news, Mr Martin’s girlfriend Rachel Janteal and Ramanujan. The first is barely literate and probably really bad at maths … then second we have discussed. You have two weeks of resources … you tutor Ms Janteal … in basic reading and writing and you sponsor Ramanujan with two weeks of phone calls and setup correspondence for him with, say, one of the two Field’s medalists who does a lot of teaching (Terry Tao or Timothy Gower). Who learns more in the course of the two weeks?

  19. Boonton,

    Correct me if I’m wrong but he was doing high level high school math at around 12 and at 17 was doing the work that a senior college math major might be expected to do. So HS to college is usually 8 years and he leaped it in 5. That would seem to indicate he did better as an autodidact than if he had followed the traditional path but had been allowed in school at an earlier age.

    Correct me if I’m wrong, but you claim no contact with teachers would have helped him. If so, why/how do teachers help anyone? Why have schools?

  20. So, let’s see. Two kids. Both went through high school. One learned much more than the other. You tutor them for two weeks, yet you expect the kid who shows less ability to learn to learn more than the other. I guess that’s liberal logic for you.

    The question is not ‘ability to learn more’ but ability to learn more on a given a finite amount of a given resource. One kid’s class average is 70%, another is 96%. If the teacher can spend an extra half hour every other day with one student, the best she can hope for is to see the 96% kid gain 4 points. Odds are the 70% kid will gain more than 4 points. That doesn’t mean the 70% kid will rise up to 96%. Say he only goes up to 81%. Fact is you get more return on investing in him than in the 96% kid. You see this in elite athletics. Initially training yields large payoffs in improved performance, after that you have to add more and more training to eek out even tiny additional improvements in performance. Consider the blood doping scandals in cycling. How much of a difference would it make for a schlub like me if I doped my blood, a rather extreme thing to do, versus just spending 3 months working out 45 minutes each day? I’d probably gain more by working out. At the elite levels of the sport, though, working out is already maxed out leaving only extreme measures that can make a small improvement in performance. Armstrong wasn’t doping, in other words, because he was too lazy to put in 45 minutes a day.

    That is the result of your analysis not mine. You are the one thinking the poor learner has more potential.

    Let’s say the 96% kid can only be increased to 98%. And the 70% kid to 85%. You’re right the 2nd kid has less total potential than the first. Let’s say the teacher is given a bonus based on the average of her entire class. Well if she could choose her students, she would rather fill the class with the first type of kid. But say her class is choosen by random lottery, her choice then comes down to how to invest her time to achieve the best bonus possible. In that case her half hour investment returns more with the 70% kid than the 96% kid.

    Here’s another way, say you’re a gym teacher and you are paid based on the average performance of your class in cycling. One of your students is Lance Armstrong and the rest are just average kids. What’s likely to boost your pay? An expensive blood doping mechanism to give Lance a slight edge to beat his best time to date…or just making the rest of the kids practice a bit more? No doubt the latter, but of course odds are non of the other kids will have anywhere near the total potential that Lance did.

    Correct me if I’m wrong, but you claim no contact with teachers would have helped him. If so, why/how do teachers help anyone? Why have schools?

    Nope, never said that he wouldn’t be helped. But in answer to your 2nd question clearly because most people do not want to learn mathematics and need to be pushed. That is why we have schools and teachers for math but no one figures there’s a need for classes on how to text message your friends or look at cat videos on YouTube.

  21. Boonton,

    The question is not ‘ability to learn more’ but ability to learn more on a given a finite amount of a given resource.

    That’s right. The good student can learn more given a finite resource. Odds are actually that the failing student will not gain a bit from your tutoring. But with the 96% kid, you don’t spend time in review, you teach him something else, something he might be interested in that might open a career, teach him some electrical engineering, how to design circuits, for example. No it won’t hurt his test scores. But he’ll learn a lot and may find a career. Point is, he’ll learn more because he is better than learning.

    Consider your athletics example. You have an elite athlete like your cyclist … and we compare him to you. Neither of you have mountain climbed ever. Which one after two weeks will be the better climber?

    In that case her half hour investment returns more with the 70% kid than the 96% kid.

