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John_Maxwell_IV comments on Rationality Quotes April 2014 - LessWrong
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http://www.reddit.com/r/askscience/comments/e3yjg/is_there_any_way_to_improve_intelligence_or_are/c153p8w
reddit user jjbcn on trying to improve your intelligence
If you're not a student of physics, The Feynman Lectures on Physics is probably really useful for this purpose. It's free for download!
http://www.feynmanlectures.caltech.edu/
It seems like the Feynman lectures were a bit like the Sequences for those Caltech students:
I've noticed that one of the biggest thing holding me back in math/physics is an aversion to thinking too hard/long about math and physics problems. It seems to me that if I was able to overcome this aversion and math was as fun as playing video games I'd be a lot better at it.
Good video games are designed to be fun, that is their purpose. Math, um, not so much.
Only a small fraction of math has practical applications, the majority of math exists for no reason other than thinking about it is fun. Even things with applications had sometimes been invented before those applications were known. So in a sense most math is designed to be fun. Of course it's not fun for everyone, just for a special class of people who are into this kind of thing. That makes it different from Angry Birds. But there are many games which are also only enjoyed by a specific audience, so maybe the difference is not that fundamental. A large part of the reason the average person doesn't enjoy math is that unlike Angry Birds math requires some effort, which is the same reason the average person doesn't enjoy League Of Evil III.
Spot on. Pure, fun math does benefit society directly in at least one way, however, in that the opportunity to engage in it can be used to lure very smart people into otherwise unpalatable teaching jobs.
In fact, that seems to be the main point of "research" in most less-than-productive fields (i.e. the humanities).
Is it clear that this is in the best interests of society? It would seem to me the end result is bad teaching. Back when I was in undergrad, the best researchers were the worst teachers (for obvious reasons- they were focused on their research and didn't at all care about teaching).
When I was in grad school in physics, the professor widely considered the strongest teacher was denied tenure (cited AGAINST him in the decision was that he had written a widely used textbook),etc.
Also, the desire for tenured track profs to dodge teaching is why the majority of math classes at many research institutions were taught by grad students.
Interesting. Did there seem to be any pedagogical benefit to having relatively easy access to research-level experts, though?
In graduate school, for special topics class there were usually only 1 or 2 professors that COULD teach a certain class (and only 3 or 4 students interested in taking it)- so when you are talking cutting edge research topics, its a necessity to have a researcher because no one else will be familiar enough with whats going on in the field.
Outside of that, not really. Good teaching takes work, so if you put someone in front of the class whose career advancement requires spending all their time on research, then the teaching is just a potentially career destroying distraction. Also, at the intro level, subject-pedagogy experts tend to do better (i.e. the physics education group were measurably more effective at teaching physics than other physics groups. So much so that I think now they exclusively teach the large physics courses for engineers)
I mean, it's easier to get research positions with those professors, and those are learning experiences, but the students generally get very little out of it during the actual class.
And at least some math instructors effectively teach that if you aren't already finding (their presentations of) math fascinating, that you must just not be a Math Person.
Math is a bit like liftening weights. Sitting in front of a heavy mathematical problem is challenging. The job of a good teacher isn't to remove the challenge. Math is about abstract thinking and a teacher who tries to spare his students from doing abstract thinking isn't doing it right.
Deliberate practice is mentally taxing.
The difficult thing as a teacher is to motivate the student to face the challenge whether the challenge is lifting weights or doing complicated math.
The job of a good teacher is to find a slightly less challenging problem, and to give you that problem first. Ideally, to find a sequence of problems very smoothly increasing in difficulty.
Just like a computer game doesn't start with the boss fight, although some determined players would win that, too.
No. Being good at math is about being able to keep your attention on a complicated proof even if it's very challenging and your head seems like it's going to burst.
If you want to build muscles you don't slowly increase the amount of weight and keep it at a level where it's effortless. You train to exhaustion of given muscles.
Building mental stamina to tackle very complicated abstract problems that aren't solvable in five minutes is part of a good math education.
