Ah yes, the rallying call of illogical morons who believe that all parents are the same. You know, not all parents are exactly like, not all parents will agree with you, and not all parents assume anyone who doesn't agree with them isn't a True Parent.
Kids are not supposed to know the full range of consequences of their actions
Not supposed to? As in, it would be a bad thing if they did?
Also, if we treat people who don't know the full range of consequences of their actions in a certain way, why aren't most adults--who are merely overgrown children--treated that way?
Not admitting that the sky is blue and not admitting that UFOs kidnapped Elvis are not the same kind of things, even though they both have to do with admitting something.
I make simple observations of reality; nothing more. There is nothing for me to admit.
And I agree that it's getting pathetic, but my reasons for thinking so differ from yours.
Do you have kids? If not, have you ever been around a small child? How the heck do you think most people learn to talk, to walk, to read, etc.?
You seem to be interpreting my comments as if I'm saying that you should never retain any information or engage in some repetition; that's not what I'm trying to say. I'm saying it shouldn't happen 99% of the time, because it damages kids' educations.
But thinking that repetition isn't an essential part of the learning process for the vast majority of people is, frankly, a bit delusional.
It's not delusional for anything even remotely advanced, because at that point, they're not truly learning anything; they're just memorizing information without understanding it. The process of attempting to understand the hows and whys will give them practice to begin with.
There are all sorts of tricks that good teachers have employed for thousands of years to make that repetition more interesting or enjoyable for kids, but it's the main way most kids acquire actual skills.
You talk of "skills," while I talk of real education and understanding. That this sort of technique (rote memorization over understanding) has been employed for thousands of years really shows; it's archaic.
Okay. More "Most people can do anything" nonsense.
So... Are you hopelessly illiterate or is there hope for you yet?
It seems you've failed to understand my idea of intelligence. Even if I did make such a mistake, that alone would not prove me to be hopelessly unintelligent (by my standards). I also don't take that position (where making a mistake = you're unintelligent) when it comes to other people, except perhaps in extreme cases where it's a very basic mistake and the same type of thing happens repeatedly.
My position is not that rote memorization is bad 100% of the time; more like 99% of the time. I may have been counting, but I never did bother memorizing multiplication tables.
Somehow, I find myself doubting your own characterization as a self-made man.
Unmotivated and/or unintelligent people tend to do that. They're amazed when someone is more motivated than them to the point where they actually have a genuine interest in education. Baffling!
I am guessing that you had quite a bit more help from your teachers at school than you are letting on.
Nope. I asked them questions like, "Why does this work?" a number of times, but they were never able to answer it. For instance, they explained the Pythagorean theorem as a set of steps to get a certain result. Since I started learning calculus soon after I started my first algebra class, the teachers would simply turn me away when I had any questions, saying that it wasn't part of the curriculum. Which was true, but they were teaching the actual curriculum very poorly.
But it's funny that you assume that no one can learn on their own; that self-education is just an impossibility. I had access to books, and for me, that was enough. What's even more funny, though, is that you seem to think that I could actually come to an understanding of the material by listening to their nonsensical explanations. No one can, as they focus on memorization of facts, not understanding. If you want the latter, then you'll have to think about it yourself.
In all honesty it will require the next generation (the current generation is still a little bit too much in the old world ways) to make educated decisions and refuse to buy vehicles that track anything until the manufacturers change anything.
But as someone who has actually taught high-school math, I can also tell you that you and I are NOT the norm.
That's another, but different, problem. Schools are one-size-fits-all environments, and do little to mitigate that problem ("advanced" classes don't really solve anything).
(3) Also, sometimes the algorithm IS the goal. For >99% of people in the world, math is only useful as a tool
That mentality is the problem. That's why rote memorization and mindless repetition are used so often.
But part of the issue is that many students need significantly more repetition to get things
I disagree, because they're *not* getting them. They're just memorizing information. I honestly don't believe it's necessary or effective to have a student do the same thing over and over again in order to get them to understand something; I think it's misleading, in fact.