    All you’ve done is highlighted problems with standardized testing. And the odds are your 70% who has made a career of pointedly not learning what is in front of him will get exactly nothing at all from your time spent tutoring. He will go from 70% to 70% while if you had spent some time you could introduced your 94%er to a whole new subject not normally covered in high school. The point that destroys your diminishing returns theory is that you aren’t starting with elite kids. You aren’t getting Lance at the top of his career. You’re getting a 17 y/old Lance who isn’t a cyclist, he’s a runner and a swimmer … and you’ll find that you probably can teach Lance more in cycling/training at that stage of his career and he’ll improve more qualitatively and quantitatively than the average in the time you get him. Again you’re trying to press the wrong claim that you can teach a person with less potential more than one with more potential for the same cost. It just isn’t true. You think dumb kids can learn more in the same time for the same teaching effort than smart ones. That’s not what “dumb” and “smart” mean. Explains a lot about the liberal mindset however. You think you “ought” to be able to teach more to dumb kids, because it ought to be true and might be better for the world. But it just isn’t true.

    But in answer to your 2nd question clearly because most people do not want to learn mathematics and need to be pushed. That is why we have schools and teachers for math but no one figures there’s a need for classes on how to text message your friends or look at cat videos on YouTube.

    But you miss the point. From a national/pedagogic standpoint maximing and increasing what we get from the elite does us far more than the average. Getting twice as much from Ramanujan is the same expense as getting 10% more from 5 average kids. But the payoff is far better.

  22. That’s right. The good student can learn more given a finite resource. Odds are actually that the failing student will not gain a bit from your tutoring. But with the 96% kid…

    96% implies some bounded subject matter, such as a standardized test. This might be appicable if you had the 70% kid and the 96% kid AT 70%. Then he might get to 96% faster than the 70% kid would….actually he had to since presumably they both began at 0%

    Consider your athletics example. You have an elite athlete like your cyclist … and we compare him to you. Neither of you have mountain climbed ever. Which one after two weeks will be the better climber?

    OK but that’s beforehand. If I had to make a calculus team but the rule was I could only pick students who never had calculus….I’d rather pull from A students in advanced algebra rather than C students in basic math.

    But again that doesn’t address the question as asked. You’re a teacher, you already have a class performing at a given level and you have an additional resource that becomes available. How do you allocate that resource? Depends on your goals.

    Say you’re paid by the performance of your best student. Then your idea makes sense…find the strongest student and try to make him better. If your’re paid by whole class’s average, then you should find the student who will gain the most absolute points and give the resource to him….and he is most likely NOT the best student. In other words, your logic works perfectly for a sports agent whose seeking to discard all the noise and find the next star.

    And the odds are your 70% who has made a career of pointedly not learning what is in front of him will get exactly nothing at all from your time spent tutoring. He will go from 70% to 70%

    Which just says that the student you should pick may not necessarily be the lowest one in the class.

    But you miss the point. From a national/pedagogic standpoint maximing and increasing what we get from the elite does us far more than the average. Getting twice as much from Ramanujan is the same expense as getting 10% more from 5 average kids

    The Ancient Greece theory, your elites are great but the bulk of your population is made up of illiterate slaves. I’m pretty sure just trying to get nothing but Ramanujans isn’t optimal, nor is just trying to get the highest population average without regard to the top of percentile. I’d think it’s somewhere in between.

  23. Boonton,

    OK but that’s beforehand.

    Of course it’s “beforehand”. To quote yourself, “potential is set in the future, not the past”.

    You’re a teacher, you already have a class performing at a given level and you have an additional resource that becomes available. How do you allocate that resource?

    We were talking admissions right?

    Then your idea makes sense…find the strongest student and try to make him better. If your’re paid by whole class’s average, then you should find the student who will gain the most absolute points and give the resource to him….and he is most likely NOT the best student.

    No. Your better strategy is to bet your better learners to learn more. Then more will be learned.

    Which just says that the student you should pick may not necessarily be the lowest one in the class.

    That’s right. He’s way more likely to be the best.

    I’m pretty sure just trying to get nothing but Ramanujans isn’t optimal, nor is just trying to get the highest population average without regard to the top of percentile. I’d think it’s somewhere in between.

    Uhm. Duh. The point is that you are best served by putting your resources to those with the most potential. If you have a genius you get him what he needs. Then you allocate your resources by potential and learning ability. Bad learners, get the least resources. That will raise both your top and your average optimally.

    If your’re paid by whole class’s average, then you should find the student who will gain the most absolute points and give the resource to him

    Which is why the scores are weighted so badly, to make it look like the below and average students are gaining more and you have a whole bunch of students clustered at the top with little to distinguish them when in actual ability they differ by far more than the poor/average ones.

