Higher Education is Actually Darwinian

Many people have not taken advanced math or advanced science. They think education is all about teaching. However, it is a mistake to believe that a smarter or more accomplished professor will be able to teach all students.

In math, people hit a learning wall. They are unable to master a foundational level of math and cannot proceed to higher levels. This could happen with multiplication, algebra, geometry, calculus or some higher levels of calculus. They could also master the prior levels but are just unable to understand the next level.

A student can be sitting in a fourth-year math class and they were doing great up to that point. Suddenly, new topics come up and the student can no longer get it. The new topics require the ability to visualize something and they cannot do it. The professor will put up new equations and provide some discussion of the principles. Other students will understand but some will be unable to get it.

You thought you were good at math and it was going to be part of your career. The lesson is that you were wrong. You can be a well-paid life insurance actuary or you can find productive work in finance. However, advanced math is now done.

Why not ask for some private sessions with the professor? The professor breezed through this level of math and went onto five levels beyond. He cannot debug your problems with it because he never had those problems. He probably did not successfully help other students with those problems either. The other students dropped the classes and realized it was over.

How about using tools like calculators, spreadsheets and computer programs? This can help with certain problems. It is possible that someone could train themselves through visualization issues.

However, if you are using crutches you will not be able to keep up with a recreational runner. You will not keep pace with a college athlete.

Many people use spreadsheets for statistics. The functions are like black boxes. They are putting in inputs and answers are coming out. The workings of the functions are a mystery.

Higher education in math, science, and medicine is doing some teaching but it is doing a lot more selection.

Modifications and Caveats

There have been comments which correctly point out modifications and caveats are needed.

Many teachers at high school and through universities are not competent. It looks the student cannot learn when it is the teachers.

In Universities, there are professors who are famous for research but are unable to teach. There are others who are able to teach. There should be separate careers for lecturers and researchers.

Math, science and other subjects are very broad. You need to parse where you are really hitting a wall and the size and impact of the problem area.

Einstein was not a natural at differential calculus. Einstein was not strong at graphing or rendering complex equations.

Great artists of the past need not have been great at all aspects of art. The Impressionists may not have been able to match Vermeer for realism, but they had other contributions to make.

However, Just because Mugsy Bogues and Spud Webb exist as short pro basketball players, do not convince yourself that you will also be the exception and also make it the NBA. This would apply to academic pursuits as well.

Thanks to the commenters for adding the needed specification.

79 thoughts on “Higher Education is Actually Darwinian”

  1. Depraved randian moralization. The stemtards cling so desperately to the myth of meritocracy as the true nature of human affairs shatters their undeveloped limbic systems into fascizing barbarism of the most pathetic character. Yes you were chosen by the great gnon to speak to combinatoric engines, but you are completely useless when it comes to anything related to how human beings are organized by distributed incentives.

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  2. We mistake our evaluation with natures. Mama Nature doesn’t care if you are stupid. All she cares about is are you surviving and are you reproducing.

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  3. Private schools don’t always do better than public schools. In affluent suburbs the public schools usually do better than the private schools because they can afford better teachers. Better teachers, smaller classes usually have better results.

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  4. This is obvious. A huge number of people going to Harvard want to be doctors or lawyers. 70% of freshman in MIT want to be engineers. But most don’t make it. They are not unmotivated. They are already the product of some of the most rigorous selection process. They receive the best we can offer in money or time. So the idea that we can all succeed with just better teacher, more time or enough motivation is just not true. Human brains are just too small to do top end work. That might be the reason why scientific progress will slow down unless AI achieves supra-human intelligence.

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  5. As my Dad, a doctor, puts it: “Anyone can pass medicine if they have the ability and motivation to sit down and memorise a phone book.”

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  6. “Being able to do derivatives means you’re evolutionarily superior to everyone else”

    Being so bad at reading comprehension that you got this interpretation of Brian’s article makes me wonder if you had trouble in school.