Yes, but if it's made more meaningful, they're at least slightly more likely to remember it. But then again, I'm not sure it should be about that.
not because they didn't get the "concept" of division
Most don't.
Currently, most high school graduates have demonstrated an ability with algebra and geometry at a minimum.
Simply incorrect. Sure, by our current standards, they can use it, but it's just rote memorization of processes and patterns. They don't understand the logic of it at all.
And yes it does make me angry when idiots start convincing people to take a self-destructive path.
His path looks much, much less destructive than the current system.
It's not because we should trust our instincts and not bother proving stuff that is obvious as the author recommends.
You said you stopped reading it, and that much is obvious.
I notice you didn't comment on what I said about people not understanding the benefits they themselves accrued under the system which they seek to destroy.
It is possible to derive at least some benefits from a terrible system while still advocating another system.
But really, I never bothered doing any of the busy work (waste of time) and learned on my own. It is almost entirely thanks to my own efforts that I understand math as much as I do now. About the only thing schools did for me was introducing me to the simplest concepts (addition, etc.), but I worked to understand it all on my own, since they weren't going to help with that.
Stop trying to make it sound tragic, you sound silly.
It's not tragic; it's comical.
I'll show Slashdot my True Ferocity soon enough. Wait and see.
I'm just blown away that you think that pdf has any valuable insights.
I'm just blown away that you don't. Well, not really.
you end up with a bunch of idiots who don't know how to paint (or do math).
Like now.
Luckily, the drudgery part of math is much shorter and much easier to learn than painting.
And also easier to forget, as we've seen. But go on ruining people's educations, except for those with an exceedingly high aptitude and willpower. Everyone suffers at least a bit under the current system.
It's hilarious that you think that paper is connected with identifying the problem in math education
I think it identifies at least part of the problem.
That paper doesn't even... oh man I don't even have the words to describe what a fail that paper is.
Are you talking about your long, angry post, or the paper? It seems more like you're talking about your post.
Well, judging from the tone of your post, you're a lost cause. Sad (not really), but true.
If students learn something for the first time they tend to use their memory mostly without much understanding.
Which is part of the problem.
Only through training, execises they learn to use the concepts behind it and find out about the subtle problems behind it.
One thing I hate is when people tell me how I learn and force me to do repetitive assignments that test only for memorization and do nothing to bolster one's understanding of the material, which is the sort of thing I was talking about. I had to deal with that garbage too much in the past, and never bothered to do any of the assignments.
Maybe I incorrectly assumed he was talking about the same kind of rote memorization I was thinking of. When I talk about that, I'm saying that they force pointless repetition on people, have people memorize meaningless facts, and skip the process of trying to get people to understand how and why it all works to begin with. What I'm not saying is that you never need to retain any information.
But really, attempting to understand how and why it all works gives you a lot of practice all by itself, from my experience.
There are experiments about what helps pupils best to get better with mathematics, and it has been shown that drill and constant exercise is the most effective way, even for complexer mathematical problems.
That's a great way to train drones who don't understand the how & why, but not a great way to make people truly understand mathematics. I do what I do because I love it, and any facts I memorize I memorize because I happen to see them often, not because forced me to sit around and work out pointless problems. That sort of thinking is why math education is so abysmal.
Slashdot Mirror
Ah yes, the rallying call of the childless.
Ah yes, the rallying call of illogical morons who believe that all parents are the same. You know, not all parents are exactly like, not all parents will agree with you, and not all parents assume anyone who doesn't agree with them isn't a True Parent.
Well, I don't care about the law, so that's an irrelevant point to me. Laws are often illogical and/or unjust.
it would be totally impractical to make this judgement on a case-by-case basis
No, it wouldn't.
No, we treat children in a certain way because they are children.
So you arbitrarily decide to treat them in a certain way based on nothing but their age. Thanks for making that clear.
I for one decide to ridicule morons, no matter their age.
Kids are not supposed to know the full range of consequences of their actions
Not supposed to? As in, it would be a bad thing if they did?