    Again. Look at your question. You have a good student and a bad student. You have two weeks to tutor. Which can you teach more, who will read more, learn more, master more? You claim nonsensically that the poor student will learn more. Which is complete hogwash. If you claim the poor student will increase more on your tests, all you’ve demonstrated is that you have a really crappy test because it figures that you just taught the poor student more when in fact you did not. To put it more pointedly, your two weeks are spent in literature. Your poor student struggles to complete and discuss two chapters of Twain’s Huck Finn which is about 40 pages long. Your good student reads and writes a 30 page paper on The Brother’s Karamazov not a short story, but 1000 pages and dense. Your good student’s test scores improved not at all. Your bad student gets 8 more vocab words and doubles his verbal score from a 300 to a 400 (200 = 0 on the SAT). But who actually learned more? If your test says the poor student it is dead wrong. Too bad for you, and the next question is why do you like such poor testing methodology?

  24. Boonton,
    Another way to look at your diminishing returns … take Timothy Gowers or Terrence Tao and somebody ordinary, say you. You spend a solid week studying math. You figure an estimate on how difficult the material you mastered and how much of it. Now Mr Gowers or Mr Tao (both Fields Medalists) spend a week working on maths. They record how much and how difficult he that they mastered this week. Who learned more? They did. They are highly talented mathematicians, this is what they do. They learn things in maths all the time, it’s their vocation and they are among the best at it. So. They learned more than you. If the choice was to take your average learning, yours and theirs before the two possible weeks (you spending the week learning maths or one of them) both the average and the elite level improved by having the person better at it improved. So to your supposition, both the average and the elite are best served by giving the most resources to those with the most potential and talent. There is no other alternative. The only way you can pretend the average increased more is by pretending that would accomplish less in a week than you. This is unsupportable as a hypothesis.

  25. We were talking admissions right?

    True but we haven’t defined what our goal is in terms of admissions. A teacher in a classroom who has an extra half hour each day is a bit more manageable since a lot of the variables have been restricted. What is the goal of a college in admitting students rather than just accepting everyone and using the tuition money to increase or shrink the capacity according to demand? If the sole goal is to cultivate a rep. for producing top notch superstars, say Nobel Prize winners, then you have a point. But other goals such as a building a broad and deep alumni network, increasing its influence internationally, etc. may not be best served by trying to just pick out the next potential star and ignoring everyone else.

    No. Your better strategy is to bet your better learners to learn more. Then more will be learned.

    In the case where you’re paid based on the average of the entire class, I think you’re just using circular reasoning. If the 70% kid will gain 11 points but the 96% kid will gain 2 points then you could say the 70% kid is a ‘better learner’ meaning he will learn more of the subject per a given resource. You’re argument seems to be you can get the 96% kid to learn 15% of a totally different subject…since he’s just so bright. Perhaps but your class is designed to teach one particular subject or grade level. Perhaps if you switched to auto repair the 70% kid will learn 90% with two weeks worth of tutoring. Perhaps the fat kid who cann’t cycle would make a wicked pool player.

    Your bad student gets 8 more vocab words and doubles his verbal score from a 300 to a 400 (200 = 0 on the SAT). But who actually learned more? If your test says the poor student it is dead wrong

    Well there’s two ways to approach the measure. One way would be linear and simply say something like the literature class consists of reading 5 books. If you read one book you’ve got 20% of the class. If you read another you’ve got 40% and so on. The other way would be exponential. For the SAT I believe you can learn 10 words and boost your score from a 300 to 400. But if you’re sitting at 600 you’re not going to achieve a perfect score by simply learning another 10 words….you’re going to maybe need 100 words. Why the difference?

    The SAT is a ranking test. The top 1% of SAT scores should roughly align with 1% of those who take the test. If 10% of those who take the test get perfect scores, then the test isn’t helpful in IDing the top 1% of students. So they will add more and more difficult questions to the test to ensure that it gets harder and harder to get a better score. So from that perspective the diminishing returns condition would hold. A half hour of extra tutoring would add more points to the lower end student compared to the lower end.

    Reading books is a quantity based metric. In that respect you may be correct. If an extra half hour lets the top student read 3 more books versus just 1 book for the bottom student, then you have a case where the best way to boost the entire class average is probably also the aligned with the boosting the best student. But….

    Most classes are designed to cover a finite span of cannon. A US literature class, for example, wants to cover 4 or 5 books that are choosen to represent major themes in US literature. Reading a bunch of extra books is nice, but not really the goal of the class. In that case you’re in a boat that’s very much like the SAT metric. If your’re measured on how many books were read (1 book read by 1 student = 1 point with books other than the 5 titles either not counting or counting at a reduced level), then the top students will probably not provide you with any increase since they are likely to have all the books read anyway. This would align with my example of the ’96% student’ versus the ’70%’. A percentage presumes some finate amount of material, not an unbounded subject that can easily consume many lifetimes (i.e. ‘higher mathematics’).