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  7. And let’s not forget that the math for it is perceived complexity is easy to teach and learn since it is very formalizeable. It can even be programmed in a dumb computer.
    Wolfram alpha can do amazing things but it is not smart per se. The question is how much effort would one like to put. If making everyone able to solve differential equation was deemed important enough, it could be done at the age of 12-14 for all the kids without sever neurological or attention issues. If one can learn the arcane grammar rules of a language (some are simpler, but probably they let the complexity budget be used to complicate some other part of the social interactions 🙂 then it means that the same units in the brain can be used to do logical and pattern matching . Now some people can get it immediately , for some could be a huge effort with extra explanations and simplifications. Therefore, the proffessors use the cheap optimization of weeding out the least performing or the ones that are less convenient.

    And sometimes the selection/filtering criteria for a given program are arbitrary or even unrelated. For example, medical doctors are selected for their stamina and ability to function even after sever sleep deprivation. Some schools by using rote memorization select for calm personality and good memory 🙂

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  8. a few points,

    1. lack of interest. I think interest is related to talent. When someone does something, if he is successful, it builds more interest. If he does not understand it, it tends to reduce interest.
    2. Unevenness of teaching, Sometimes a bad teacher can sour the student from a subject and a good teacher can elicit more interest from the students. Overall though, the amount of talent or lack of it does put a limit on how far one can go. We cannot blame the teachers, they too, are limited human beings, some a good, some a bad.
    3. Sometimes, one gets a decent grade without completely understanding a topic, when advanced to the next level, he gets in trouble due to shaky foundation from the previous year. I saw this happened to some students.
    4. In the old days, calculus was the domain of a privileged few. Everyone of them would be able learn since they were all exceptional students. Now it is taught in most high schools. The push for more and more education for everyone have exposed the limitation of the students. Unlike in Lake Wobegon, not everyone could be above average.
    5. The lack of a fighting spirit due to the good life have compounded the problem as most kids are not able to take hardships and strife.
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  9. I do not agree entirely with your premise Brian.
    I work with learning disabled kids (varying from low iq to high iq) e.g. G5 dyslexic kids high IQ only reads at G1 level – an effective teacher can get the child to learn to read.
    I agree that you need to have the “ability” to do advanced anything i.e. education only gets you so far, but education provides the basis for your learning and a good teacher is invaluable in that learning process

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  10. “Colleges should do a better job of differentiating between lecturing professors and research professors.”

    You left out the TAs. TAs should be chosen on some basis other than their need of a job so that they can continue to be cannon fodder for their professors’ pet projects. As a simple filter, I’d suggest proficiency in English and an accent that isn’t so thick that their sections are spending half the time wondering what the hell they said.

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  11. LOL I saw a stone thrown my direction.

    Yeah, it sounds like touchy feely talk, but I do believe in the influence of mundane exposition to science and technology in child friendly settings.

    First at home with mom and dad, then in accessible, nearby places.

    That doesn’t exclude passing them through assembler courses before admission to CS, or exams or any other of the known admission filters we already have.

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  12. Yep. However, people here have already opined that there’s something to ”and Sally came into the program already primed with a keen sense of wonder (for the subject) and equally laudable talent for digging and and trying to suss out the abstractions presented as part of the coursework.”

    It was a sheer genius to force every UCBerkeley CS-1 student to code up a tiny program in hand-decoded binary, and key it into a PDP 11-2. All of 20 or so words of memory, the little program had to read keystrokes on a terminal, and simply echo them back, so that one could see what one was typing.

    Got rid of half the class, that one assignment.
    Either you had the talent, or you didn’t.
    Very valuable assignment.

    Later, we were ‘forced’ to code tough little chess-piece-move programs in Fortran, on decks of Hollerith cards, and had to wriggle through the machinations of that bubblegum-and-bailing-wire computer interface. Again, excellent results. Another 75% of the class was trimmed out.

    By time we were done, only 8% of the original class remained.
    Darwin, 101

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  13. Maybe I took too many lunk pills today, but I just don’t get what the thrust of the article is about. It seems to be defending the hypothesis: progressive learning is a process not unlike the survival-of-the-most-apt aspects of Darwinian species selection.  Faster time scale. Especially in the sciences. Right?