Also, if we treat people who don't know the full range of consequences of their actions in a certain way, why aren't most adults--who are merely overgrown children--treated that way?
That seems highly unlikely.
Not admitting that the sky is blue and not admitting that UFOs kidnapped Elvis are not the same kind of things, even though they both have to do with admitting something.
I make simple observations of reality; nothing more. There is nothing for me to admit.
And I agree that it's getting pathetic, but my reasons for thinking so differ from yours.
But I personally have nothing to hide.
Nonsense.
But really, desiring privacy is not wrong. There's nothing wrong with having something to hide.
Just like real college, many will fail and few will succeed.
Except in real college, even the ones who have no clue what they're doing often succeed.
I don't want to admit that 1 + 1 = 3, either.
Do you have kids? If not, have you ever been around a small child? How the heck do you think most people learn to talk, to walk, to read, etc.?
You seem to be interpreting my comments as if I'm saying that you should never retain any information or engage in some repetition; that's not what I'm trying to say. I'm saying it shouldn't happen 99% of the time, because it damages kids' educations.
But thinking that repetition isn't an essential part of the learning process for the vast majority of people is, frankly, a bit delusional.
It's not delusional for anything even remotely advanced, because at that point, they're not truly learning anything; they're just memorizing information without understanding it. The process of attempting to understand the hows and whys will give them practice to begin with.
There are all sorts of tricks that good teachers have employed for thousands of years to make that repetition more interesting or enjoyable for kids, but it's the main way most kids acquire actual skills.
You talk of "skills," while I talk of real education and understanding. That this sort of technique (rote memorization over understanding) has been employed for thousands of years really shows; it's archaic.
It seems you've failed to understand my idea of intelligence.
Or, in this case, you have no idea what it even is.
Difficulty reading? Not "I", but "most people".
Okay. More "Most people can do anything" nonsense.
So... Are you hopelessly illiterate or is there hope for you yet?
It seems you've failed to understand my idea of intelligence. Even if I did make such a mistake, that alone would not prove me to be hopelessly unintelligent (by my standards). I also don't take that position (where making a mistake = you're unintelligent) when it comes to other people, except perhaps in extreme cases where it's a very basic mistake and the same type of thing happens repeatedly.
More "I can do anything" nonsense.
Get over yourself. Most people can't succeed in more advanced intellectual pursuits, even if they're willing to put in the effort.
Much of the remaining 30% was things like defense and infrastructure -- this may be bloated, but in theory it benefitted fuure generations
Not defense.
My position is not that rote memorization is bad 100% of the time; more like 99% of the time. I may have been counting, but I never did bother memorizing multiplication tables.
Smart people don't use Twitter, either.
Somehow, I find myself doubting your own characterization as a self-made man.
Unmotivated and/or unintelligent people tend to do that. They're amazed when someone is more motivated than them to the point where they actually have a genuine interest in education. Baffling!
I am guessing that you had quite a bit more help from your teachers at school than you are letting on.
Nope. I asked them questions like, "Why does this work?" a number of times, but they were never able to answer it. For instance, they explained the Pythagorean theorem as a set of steps to get a certain result. Since I started learning calculus soon after I started my first algebra class, the teachers would simply turn me away when I had any questions, saying that it wasn't part of the curriculum. Which was true, but they were teaching the actual curriculum very poorly.
But it's funny that you assume that no one can learn on their own; that self-education is just an impossibility. I had access to books, and for me, that was enough. What's even more funny, though, is that you seem to think that I could actually come to an understanding of the material by listening to their nonsensical explanations. No one can, as they focus on memorization of facts, not understanding. If you want the latter, then you'll have to think about it yourself.
There are also three-headed monkeys. That doesn't mean that every monkey is one of them.
Straw man.
Anyway, you are distracting from the original point which was that the assumption that absolutely everyone except yourself is an idiot
Straw man.
In all honesty it will require the next generation (the current generation is still a little bit too much in the old world ways) to make educated decisions and refuse to buy vehicles that track anything until the manufacturers change anything.