    Now Mr Gowers or Mr Tao (both Fields Medalists) spend a week working on maths.

    What mathematical insights were produced by Mr. Gowers and Tao last week? Probably none but maybe a paper or two was just published by them. Among simple mortals, how many had insights by taking summer courses in basic or entry level higher level math (or doing online courses, books etc.)? Let’s say a hundred thousand learned how to correctly calculate and use the concept of an average. In terms of increased output, improved outcomes etc., suppose a UFO lands and offers humanity this deal….they will run a computer program that will spit out two or three papers on par with the best work of Gowers & Tao, but the price of this computer program will be altering the brains of several million people to make them forget everything they know about the concept of ‘average’. Would this be a sensible deal or not?
    .

  26. Boonton,

    True but we haven’t defined what our goal is in terms of admissions

    Yes, but increasing either the average or getting the best “team” is accomplished by getting those with the highest potential the priority for resources and conversely to not prefer resources to the poor performers.

    In the case where you’re paid based on the average of the entire class, I think you’re just using circular reasoning.

    And I think you’re using faulty reasoning. Again put it simply. Better learners learn more with the same resources. In the case where you’re paid based on the average of the entire class, I think you’re just using circular reasoning. To have more learning you want the better learners learning as much as they can and push that “much as they can” as far down the learning potential slope as you have resources. That maximizes your average and your best team at the same time.

    Look. What defines a better learner is that he can learn more quicker. The logic is inescapable. To maximize actual learning you are best off if the better learners are maxed out. No two ways about it. I think your fundamental fallacy is assuming 30 more minutes is going to make any sort of impact on the poor learner.

    then the top students will probably not provide you with any increase since they are likely to have all the books read anyway

    All that points to is that your test is flawed. It isn’t actually measuring ability to learn or what has been learned in any useful way. If person “A” learns 6 new things that should reflect the same increase in his score no matter if his at the top or he bottom of the scale if you want to use it to measure any average that is meaningful.

    One way would be linear and simply say something like the literature class consists of reading 5 books. If you read one book you’ve got 20% of the class. If you read another you’ve got 40% and so on.

    On a completely unrelated note, during High School my brother estimated I read about 500-600 books a year (back when I had leisure time, eh?). I however didn’t get an 90000 on my verbal SAT.

    What mathematical insights were produced by Mr. Gowers and Tao last week?

    I don’t know. Check their blogs. The points wasn’t about millions. We took an average person (you) and an exceptional one who is a specialist. Both studied maths for two weeks. Your claim is that because you have so much more to learn you would learn more. I don’t agree even with that. You will learn less than they in an absolute sense. Their job is learning new maths and they are among the best in the world at that. They do it every day of every week. They still learn more than you do in a given timespan. You have a theory drawn from fitness that those who start the lowest will show the most gains. I doubt the truth of that in fitness, if you and Lance train hard for two weeks, Lance will probably gain more than you in VO2Max or strength than you do, because he has emotional, genetic, and cellular advantages, his body responds to training better than the average person. However “learning” is not like training. There is always more to learn and it doesn’t have the same physical/physiological limits as does athletics. There are actually people who learn faster than others. Those are the ones that benefit most from education.

    I think another (liberal?) assumption arose in this last comment. You suppose

    Perhaps if you switched to auto repair the 70% kid will learn 90% with two weeks worth of tutoring. Perhaps the fat kid who cann’t cycle would make a wicked pool player.

    Life isn’t fair. It is more likely that that smart kid, if he tried, might be better at auto repair if he studied it and better at pool too. There is a myth in liberal academic circles is that everyone is “best/better” at something. It just ain’t so. Some people are just better at everything than some others. However, that being said, it is true that some people have aptitude for different things. Mr Armstrong would likely not, if he decided to change careers, be able to become really good at maths or engineering. If you are considering state or federal aid, then the question arises, why give aid to anything but STEM fields. In fact, that is a little bit of what we do, in STEM fields graduate school is typically state/grant supported while in other fields it is not. You might be able to figure out some reason why Harvard and the Ivies don’t give grants to those who show aptitude in auto repair or evening bar games.

    In the morning commute, I listen to the ESPN radio show “Mike & Mike”. One Mike (whose last name I don’t know) has always been a professional sports fan and sportscaster. The other Mike (Golic) was a very funny man and a professional nose-tackle (defensive line) for various teams. Mike (not Golic) as an amateur enjoys and plays tennis for fun. He was shocked and surprised that once when he tried playing tennis with the other Mike who had basically never played tennis before and has been out of sports for decades and is no longer at the fitness level of a professional athlete that Mike Golic beat him easily at tennis. A professional athelete has more potential for sports, has better natural hand eye coordination, agility, competitive instincts and natural ability that he could just win. Mike Golic started with “more to learn”, he knew nothing of tennis. But is potential was so much higher he could in the course of a match, overcome an avid amateur. Learning is like that for the gifted. Give them resources and they’ll even go farther.