Deliberate practice is supposed to feel hard. A computer game is supposed to feel fun. You can play a computer game for 12 hours. A few hours of delibrate practice are on the other usually enough to get someone to the rand of exhaustion.
If you only face problems in your education that are smooth like a computer game, you aren't well prepared for facing hard problems in reality. A good math education teaches you the mindset that's required to stick with a tough abstract problem and tackle it head on even if you can't fully grasp it after looking 30 minutes at it.
You might not use calculus at your job, but if your math education teaches you the ability to stay focused on hard abstract problems than it fulfilled it's purpose.
You can teach calculus by giving the student concrete real world examples but that defeats the point of the exercise. If we are honest most students won't need the calculus at their job. It's not the point of math education. At least in the mindset in which I got taught math at school in Germany.
You don't put on so much weight than you couldn't possibly lift it, either (nor so much weight that you could only lift it with atrocious form and risk of injury, the analogue of which would be memorising a proof as though it was a prayer in a dead language and only having a faulty understanding of what the words mean).
Yes, memorizing proof isn't the point. You want to derive proofs. I think it's perfectly fine to sit 1 hours in front of a complicated proof and not be able to solve the proof.
A ten year old might not have that mental stamia, but a good math education should teach it, so it's there by the end of school.
This kind of philosophy sounds like it's going to make a few people very good at tackling hard problems, while causing everyone else to become demotivated and hate math.
Motivation has a lot to do with knowing why you are engaging in an action. If you think things should be easy and they aren't you get demotivated. If you expect difficulty and manage to face it then that doesn't destroy motivation.
I don't think getting philosophy right is easy. Once things that my school teachers got very wrong was believing in talents instead of believing in a growth mindset.
I did identify myself as smart so I didn't learn the value of putting in time to practice. I tried to get by with the minimum of effort.
I think Cal Newport wrote a lot of interesting things about how a good philosophy of learning would look like.
There a certain education philosophy that you have standardized tests, than you do gamified education to have children score on those tests. Student have pens with multiple colors and are encouraged to draw mind maps. Afterwards the students go to follow their passions and live the American dream. It fits all the boxes of ideas that come out of California.
I'm not really opposed to someone building some gamified system to teach calculus but at the same time it's important to understand the trade offs. We don't want to end up with a system where the attention span that students who come out of it is limited to playing games.
I think that the way good games teach things is basically being engaging by constantly presenting content that's in the learner's zone of proximal development, offering any guidance needed for mastering that, and then gradually increasing the level of difficulty so as to constantly keep things in the ZPD. The player is kept constantly challenged and working at the edge of their ability, but because the challenge never becomes too high, the challenge also remains motivating all the time, with the end result being continual improvement.
For example, in a game where your character may eventually have access to 50 different powers, throwing them at the player all at once would be overwhelming when the player's still learning to master the basic controls. So instead the first level just involves mastering the basic controls and you have just a single power that you need to use in order to beat the level, then when you've indicated that you've learned that (by beating the level), you get access to more powers, and so on. When they reach the final level, they're also likely to be confident about their abilities even when it becomes difficult, because they know that they've tackled these kinds of problems plenty of times before and have always eventually been successful in the past, even if it required several tries.
The "math education is all about teaching people how to stay focused on hard abstract problems" philosophy sounds to me like the equivalent of throwing people at a level where they had to combine all 50 powers in order to survive, right from the very beginning. If you intend on becoming a research mathematician who has to tackle previously unencountered problems that nobody has any clue of how to solve, it may be a good way of preparing you for it. But forcing a student to confront needlessly difficult problems, when you could instead offer a smoothly increasing difficulty, doesn't seem like a very good way to learn in general.
When our university began taking the principles of something like cognitive apprenticeship - which basically does exactly the thing that Viliam Bur mentioned, presenting problems in a smoothly increasing difficulty as well as offering extensive coaching and assistance - and applying it to math (more papers), the end result was high student satisfaction even while the workload was significantly increased and the problems were made more challenging.
