8 ms·

First of all, I don't think math/science is harder than history or art. I consider both Newton and Shakespeare to be geniuses; same with Bach and Leibniz. I thi

by dvt 13y ago

First of all, I don't think math/science is harder than history or art. I consider both Newton and Shakespeare to be geniuses; same with Bach and Leibniz. I think it's an established empirical fact (maybe not -- see NYT article) that to become an expert at anything, it will take you upwards of 10,000 hours -- be it playing violin, studying history, or doing number theory. So I don't think the effort is any differentiating factor. But I do think that in math/engineering classes there is a disproportional amount of trickery. There are numerous memes that exemplify this: http://www.thefunnyblog.org/wp-content/uploads/2012/05/funny-engineering-class-homework-exam-have-fan.jpg http://www.thefunnyblog.org/wp-content/uploads/2012/05/funny... You'd be surprised how often this happens. In my calculus classes it was virtually rampant. We'd get some material that was non-trivial to figure out on an exam. That's just bad teaching. Sure, some people will argue that it separates those a better grasp of the material from those with a worse one (maybe it does), but to me it seems unfair. Say I'm not a bright student but I understand the homework very well; the exam, however, uses a non-trivial combination of the elements found in the homework. I personally think that's bullshit. Why not go over the most mind-numbingly difficult problems in class? Often times, there are only a limited number of tricks that can trip you up; if professors would go over these, everyone would pass. But I guess we don't want that (why not?). Consider an analogy: I decide to prepare for a running competition. My trainer shows me how to keep my heart-rate up, how to jog briskly, etc. All this is done on a treadmill on the low setting. Come competition day, it turns out that it's a 25k through the Australian outback. I'm not sure how anyone in their right mind would think the trainer did a good job if he knew exactly what I was getting into.