    By one of those inversions-of-nature that are so vexing, my own experience with higher learning (UCBerkeley) showed that I have an unusual talent for remembering most-everything I’ve ever learned to near-eidetic clarity, but I also possess a terrible anti-talent of not being able to learn anything at all at what others consider a normal rate. Hence, while I can still help my grad school “kids” with their Laplace transforms and cross-convolution spectral coding … without books … it also took over 10 years for me to learn those things whilst the rest of my engineering buddies where rocketing past.  

    Which brings me to an interesting point.

    Namely, that most people either internally, but certainly externally, have their SPEED-of-learning talent (or in my case, lack of it) underestimated. And conflated with their retention talent.  

    Just saying,
    GoatGuy

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  14. Then why doesn’t Mexico rule the world instead of the US? Like most non-US countries, Mexico has mandatory calculus in high school. US math curricula is so poor that when foreigners who know calculus come to the US, US calculus teachers fail them for the usual US teacher bullshit, like “you didn’t solve it the way I wanted you to.” You know, the type of thing actual mathematicians hate about how math is taught in the US.

    “Being able to do derivatives means you’re evolutionarily superior to everyone else” is not only incorrect, it’s pseudo-science, of the kind that shows you don’t know the history of the manipulation of science by racists. And it makes me wonder how you feel about black people and, ironically enough, Mexicans.

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  15. No, just the opposite. “of the fittest” … implies that there is a LOT of variation in talents and abilities between people; this is borne out in real-life as anyone observes in less than an hour of social interaction with completely random people. Just saying,
    GoatGuy

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  16. Saw this problem when I was teaching at a large university. We had two concerns, to teach those who could be taught, and to eliminate those who could not be.

    The problem was that most instructors are not able to handle both missions at the same time. Most instructors tend to float to one extreme or the other. The first kind starts cutting, cutting, cutting; if the student doesn’t pass muster right then, eliminate them, with no concern that the teaching method might be inappropriate (like trying to teach a visual learner through lectures). The second type of instructor develops a philosophy that it is their sacred duty to lift up every student to ultimately succeed.

    The problem being that there is a very large subjective gray area in between where one or the other action should be clear, and it can be made wider by the instructor being less skilled in teaching than they could be, the instructor being less than confident in either their teaching abilities or in their assessment capabilities, the instructor being overconfident in either their teaching abilities or in their assessment capabilities, or even the student being too stubborn to admit defeat. The last may sound like a good thing ,and sometimes it is, but it usually turns out badly more often than not as it tends to waste time, money, and resources, in addition to being enormously demoralizing.

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  17. Convergent series in 3rd quarter calculus washed me out of aerospace engineering, but there were signs I was struggling earlier. Doesn’t help when the TAs struggle with the language so they can’t explain the concepts, but the basic issue was a lack of both natural aptitude and desire to overcome that lack. Brian’s point about it being difficult to help someone when you don’t understand why they are struggling is a very good one. And definitely not limited to the teaching professions,

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  18. Testing Procedure Specification. It’s paperwork from Information Technology Quality Assurance standards. Quoth IEEE 829:

    The Test Procedures are developed from both the Test Design and the Test Case Specification. The document describes how the tester will physically run the test, the physical set-up required, and the procedure steps that need to be followed. The standard defines ten procedure steps that may be applied when running a test.

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  19. Its very important for me when teacher explains not only how it works but why IT works that way and what are potential practical applications of quaternions for example.

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  20. This sounds like Brian is not all that skilled at Math himself… “higher levels of level of calculus” whatever that means… it sure doesn’t correlate with things I studied for my Mathematics degree.

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  21. Though, I do have a friend who started half a dozen companies, the first when he was still in high school.
    Many did very well, with big contracts and cushy government deals.
    And now he’s 76 years old and broke, sleeping on a friend’s spare bed.

    Seems all that stuff about “do what you love and the money will come” needs a dose of “but when it comes, don’t let it slip through your fingers”.

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  22. Common misinterpretation of the results.

    Reading Harry Potter moves you closer to the mentality of a 13 year old.

    So if you are below 13 then it is usually a move UP. But if you are 27 then…

    It’s reading the post publication “clarifications” by JKR that decreases everyone’s intelligence.

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  23. That is of course true, and that is where the teacher is sooo important. It is his job to awaken an interest in the subject to achieve an acceptable standard – pass mark. If he can’t do that, he should not be a teacher. But with teachers being mostly government employees, it is difficult in nearly all countries to get rid of incompetent ones. I suppose that is where private schools score.