This is a very strong set of assertions which I find deeply counter intuitive. Of course that doesn't mean it isn't true. Do you have any evidence for any of it?
Which one's do you find counter intuitive? It's a mix of referencing a few very modern ideas with more traditional ideas of education while staying away from the no-child-left-behind philosophy of education.
I can make any of the points in more depths but the post was already long, and I'm sort of afraid that people don't read my post on LW if they get too long ;) Which ones do you find particularly interesting?
Of course bad instructors can say this as easily as good ones.
But isn't it true to say that if you have reasonably wide experience with different presentations of math, and you don't find any of them fascinating, then you're probably not a Math Person? Or do Math People not exist as a natural category?
I'd be ever so interested in the answer to this question. It seems really obvious that some people are good at maths and some people aren't.
But it's also really obvious that some people like sprouts. And it turns out as far as I'm aware that it's possible to like sprouts for both genetic and environmental reasons. I'd love to know the causes of mathematical ability. Especially since it seems to be possible to be both 'clever' and 'bad at maths'. Does anyone know what the latest thinking on it is?
My recent experiences trying to design IQ tests tell me that that's both innate and very trainable. In fact I'd now trust the sort of test that asks you how to spell or define randomly chosen words much more than the Raven's type tests. It's really hard to fake good speling, whereas the pattern tests are probably just telling you whether you once spent half an hour looking closely at the wallpaper. Which is exactly the reverse of the belief that I started with.
Related: some people believe that programming talent is very innate and people can be sharply separated into those who can and cannot learn to write code. Previously on LW here, and I think there was an earlier more substantive post but I can't find it now. See also this. Gwern collected some further evidence and counterevidence.
It was probably mentioned in the earlier discussions, but I believe the "two humps" pattern can easily be explained by bad teaching. If it hapens in the whole profession, maybe no one has yet discovered a good way to teach it, because most of the people who understand the topic were autodidacts.
As a model, imagine that a programming ability is a number. You come to school with some value between 0 and 10. A teacher can give you +20 bonus. Problem is, the teacher cannot explain the most simple stuff which you need to get to level 5; maybe because it is so obvious to the teacher that they can't understand how specifically someone else would not already understand it. So the kids with starting values between 0 and 4 can't follow the lessons and don't learn anything, while the kids with starting values 5 to 10 get the +20 bonus. At the end, you get the "two humps"; one group with values 0 to 4, another group with values 25 to 30. -- And the worst part is that this belief creates a spiral, because when everyone observed the "two humps" at the adult people, then if some student with starting value 4 does not understand the lesson, we don't feel a need to fix this; obviously they were just not meant to understand programming.
What are those starting concepts that some people get and some people don't? Probably things like "the computer is just a mechanical thing which follows some mechanical rules; it has no mind, and it doesn't really understand anything", but you need to feel it in the gut level. (Maybe aspies have a natural advantage here, because they don't expect the computer to have a mind.) It could probably help to play with some simple mechanical machines first, where the kids could observe the moving parts. In other words, maybe we don't only need specialized educational software, but also hardware. A computer in a form of a black box is already too big piece of magic, prone to be anthropomorphized. You should probably start with a mechanical typewriter and a mechanical calculator.
Bad teaching? There's an even simpler explanation (at least regarding programming): autodidacts with previous experience versus regular students without previous experience. The fact that the teaching is often geared towards the students with previous experience and suffers from a major tone of "Why don't you know this already?" throughout the first year or two of undergrad doesn't help a bit.
"I can teach you this only if you already know it" seems like bad teaching to me. Not sure if we are not just debating definitions here.
A lot of effort has gone into trying to invent ways of teaching programming to complete newbies. If really no-one has succeeded at all, then maybe it's time to seriously consider that some people can't be taught.
A claim that someone cannot be taught by any possible intervention would be a very strong claim indeed, and almost certainly false. But a claim that no-one knows how to teach this even though a lot of people have tried and failed for a long time now, makes predictions pretty similar to the theory that some people simply can't be taught.