Afforess 13y ago
On a tangent: >to become an expert at anything, it will take you upwards of 10,000 hours Wrong. 10,000 hours will make a unskilled person moderately skilled, but if they lack the innate talent or intellectual capacity, it won't make them an expert. This sort of meritocracy where people just need to try harder is completely wrong, and dangerous to encourage. [1] http://healthland.time.com/2013/05/20/10000-hours-may-not-make-a-master-after-all/ http://healthland.time.com/2013/05/20/10000-hours-may-not-ma... I agree with your overall point though.
- dvt 13y ago
  I'm not sure how the article supports your argument. Looking at its conclusion, it looks like the "10,000-hour hypothesis" is an open question (at the very least).
- dalke 13y ago
  That Time article leads with a mischaracterization of the debate. I haven't read Outliers, but I did read a bit of K. Anders Ericsson's original work. Ericsson qualified the 10,000 hours saying that it had to be a certain type of deliberative practice, and that there was a limit of about 4 hours per day which could be spent on it. In other words, it has never been the case that 10,000 hours is all that's needed, only that that is a minimum number. However, you reject here Ericsson's entire thesis, that being summarized in the Time article as "Ericsson doesn’t deny that genetic limitations, such as those on height and body size, can constrain expert performance in areas like athletics — and his research has shown this. However, he believes there is no good evidence so far that proves that genetic factors related to intelligence or other brain attributes matter when it comes to less physically driven pursuits." You made a claim that "innate talent or intellectual capacity" is essential to being an expert. This is a widely held belief, first articulated (I'm told) in Vasari's "The Lives of the Artist" (1568). The debate is - where is the evidence which justifies this widely held belief? You see a danger in promoting this "meritocracy" ideal. I have two objections to that. First, I think you are using the term incorrectly. Suppose we only have innate talents as part of our genetic nature. Under a meritocracy, those who are naturally smarter, etc. will get a better job or higher position than those who aren't. It doesn't make a difference if it was achieved through deliberative practice or innate nature. Instead, I think the better word is 'egalitarianism.' Second, it reminds me too much of various view of "noble blood" and rusty arguments that women by nature can't do X, that black people by nature can't do Y, and that Swedes are by nature dumb squareheads. There's any number of these stereotypes once fervently held to be true, but which haven't stood up to the test of time. Also, there shouldn't be a good argument that "people just need to try harder." Ericsson's view is that "deliberate practice requires effort and does not lead to immediate reward" (quoting from a summary by David Zach Hambrick). There are many good reasons to not become an expert on a topic, including: 1) the person could be interested in becoming an expert in another topic, 2) it can be hard to find the 10,000 hours needed for practice, especially if that time is spent making money needed for rent and food, and 3) other requirements may be missing; it's hard to be an expert surfer if one lives in Colorado, or downhill skier in Miami. The path towards being an expert in anything is chaotic. I am one of the world experts in writing software for a certain subset of biochemistry. But had I gotten a different job just out of college, I would probably be in a completely different field. It's really hard for me to believe that I was born with this talent, given how much education and job-related experience I had through to get to this point.
rayiner 13y ago
Exams like that are where the teaching function of school collides headlong with the (more important) sorting function of school. I found the phenomenon frustrating in engineering school, and even more frustrating in law school. They both prominently featured exams that looked nothing like what was taught in class. They both favor the kind of cynical person who ignores the larger ideas taught in class to focus on day 1 on the final exam, and also the socially competent who can get previous exams and the like from social networks. They also, completely incidentally, identify the few people who are so beyond the curve they could answer anything the professor might ask without studying, which lends them an air of legitimacy that perpetuates their existence. You see it less in the humanities because the sorting function of school is so much less important than the teaching function. No lucrative jobs are riding on getting a 3.7 in art history versus a 3.4. (Everyone will be unemployed anyway...) As an aside, I'm convinced grades are just an awful aspect of "education." They don't serve any purpose other than making it easier for employers to figure out who to hire, which I don't think is a legitimate function of school.
- dvt 13y ago
  The irony here is that most R&D/engineering jobs do their own training. My mom, for example, works as a chem engineer/researcher -- every time they hire someone, they also train them. I think it's ironic that people bust their asses in school to get a 3.5+ and end up being trained like little robots anyway once they find their "dream job." Anyone with some elementary knowledge of chemistry could pass these training courses and get to work in a couple of weeks. It just goes to show how disconnected academia is from real life.