  27. Boonton,

    A half hour of extra tutoring would add more points to the lower end student compared to the lower end.

    Except that’s just gaming the test. The test is allegedly there to serve as a measure to rank people by the learning/learned potential and achievement. If a bad student gets boosted, he’s just going score higher than he would and fail at the next level. And … almost all the top students already spend far more than a few half hour session learning to game the test.

    Educators like Mr Darrell who comments here decry “teaching to the test” and gaming the test as a replacement for real education. So … here you are, with your liberal membership card and all, arguing the advantages of getting the poor students to game the test, because the gaming payoff is better.

    I think you might want to reconsider.

  28. Except that’s just gaming the test. The test is allegedly there to serve as a measure to rank people by the learning/learned potential and achievement.

    Is it? The SAT asserts it’s about aptitude. It claims a student who scores higher on the test is more likely to do better in college. It doesn’t promise to be a ranking test in that the student who scores the best will do the best in college. Two different concepts.

    And other tests, say the written test for a drivers license, isn’t looking for the best but is looking for whether a given body of knowledge has been mastered. “Teaching to the test” may be a good thing or a bad thing depending on what the test is *really* measuring.

  29. Boonton,
    There are companies that make money off the average-but-ambitious student teaching them test techniques. Hows is that different from your tutor-to-the test.

  30. Boonton,

    The SAT asserts it’s about aptitude. It claims a student who scores higher on the test is more likely to do better in college. It doesn’t promise to be a ranking test in that the student who scores the best will do the best in college. Two different concepts.

    Two problems. It’s not “two different concepts” it’s just an absolute claim or one with a disclaim of not being perfect. The other problem is look at your game. You claim that teaching a poor student 10 vocab words might increase his score by 50 points. If true, …. how exactly does that actually increase his likelihood of doing better in college. It does nothing for his chance of going better in college, in fact it might do him a disservice, putting him in a school at which be likely to fail.

  31. You claim that teaching a poor student 10 vocab words might increase his score by 50 points. If true, …. how exactly does that actually increase his likelihood of doing better in college.

    I’m unclear how a poor kid studying vocab words is ‘gaming’ the SAT? What do you think happens in the prep courses that upper and middle class parents shell out hundreds of dollars for their kids to take? As for how this makes one better at college, isn’t that irrelevant?

    The people who make the SAT make a pretty good dollar selling their results. Making sure the test measures something relevant and useful is their problem, not the problem of ‘poor kids’.

  32. There are companies that make money off the average-but-ambitious student teaching them test techniques. Hows is that different from your tutor-to-the test.

    The only ‘test techniques’ I’ve ever really come across is time management and some analysis on when it makes sense to guess and when it makes sense to leave the question blank. Other than that test prep is really taking practice tests, reviewing the stuff you got wrong, then taking more.

    In itself, that probably has some educational value on its own.

  33. Boonton,
    By poor I’m hoping we both meant poor learners not some class crap.

    Test taking techniques that work involve strategies of working maths problems from both ends after first eliminating obvious “trap” solutions. Not calculating the answer to the finish but only to where the choices which might possibly becomes one. Scanning questions prior to reading the comprehensive sections prior to reading the section. When to guess. There are negative scores for wrong answers, but the weighting advocates guessing if you can eliminate one or two possibles … how many to eliminate before guessing pays off …

    Look at “KapTest” … what are they selling. According to you it is worthless. The two questions in the air are whether this is “gaming the system” and not reflective of college success or learning ability or is it not? And the second question is the Kaplan tutoring any different than your vocab suggestion?

  34. Boonton,
    Unless NJ school systems are different than here, multiple guess and automated test result reading is the standard practice for all tests, which is of less pedagogic value than other methods but so much cheaper and because teaching to the test (and the “test” in question is multiple guess) .. but is it educational in any real sense? Not really.

  35. The ‘tricks’ are part of the tests design. Take ten questions. One student can get them all. Another can only eliminate a few possible answers. Another can only guess or skip. Since guessing after elimination only increases your odds of a right answer, it’s very unlikly the second student will guess all the questions correctly leaving him with a score equal to the first student.

    Unlike most classroom tests and quizzes, the SAT has to be designed so that most students will NOT answer every question. If not then you’d have a problem where the top 1% of scores would be something like 10% of test takers.

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