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  24. Whenever someone use the term Darwinian I know there is going to be trouble. Survival of the fittest implies that everyone living is equal.

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  25. My wealtest friends started companies when they were young doing technology or trades. Everyone else is broke or struggling. I agree with old school innovative govt jobs even better if you learned technical russian… They have beurocrotized those out of existence. OHSA wins the mild and meek own the world and it costs too much

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  26. Bad choice of evolution picture by the way. Giraffes are the textbook example of an evolutionary change (long necks) that seems to be for an obvious purpose (eating leaves off trees) but actual evolutionary biologists are not at all convinced and just don’t know why they grew longs necks.

    Google “Why giraffes have long necks”

    One leading theory is mating selection.

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  27. Also, besides a propitious home environment, this motivation can come from the most weird, unlikely places, but mostly related to instilling a sense of wonder.

    For example, and for several students in STEM I have known, their initial motivation seemed to be exposition to something they faced as little kids that made them experience a sense of wonder or a feeling of something grander, beyond their current understanding and abilities, but that they ‘got’ even partially and made them feel special and smarter.

    Visits to science museums and planetariums without peer judgement, illustrated books, sci/fi movies and series that made them ‘want to be a scientist’ or an engineer.

    But this works better when they are pretty young. Teens without such previous exposition will hardly make fond memories or experience such sense of wonder.

    And peer pressure tends to be detrimental for a teenager, considering any such precocious intellectual interests as weird or marking them as ‘nerds’.

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  28. And to answer the OP question: I stopped advancing in Math at about the LaPlace transform stage of partial differential equations and the student test level of statistics.

    I could do them. I got decent marks. But I didn’t understand what I was doing, just going through the learned motions to solve the problems. And hence when given choices after that stage… I chose the choices that didn’t involve using that level of math.

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  29. I’d like to reinforce TRM’s point 5 here.

    You learn addition and subtraction until you can do it without thinking about it.
    Then you do multiplication and division, until you can do it without thinking about it.
    Then you do fractions, until you can do it without thinking about it.
    Then you do algebra, until you can do it without thinking about it.

    The problem is that humans can’t think about too many things at the same time.

    If you are trying to learn fractions while you still have to stop and think about “what is 3×6?” then you can never be concentrating on the fractions.

    If you are trying to solve 2A + B/6 = 3A and you still aren’t completely smooth with your fractions because you still have to stop and think “so what is 3 x 6?” then… algebra is going to be a huge struggle and calculus will be a dealbreaker.

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  30. It’s still darwinian. Just that the qualities being selected for are now persistence in the face of meaninglessness and ability to deal with interpersonal relationships within a politically charged atmosphere.

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  31. Yes. Brian’s model works within an existing educational environment. With a change in teaching style the stopping point for different students would be different*.
    HOWEVER, given that most students are operating within a single educational environment, the model works most of the time.

    *A different teaching style might let many students go further than before, but it’s also possible that some students would be less suited to the new environment and hence do less well.

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  32. It is a sad, sad truth that when I am called on to give advice to students as to what will really help them in their careers, I list:

    1. Learn to type properly. Good touch-typing will make 50 to 100% of your daily work tasks take less time and less effort. I guess that an engineer (for example) would probably have another 30 mins to an hour in each day to do real work if their typing speed went from 60 to 120 words/minute.
    2. Learn advanced skills with excel, powerpoint, word, emacs, vi, and a couple of other things selected for your major. Like the typing, just knowing all those hot-keys and hidden menu functions will probably mean that you get that report done before lunch, and not have to miss 20 minutes of break time.
    3. Public speaking. Join a debate club. Do the readings at church. Something. The person who is comfortable standing up in a meeting and talking is going to get the promotion compared to the equally skilled person who kept their head down.
    4. Private speaking. This is the one I don’t have. Quite different from public speaking, this is the skill/aptitude of going up to that person over there and initiating a conversation.
    5. And yes, get a degree or trade in something useful. But this is number 5. And this is because I’m talking to a student. You can do just fine using sales or something without any piece of paper. But I can’t advise on that.
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  33. What you’re really doing is making a point about learning math in a classroom. Different people are going to get hung up on different skills. But just because you struggle with a particular skill doesn’t mean that you won’t find the downstream skills very simple, once you’ve mastered your problem–except in a classroom. There, the first thing you can’t master in the time allotted pretty much kills you.