  - eli_gottlieb 13y ago
    Well it's the employers who claim they need fresh workers with all that academic training!
- deleted 13y ago
  [deleted]
- huherto 13y ago
  > They don't serve any purpose other than making it easier for employers to figure out who to hire, which I don't think is a legitimate function of school. Interesting point. At the same time it justifies the existence of schools since a lot of people go to school to get a better job.
gems 13y ago
"We'd get some material that was non-trivial to figure out on an exam. That's just bad teaching." You should reconsider what you just said. I tend to think that most 'good' universities do that.
- dvt 13y ago
  The quoted part is admittedly a bit awkward to read -- I exemplified exactly what I meant in my analogy. It's true that most good universities "sort" rather than "teach." My argument is that sorting is not what schools were invented for. We have Olympiads for that.
  - ericssmith 13y ago
    "My argument is that sorting is not what schools were invented for" Hmmm, are you sure about that? Being a student and learning are not the same thing. To be successful in school, you have to excel at the former.
    - dvt 13y ago
      Plato's academy (and most of the ancient academies) were not built to "find out who was the best" at X or Y. They were built to a) teach current ideas and b) develop new ones. The problem with post-scholastic (and I would argue even scholastic) thought is that we've mixed up the two roles. Grading (as we know it now) is a relatively new invention... probably invented around the late 18th century at Cambridge. And yet these non-sorting educational institutions still produced Newton, Galileo, Augustine, and so many others.
model-m 13y ago
As a teacher, I take strong issue with dvt's comment: "We'd get some material that was non-trivial to figure out on an exam. That's just bad teaching." Exams are supposed to be non-trivial, if they are to test your understanding of the material. When I teach freshman calculus, I invariably get this kind of comments from students who aced math in high school because they had basically memorized all possible question patterns from the textbook. But did they understand it? More often than not, they hadn't, really. And when they get a question that doesn't fit a pattern they've seen before, they call it a "trick", when it's anything but. I work hard at getting my students to understand that math is not about memorizing stuff but about understanding stuff. You have to know the basic concepts and techniques by heart, of course, same as any subject, but anything more is just icing (unless your brain works in such a way that memorizing patterns helps you understand general principles, in which case memorize away, but don't mistake the means for the end. Many students tell me they don't understand why they got a failing mark on an exam because they did all the homework and/or put in tens of hours of study. They seem to think that these actions should somehow guarantee them a passing grade, and if it didn't, it's obviously because the exam was unfair. Now let me be perfectly clear: I don't give hard exams. In fact, most of the questions I ask are downright easy, provided you understand the material. Here's an example: "Sketch the graph of a twice-differentiable function f(x) whose domain is the real numbers and which satisfies the following two conditions: f'(x) is negative for all x, and f''(x) always has the same sign as x." This was in fact a question in my calc 1 midterm last year. Out of 60 students, 10 did not write anything. 10 drew something that was not the graph of a function. 10 drew a function that did not satisfy any of the requirements. 10 drew a decreasing function but got the concavity wrong somehow. 20 gave a correct answer. (This is all approximate, of course.) The average mark for this question was probably around 2/5. Was this exam question harder than my homework problem sets? Absolutely not! It's just different. Here's an example of a homework question relating to the same material in a similar way: "A differentiable function f(x) is such that f'(x) never changes sign. What can be said about the number of zeros of f?" This is more difficult than the exam question because the step linking the sign of f' to the number of zeros of f (drawing a graph) is not explicitly suggested, and because the answer is "f has at most one zero" and not "f has exactly one zero".
- dvt 13y ago
jacques_chester 13y ago
Sports scientists have pointed out[1] that people who are innately good at a thing will do more of it, with less resistance to training, than people who aren't. The 10,000 hours are done by people who enjoy a subject or activity enough to do it almost constantly. And that usually comes about because of early successes. This is sometimes called "talent". [1] http://www.sportsscientists.com/2011/08/talent-training-and-performance-secrets.html http://www.sportsscientists.com/2011/08/talent-training-and-...
Jach 13y ago
There are geniuses in every field, therefore every field is just as difficult intellectually? I don't follow your reasoning here. What sort of evidence would convince you that math/science are in fact harder for humans than history or art? (Edit: A somewhat different perspective I have is expressed by Feynman here: http://www.youtube.com/watch?v=NWjV0bNBPY4 http://www.youtube.com/watch?v=NWjV0bNBPY4 The good men and women of a field are more important than the field, and you can probably find good men and women in every field if you look hard enough.)