This model matches the known facts, but it doesn't tell us what we really want to know. What determines what value people start out with? Does everyone start out with 0 and some people increase their value in unknown, perhaps spontaneous ways? Or are some people just born with high values and they'll arrive at 5 or 10 no matter what they do, while others will stay at 0 no matter what?
I don't know if educators have tried teaching the concepts you suggest explicitly.
http://www.eis.mdx.ac.uk/research/PhDArea/saeed/
The researcher didn't distinguish the conjectured cause (bimodal differences in students' ability to form models of computation) from other possible causes (just to name one — some students are more confident, and computing classes reward confidence).
And the researcher's advisor later described his enthusiasm for the study as "prescription-drug induced over-hyping" of the results ...
Clearly further research is needed. It should probably not assume that programmers are magic special people, no matter how appealing that notion is to many programmers.
Once upon a time, it would have been a radical proposition to suggest that even 25% of the population might one day be able to read and write. Reading and writing were the province of magic special people like scribes and priests. Today, we count on almost every adult being able to read traffic signs, recipes, bills, emails, and so on — even the ones who do not do "serious reading".
A problem with programming education is that it is frequently unclear what the point of it is. Is it to identify those students who can learn to get jobs as programmers in industry or research? Is it to improve students' ability to control the technology that is a greater and greater part of their world? Is it to teach the mathematical concepts of elementary computer science?
We know why we teach kids to read. The wonders of literature aside, we know full well that they cannot get on as competent adults if they are literate. Literacy was not a necessity for most people two thousand years ago; it is a necessity for most people today. Will programming ever become that sort of necessity?
That seems like rather a strong claim. Everyone who can program now was a complete newbie at some point. Presumably they did not learn by a bolt of divine inspiration out of the blue sky.
My bet would be on childhood experience. For example the kinds of toys used. I would predict a positive effect of various construction sets. It's like "Reductionism for Kindergarten". :D
The silent pre-programming knowledge could be things like: "this toy is interacted with by placing its pieces and observing what they do (or modelling in one's mind what they would do), instead of e.g. talking to the toy and pretending the toy understands".
You have to want to be a wizard.
Plenty of us took the Wizard's Oath as kids and still have a hard time in math classes sometimes.
I think everyone has trouble in math class, eventually.
Not in my experience, unless you're talking about trouble teaching them. It's very possible to run out of classes before you hit anything truly difficult (in my country there are no more classes after Masters level, a PhD student is expected to be doing research - the american notion of "all but dissertation" provokes endless amusement, here you're "all but dissertation" from day 1).
A system where a non-genius math student never faces a challenging math class would probably "provoke endless amusement" from an American grad student, since to them it means that the program is too weak to be considered serious.
If you literally never had trouble in math class, you are a rare mind of the Newton/Gauss calibre, and you should go get your Field's medal before you are 40 :).
I had trouble in my Masters (a combination of course choice and bad luck) and so didn't do a PhD. But we're talking about the top university in at least the country, and by some accounts the hardest non-research course in the world. I'm pretty sure that going a different route I could've got to the point of starting a PhD before hitting anything difficult.
I do sometimes think I should've chased the Fields medal, but I'm ultimately happier the way things turned out. I worked my ass off the whole time in school/university; nowadays I earn a good living doing fun things, but my evenings and weekends are my own, and I've got a much better social life.
From here. Or as I just think of it, if you don't at least have a hard time sometimes, if not fail sometimes, you're not shooting high enough.
If I don't get a game over at least once, the game is too easy.
Is that an Umeshism?
Almost, but not quite. "If you never get a game over, you're playing games that are too easy" would indeed be a Umeshism, but this is a complaint about easy games rather than a suggestion that I should be playing harder ones.
Huh. Yes, I guess that in retrospect I wouldn't be the only one.
This is your secret?
You have to want to learn how to be a wizard.
You have to like to learn how to be a wizard.
Thinking for a long time is one of the classic descriptions of Newton; from John Maynard Keynes's "Newton, the Man":
Paul Graham also mentions focus in this article.
I think math is more fun than playing video games. But I guess it's subjective.
Lucky you.