    Are there variations in overall mathematical ability? Of course. But the modern classroom only measures the first place you have a problem, not your overall ability. If you fix that by making the learning self-paced, and preventing students from moving on until they’ve mastered their problem, only then are you in a position to distinguish their overall ability.

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  34. Einstein never “almost failed” HS math. That’s just a story that people made up to make themselves feel better when they fail. He was a child prodigy in math and physics.

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  35. I wish they’d teach kids a simple assembly language in about third grade. Until you understand how a computer works, the temptation to try to “lawyer” your high-level language is overwhelming. Once you realize that your HLL isn’t magic, you can figure out what’s likely to work as an expression in it.

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  36. A few thoughts:

    1) I think Brian’s under-selling the significance of mastering all the antecedents to the skill you’re trying to learn. The vast majority of cases of hitting the wall are because the student is too deficient in a prerequisite skill that’s essential to mastering the skill at hand. This means that, as long as you’re willing go back and work on the prerequisites that are giving you trouble, you can usually make progress. Being slow and being incompetent are two different things.

    2) That said, being slow at mastering any math skill in a modern classroom context is just as bad as hitting the wall. If you can’t keep up with the class, then you’re going to get a bad grade.

    3) One of the things I like best about Khan Academy and stuff like it is that it’s very good about making the student good at the prerequisites before throwing them into something new. It allows somebody who’s having a problem with one thing to slow down without being blown out of the class.

    4) If you have skills A–>B–>C, just because you’re having trouble with B doesn’t mean that C (and D and E) won’t be a breeze for you–except in a classroom.

    5) For those of you with small children, I can’t emphasize enough how important it is for kids to memorize their addition and multiplication math facts. These are the sine qua non prerequisites for everything that follows, and learning them at a fairly young age carves out some neural real estate for mathematical thinking.

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  37. Just to add more to my other comment.

    Teaching vs selection (which I read to mean “innate ability”?) seems to me to be a gross simplification and so a false dichotomy. You can easily have someone with a high IQ that does not do so well in the end because of an uninspired teacher or social environment. Conversely you can have someone with not such a high IQ but who is inspired and passionate who in the long run does better than the person with a high IQ. A good set of teachers can make this difference. In other words both factors are important.

    If you ask people at the top of their profession they will usually cite an inspiring mentor or teacher that helped push them to the top. At the same time, if they are really at the top internationally, then they will probably have an innate talent for it as well.

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  38. This does make sense. Being weak in particular aspect does not mean that all higher levels are cut off. There is also bad or incompetent teaching. The wall could be an illusion when it was teaching. You can go very far in another area.

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  39. Well I agree students have varying innate abilities for all kinds of skills. Some people are colour blind, some people have photographic memories. Saying that some people are better at maths than others seems self-evident and trivial. At the same time, passion, hard work, good teaching and persistence can account for more than people think. I still don’t see the point of this article. Who are these people that think that anyone can be taught to do anything? I think everyone probably recognises that individuals have varying talents.

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  40. This assumes that the brain structure remains fixed upon encountering the wall. Essentially it embodies a belief that the brain itself does not evolve on encountering the challenge. I am not sure this is the case. The brain is inherently fluid and can adapt.

    https://www.newsweek.com/learning-read-can-dramatically-change-adult-brain-615077

    I liken this to reformatting the brain to better accommodate the new class of information. I have personally had to do so several times upon hitting such walls.

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  41. While I do believe there is a degree of talent involved (not everyone can be a virtuoso, and there are only a few), in my experience actual results come from how decided and obsessive the student is to learn something, specially in topics that most people won’t find any practical value learning.

    This tenaciousness or relentless motivation, I’m afraid is out of reach of formal education. People already bring it to school since childhood, and tend to carry it through all their academic life.

    And again, in my experience, I’ve see that a lot of it comes from home. From parents that actually pass time reading books at home, discuss complex topics and enjoy some intellectual life.