by dvt 13y ago

Afforess 13y ago

On a tangent: >to become an expert at anything, it will take you upwards of 10,000 hours Wrong. 10,000 hours will make a unskilled person moderately skilled, but if they lack the innate talent or intellectual capacity, it won't make them an expert. This sort of meritocracy where people just need to try harder is completely wrong, and dangerous to encourage. [1] http://healthland.time.com/2013/05/20/10000-hours-may-not-make-a-master-after-all/ http://healthland.time.com/2013/05/20/10000-hours-may-not-ma... I agree with your overall point though.

dvt 13y ago
I'm not sure how the article supports your argument. Looking at its conclusion, it looks like the "10,000-hour hypothesis" is an open question (at the very least).
dalke 13y ago
That Time article leads with a mischaracterization of the debate. I haven't read Outliers, but I did read a bit of K. Anders Ericsson's original work. Ericsson qualified the 10,000 hours saying that it had to be a certain type of deliberative practice, and that there was a limit of about 4 hours per day which could be spent on it. In other words, it has never been the case that 10,000 hours is all that's needed, only that that is a minimum number. However, you reject here Ericsson's entire thesis, that being summarized in the Time article as "Ericsson doesn’t deny that genetic limitations, such as those on height and body size, can constrain expert performance in areas like athletics — and his research has shown this. However, he believes there is no good evidence so far that proves that genetic factors related to intelligence or other brain attributes matter when it comes to less physically driven pursuits." You made a claim that "innate talent or intellectual capacity" is essential to being an expert. This is a widely held belief, first articulated (I'm told) in Vasari's "The Lives of the Artist" (1568). The debate is - where is the evidence which justifies this widely held belief? You see a danger in promoting this "meritocracy" ideal. I have two objections to that. First, I think you are using the term incorrectly. Suppose we only have innate talents as part of our genetic nature. Under a meritocracy, those who are naturally smarter, etc. will get a better job or higher position than those who aren't. It doesn't make a difference if it was achieved through deliberative practice or innate nature. Instead, I think the better word is 'egalitarianism.' Second, it reminds me too much of various view of "noble blood" and rusty arguments that women by nature can't do X, that black people by nature can't do Y, and that Swedes are by nature dumb squareheads. There's any number of these stereotypes once fervently held to be true, but which haven't stood up to the test of time. Also, there shouldn't be a good argument that "people just need to try harder." Ericsson's view is that "deliberate practice requires effort and does not lead to immediate reward" (quoting from a summary by David Zach Hambrick). There are many good reasons to not become an expert on a topic, including: 1) the person could be interested in becoming an expert in another topic, 2) it can be hard to find the 10,000 hours needed for practice, especially if that time is spent making money needed for rent and food, and 3) other requirements may be missing; it's hard to be an expert surfer if one lives in Colorado, or downhill skier in Miami. The path towards being an expert in anything is chaotic. I am one of the world experts in writing software for a certain subset of biochemistry. But had I gotten a different job just out of college, I would probably be in a completely different field. It's really hard for me to believe that I was born with this talent, given how much education and job-related experience I had through to get to this point.

rayiner 13y ago

Exams like that are where the teaching function of school collides headlong with the (more important) sorting function of school. I found the phenomenon frustrating in engineering school, and even more frustrating in law school. They both prominently featured exams that looked nothing like what was taught in class. They both favor the kind of cynical person who ignores the larger ideas taught in class to focus on day 1 on the final exam, and also the socially competent who can get previous exams and the like from social networks. They also, completely incidentally, identify the few people who are so beyond the curve they could answer anything the professor might ask without studying, which lends them an air of legitimacy that perpetuates their existence. You see it less in the humanities because the sorting function of school is so much less important than the teaching function. No lucrative jobs are riding on getting a 3.7 in art history versus a 3.4. (Everyone will be unemployed anyway...) As an aside, I'm convinced grades are just an awful aspect of "education." They don't serve any purpose other than making it easier for employers to figure out who to hire, which I don't think is a legitimate function of school.

dvt 13y ago
The irony here is that most R&D/engineering jobs do their own training. My mom, for example, works as a chem engineer/researcher -- every time they hire someone, they also train them. I think it's ironic that people bust their asses in school to get a 3.5+ and end up being trained like little robots anyway once they find their "dream job." Anyone with some elementary knowledge of chemistry could pass these training courses and get to work in a couple of weeks. It just goes to show how disconnected academia is from real life.
- eli_gottlieb 13y ago
  Well it's the employers who claim they need fresh workers with all that academic training!
deleted 13y ago
[deleted]
huherto 13y ago
> They don't serve any purpose other than making it easier for employers to figure out who to hire, which I don't think is a legitimate function of school. Interesting point. At the same time it justifies the existence of schools since a lot of people go to school to get a better job.

gems 13y ago

"We'd get some material that was non-trivial to figure out on an exam. That's just bad teaching." You should reconsider what you just said. I tend to think that most 'good' universities do that.