That's not likely to happen.
But as someone who has actually taught high-school math, I can also tell you that you and I are NOT the norm.
That's another, but different, problem. Schools are one-size-fits-all environments, and do little to mitigate that problem ("advanced" classes don't really solve anything).
(3) Also, sometimes the algorithm IS the goal. For >99% of people in the world, math is only useful as a tool
That mentality is the problem. That's why rote memorization and mindless repetition are used so often.
But part of the issue is that many students need significantly more repetition to get things
I disagree, because they're *not* getting them. They're just memorizing information. I honestly don't believe it's necessary or effective to have a student do the same thing over and over again in order to get them to understand something; I think it's misleading, in fact.
People tend to forget stuff they don't use.
Yes, but if it's made more meaningful, they're at least slightly more likely to remember it. But then again, I'm not sure it should be about that.
not because they didn't get the "concept" of division
Most don't.
Currently, most high school graduates have demonstrated an ability with algebra and geometry at a minimum.
Simply incorrect. Sure, by our current standards, they can use it, but it's just rote memorization of processes and patterns. They don't understand the logic of it at all.
And yes it does make me angry when idiots start convincing people to take a self-destructive path.
His path looks much, much less destructive than the current system.
It's not because we should trust our instincts and not bother proving stuff that is obvious as the author recommends.
You said you stopped reading it, and that much is obvious.
I notice you didn't comment on what I said about people not understanding the benefits they themselves accrued under the system which they seek to destroy.
It is possible to derive at least some benefits from a terrible system while still advocating another system.
But really, I never bothered doing any of the busy work (waste of time) and learned on my own. It is almost entirely thanks to my own efforts that I understand math as much as I do now. About the only thing schools did for me was introducing me to the simplest concepts (addition, etc.), but I worked to understand it all on my own, since they weren't going to help with that.
Stop trying to make it sound tragic, you sound silly.
It's not tragic; it's comical.
I'll show Slashdot my True Ferocity soon enough. Wait and see.
I'm just blown away that you think that pdf has any valuable insights.
I'm just blown away that you don't. Well, not really.
you end up with a bunch of idiots who don't know how to paint (or do math).
Like now.
Luckily, the drudgery part of math is much shorter and much easier to learn than painting.
And also easier to forget, as we've seen. But go on ruining people's educations, except for those with an exceedingly high aptitude and willpower. Everyone suffers at least a bit under the current system.
It's hilarious that you think that paper is connected with identifying the problem in math education
I think it identifies at least part of the problem.
That paper doesn't even... oh man I don't even have the words to describe what a fail that paper is.
Are you talking about your long, angry post, or the paper? It seems more like you're talking about your post.
Well, judging from the tone of your post, you're a lost cause. Sad (not really), but true.
If students learn something for the first time they tend to use their memory mostly without much understanding.
Which is part of the problem.
Only through training, execises they learn to use the concepts behind it and find out about the subtle problems behind it.
One thing I hate is when people tell me how I learn and force me to do repetitive assignments that test only for memorization and do nothing to bolster one's understanding of the material, which is the sort of thing I was talking about. I had to deal with that garbage too much in the past, and never bothered to do any of the assignments.
Maybe I incorrectly assumed he was talking about the same kind of rote memorization I was thinking of. When I talk about that, I'm saying that they force pointless repetition on people, have people memorize meaningless facts, and skip the process of trying to get people to understand how and why it all works to begin with. What I'm not saying is that you never need to retain any information.
But really, attempting to understand how and why it all works gives you a lot of practice all by itself, from my experience.
There are experiments about what helps pupils best to get better with mathematics, and it has been shown that drill and constant exercise is the most effective way, even for complexer mathematical problems.
That's a great way to train drones who don't understand the how & why, but not a great way to make people truly understand mathematics. I do what I do because I love it, and any facts I memorize I memorize because I happen to see them often, not because forced me to sit around and work out pointless problems. That sort of thinking is why math education is so abysmal.