    I’ve seen it flourish in a background without that, but it is very rare. But what I’m certain is that if you aren’t motivated by the time you are in high school, any obstacle that makes you start sweating for it will frustrate and demotivate you.

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  42. My personal experience (anecdotal evidence, but evidence still): I failed factoring and managed to escape more complex math after that in high school. I started college at 21, and had fantastic remedial math teachers. I went on to earn a bachelor’s in math (with high honors) and recently completed a PhD in a math heavy field (statistics/informatics).

    I do struggle with abstract conceptualization – something my undergrad advisor and I talked about when I was planning out applications to grad school (he was blunt and told me a pure math advanced degree was likely out of reach for me). But I learned how to deal with my own limitations through excellent teaching.

    Because of my background, I’ve successfully TA’d math strugglers and built their confidence. In short, yes, we each have our limits, but good teaching can raise the level many individuals are capable of reaching. It’s not a failure for someone to recognize they don’t have interest or aptitude in a given subject, but we do need to make sure good teaching is provided before assuming failure is completely due to a students’ aptitude.

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  43. read the bell curve by charles murray. Or if you want a little less controversy, the g factor by arthur jensen.

    Unlike the public firestorm around the bell curve would suggest, its main hypothesis is NOT about the difference in IQ between races. It is about the relationship between IQ and success; that modern society like no other has made IQ a primary driver of a person’s career and earning ability.

    hence the name the ‘bell curve’ – his main point is that newer, decent jobs are so technical that our society is becoming stratified as a result, and that a lot of the alienation and decay in traditional communities is because of this stratification.

    I’d say that brian is spot on here – it holds with my experience as a software engineer. Hiring someone who isn’t technically astute enough is just asking for a headache; they will not get it and as someone who is managing them they will have a NEGATIVE impact rather than a positive one.

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  44. As a freshman in high school, I got a D in Algebra… it wasn’t me… it was the teacher. How do I know? Because I had to take it again for summer school from a real math teacher, not the P.E. coach teaching freshman algebra on the side cause there weren’t enough real math teachers. Oh… and I am now an expert in digital image processing.

    When I was struggling as a primary student pilot trying to land my aircraft (yes, mine)… my 19 year old instructor could not explain what I was doing wrong. One phone call to the previous owner of my airplane, a professional pilot working for the FAA, got me over the hump. Now I’m a flight instructor.

    I was once sitting next to a tutor trying to help a young woman understand negative numbers. The young woman just could NOT “get it”… finally, in exasperation, I jumped and drew a picture of a swimming pool with a diving board… the talked about the difference, the number of feet a diver fell when she jumped from a ten foot board and touched the bottom of a six foot deep pool…. positive number above the water, negative numbers below. Suddenly, as if by magic, negative number and their basic math properties started to click into place.

    A college prof. let me in on the truth of advanced math textbooks… he explained that they weren’t written to be used to actually teach… they were written to gain tenure… and to do that they had to impress other math professors. It’s not the students who are failing, its the professors.

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  45. Such. pain! No. news. Ugh.

    I had to work my arse off in math and I’ve forgotten more than most will ever know. When I felt weak in a subject, it caused me great anxiety. The only way I could alleviate the anxiety was to beat my head against the concepts until they made sense. This worked 3.7/4.0 of the time, so – yeah fun being me: undulations of anxiety chasing calmness until it was over and I became BORED TO DEATH IN THE WORKPLACE. Now I put cover sheets on TPS reports. I handle several TPS reports a week and they require various flavors of cover-sheets. SAVE ME PLEASE!

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  46. A teacher implies the existence of pedagogy. Pedagogy is not obvious and some are much worse than others.

    I took more than enough Calculus in my life to know that some teachers suck and have no business being in front of students.

    Colleges should do a better job of differentiating between lecturing professors and research professors. Research professors should never be allowed to teach at the undergraduate level and lecturing professors should be hired and fired based on their ability to actually teach students.

    As the child of two parents who were teachers who spent most of my childhood around teachers who were friends with my parents I can say that half the teachers at any school are there to phone in their job and don’t really care about their kids learning.