dvt 13y ago
The quoted part is admittedly a bit awkward to read -- I exemplified exactly what I meant in my analogy. It's true that most good universities "sort" rather than "teach." My argument is that sorting is not what schools were invented for. We have Olympiads for that.
- ericssmith 13y ago
  "My argument is that sorting is not what schools were invented for" Hmmm, are you sure about that? Being a student and learning are not the same thing. To be successful in school, you have to excel at the former.
  - dvt 13y ago
    Plato's academy (and most of the ancient academies) were not built to "find out who was the best" at X or Y. They were built to a) teach current ideas and b) develop new ones. The problem with post-scholastic (and I would argue even scholastic) thought is that we've mixed up the two roles. Grading (as we know it now) is a relatively new invention... probably invented around the late 18th century at Cambridge. And yet these non-sorting educational institutions still produced Newton, Galileo, Augustine, and so many others.

model-m 13y ago

As a teacher, I take strong issue with dvt's comment: "We'd get some material that was non-trivial to figure out on an exam. That's just bad teaching." Exams are supposed to be non-trivial, if they are to test your understanding of the material. When I teach freshman calculus, I invariably get this kind of comments from students who aced math in high school because they had basically memorized all possible question patterns from the textbook. But did they understand it? More often than not, they hadn't, really. And when they get a question that doesn't fit a pattern they've seen before, they call it a "trick", when it's anything but. I work hard at getting my students to understand that math is not about memorizing stuff but about understanding stuff. You have to know the basic concepts and techniques by heart, of course, same as any subject, but anything more is just icing (unless your brain works in such a way that memorizing patterns helps you understand general principles, in which case memorize away, but don't mistake the means for the end. Many students tell me they don't understand why they got a failing mark on an exam because they did all the homework and/or put in tens of hours of study. They seem to think that these actions should somehow guarantee them a passing grade, and if it didn't, it's obviously because the exam was unfair. Now let me be perfectly clear: I don't give hard exams. In fact, most of the questions I ask are downright easy, provided you understand the material. Here's an example: "Sketch the graph of a twice-differentiable function f(x) whose domain is the real numbers and which satisfies the following two conditions: f'(x) is negative for all x, and f''(x) always has the same sign as x." This was in fact a question in my calc 1 midterm last year. Out of 60 students, 10 did not write anything. 10 drew something that was not the graph of a function. 10 drew a function that did not satisfy any of the requirements. 10 drew a decreasing function but got the concavity wrong somehow. 20 gave a correct answer. (This is all approximate, of course.) The average mark for this question was probably around 2/5. Was this exam question harder than my homework problem sets? Absolutely not! It's just different. Here's an example of a homework question relating to the same material in a similar way: "A differentiable function f(x) is such that f'(x) never changes sign. What can be said about the number of zeros of f?" This is more difficult than the exam question because the step linking the sign of f' to the number of zeros of f (drawing a graph) is not explicitly suggested, and because the answer is "f has at most one zero" and not "f has exactly one zero".

dvt 13y ago

jacques_chester 13y ago

Sports scientists have pointed out[1] that people who are innately good at a thing will do more of it, with less resistance to training, than people who aren't. The 10,000 hours are done by people who enjoy a subject or activity enough to do it almost constantly. And that usually comes about because of early successes. This is sometimes called "talent". [1] http://www.sportsscientists.com/2011/08/talent-training-and-performance-secrets.html http://www.sportsscientists.com/2011/08/talent-training-and-...

Jach 13y ago

There are geniuses in every field, therefore every field is just as difficult intellectually? I don't follow your reasoning here. What sort of evidence would convince you that math/science are in fact harder for humans than history or art? (Edit: A somewhat different perspective I have is expressed by Feynman here: http://www.youtube.com/watch?v=NWjV0bNBPY4 http://www.youtube.com/watch?v=NWjV0bNBPY4 The good men and women of a field are more important than the field, and you can probably find good men and women in every field if you look hard enough.)