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  47. As the Chinese say: when the student is ready, the teacher will come. The choice to learn to the point of mastery doesn’t necessarily happen within the confines of a higher education (system) and the failure to (commit to) a study doesn’t preclude succeeding at mastering a field in later years. One can argue intelligence, but usually that is not the issue for people who start higher education. One can also argue that education has as a goal a degree or a career or a skill, but many people do not think that way. Many go to university, naively, to be exposed to engaging ideas. If they turn out to be less than interesting or too labor intensive to master (which is an intuited cost benefit calculation), people second guess their goal of getting a degree and stop doing the work. I agree with a comment below stating that (social) Darwinism is not the right lens.

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  48. It should be pointed out that many degrees in higher education are not Darwinian. if a degree lacks empirically measurable milestones then it really isn’t Darwinian because success or failure isn’t a byproduct of learning.

    E.g. English majors, <*>studies, etc.

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  49. Counterpoint:

    Years ago I had a friend whose math major girlfriend was struggling with her C++ programming class. She had been in class for half a semester and just wasn’t getting the language. So I taught her C++ from the ground up by explaining how computer memory works and then by showing how everything in C++ is basically memory manipulation. All of a sudden things like pointer arithmetic made perfect sense to her.

    Sometimes the instructor just sucks at explaining stuff. In this case I explained how the lower level hardware actually worked and then the higher level language became obvious.

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  50. Not your best article, Brian.

    Your thesis may be correct, but your argument is not sufficient, precisely because you attempt to elide quality-of-instruction. Whether or not the instructor found X difficult has no bearing on how easily he or she should be able to teach it.

    It’s a worthy concept you should revisit with considerably more attention to faults and cracks in the argumentation.

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  51. Part of the problem with this wall is that pacing is not controlled by students.

    Maybe the student *could* get the new concept, but it would take three weeks instead of one. In the current lecture based semester model, that is not an option. New concepts that are dependent on the hard one are arriving in a week so now the class has become impossible.

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  52. I would argue you simply arent part of a lucrative opportunity. So you muddle along without math is immaterial to the fact that some use it to excel beyond your wildest dreams. Most people just dont care. THose who do are alone on islands of intellectual and political dispair…

    Math is just a placeholder and example

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  53. All the comments so far dont seem to get the point. Perhaps they never made it to higher math, dont use higher math. I dunno interesting tho that anyone would disagree with this. I think it would be neat to see how this would play into the singuarty and AI. IF humans have to compete with AI in college im not sure any AI teachers will have the time for humans.

    The point is the purpose of the education system it to find the winners and clear the losers so employers can get someone useful

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  54. in My opinion the real real people hit a wall is because the higher you go in math the less they explain and practice in the textbook with larger incremental steps in the examples… then you get a PhD level math book and you spend 10 hours trying to add 1+2 simply because they didn’t explain you needed to add 1+2…. of course over time the barrier to entry becomes lower as more people learn the topic and start telling others the secret handshake… then you have a million people over in India making YouTube videos about how to add 1+2 in an “advanced” math book… then you realize it’s just as stupid as the lower level math…

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  55. I did not say higher level math is needed for success. You can do fine and even better without it. In fact you can make more money as an actuary or a finance person. You can delegate to the quant. I am just saying at certain point learning and teaching stop and selection takes over. I am talking for individuals.

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  56. I am making a point about teaching versus selection in higher education. If you do not want to believe this is the case then you are free to keep believing it is all teaching.

    I can go find evidence, but my hypothesis is that you will not be convinced and I will waste my time.

    I would ask. How far did you get in your studies in math? When did you stop and why?

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  57. I am saying that almost everyone will not be able to get past certain learning challenges. If there is new teaching this could enable a percentage who did not understand to get past certain learning hurdles.

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  58. Nonsense. At the societal level non math minded can delegate math tasks and not suffer any negative consequences. You don’t need to use a spreadsheet or another tool, you employ a nerd with a brain as your tool.

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  59. Okay, so I guess the point of the article is you need a teacher who can relate to your struggles.
    Or, nowadays, you can go online and get free help in many areas, if you’re willing to put in the time and effort.

    Not sure how that’s “darwinian”.

    Reply

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