Are you smarter than a 4th grader?

Gurgeh

Gurgeh

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Saying memorization is for dumb kids is godamn insult to the brightest mathematicians. I don't know about the USA, but in France (or in Russia for that matter) that has the most fields medal per capita in the world, kids preparing for the top schools spend 20 hours a week doing maths exercices, and by that I mean memorizing them. It might feels dumb, but even among the most gifted students they can only solve exercices that are at a "close" range from exercices they know. Imagine maths as 3d space, and exercices being small dots in it, and your gift is how far you can reach from those dots. And even for Einstein or the like, that distance is : not very far.

The current education has gone way to far in demonizing knowledge, now we've got kids that can't drive their car without a gps, can't compute 12x5 without their phone, haven't learnt any history, because they can check on wikipedia. We make them believe (or convince ourselves) that we don't need the foundations and we can just move on the more gratifying and complex stuff, but the reality is we cannot. Anyone that has actually worked in any, even semi-technical field, knows that millenials are just, as a whole, horrible at it. And they are the Incarnation of that belief, you don't need to memorize, it's on the Internet.

You don't need to just "understand" multiplications", you need to be able to be able to compute them very quickly if you are to do any maths. And that require, for 99% of the kids, to learn the godamn table, even if they're super smart.
 
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maskedmelon

maskedmelon

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A lot of highly intelligent persons weighing in here. We ought to be able to arrive at consensus soon.

*passes around a bouncing basket of hugs and kisses*
 
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maskedmelon

maskedmelon

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Gurgeh said:
Saying memorization is for dumb kids is godamn insult to the brightest mathematicians. I don't know about the USA, but in France (or in Russia for that matter) that has the most fields medal per capita in the world, kids preparing for the top schools spend 20 hours a week doing maths exercices, and by that I mean memorizing them. It might feels dumb, but even among the most gifted students they can only solve exercices that are at a "close" range from exercices they know. Imagine maths as 3d space, and exercices being small dots in it, and your gift is how far you can reach from those dots. And even for Einstein or the like, that distance is : not very far.
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This is a highly relevant point. Goes back to my post on how we actually calculate things. We rely on knowns to solve for unknowns and are only able to solve for unknowns insofar as we are able to parse them into sets of operations for, which solutions are known. good post my frank 👍
 
wormie

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Gurgeh said:
Saying memorization is for dumb kids is godamn insult to the brightest mathematicians. I don't know about the USA, but in France (or in Russia for that matter) that has the most fields medal per capita in the world, kids preparing for the top schools spend 20 hours a week doing maths exercices, and by that I mean memorizing them. It might feels dumb, but even among the most gifted students they can only solve exercices that are at a "close" range from exercices they know. Imagine maths as 3d space, and exercices being small dots in it, and your gift is how far you can reach from those dots. And even for Einstein or the like, that distance is : not very far.
Click to expand...
Uhhh yeah thats will be a nope dawg. The top math students arent spending 20 hours a week memorizing math exercises. They are spending 20 hours learning how a mathematical object behaves when poked in some fashion.
 
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wormie said:
Uhhh yeah thats will be a nope dawg. The top math students arent spending 20 hours a week memorizing math exercises. They are spending 20 hours learning how a mathematical object behaves when poked in some fashion.
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at high school level?
 
Gurgeh

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wormie said:
Uhhh yeah thats will be a nope dawg. The top math students arent spending 20 hours a week memorizing math exercises. They are spending 20 hours learning how a mathematical object behaves when poked in some fashion.
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No they are not. Not in France anyhow. From 15 to 20 they literally do 20 hours of exercices a week, memorizing entire books of them. And that produce the most field's medal per capita in the world.

It's not 'poking' it's thousands and thousands of exercices that read like "prove that subgroups of R are either dense in R or of the form aZ", an exam look like this:


It's for 18 to 21 year old, of course it's in french. But you should get the gist of it: it's not something you'll succeed at at 19 if all you've done is pocking around.

This shit is boring, most students dislike that part of their studies, but it does produce great results by any metric. You don't need to vaguely understand the basic concepts, you need to completely master them. One of the favourite quote of my maths teacher was 'Even if we wave you up in the middle of the night you should be able to give that answer'
 
wormie

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Gurgeh said:
No they are not. Not in France anyhow. From 15 to 20 they literally do 20 hours of exercices a week, memorizing entire books of them. And that produce the most field's medal per capita in the world.

It's not 'poking' it's thousands and thousands of exercices that read like "prove that subgroups of R are either dense in R or of the form aZ", an exam look like this:


It's for 18 to 21 year old, of course it's in french. But you should get the gist of it: it's not something you'll succeed at at 19 if all you've done is pocking around.

This shit is boring, most students dislike that part of their studies, but it does produce great results by any metric. You don't need to vaguely understand the basic concepts, you need to completely master them. One of the favourite quote of my maths teacher was 'Even if we wave you up in the middle of the night you should be able to give that answer'
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You dont master those topics by memorizing them. You master them by understanding what and why.
 
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iannis

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Gurgeh said:
Saying memorization is for dumb kids is godamn insult to the brightest mathematicians. I don't know about the USA, but in France (or in Russia for that matter) that has the most fields medal per capita in the world, kids preparing for the top schools spend 20 hours a week doing maths exercices, and by that I mean memorizing them. It might feels dumb, but even among the most gifted students they can only solve exercices that are at a "close" range from exercices they know. Imagine maths as 3d space, and exercices being small dots in it, and your gift is how far you can reach from those dots. And even for Einstein or the like, that distance is : not very far.

The current education has gone way to far in demonizing knowledge, now we've got kids that can't drive their car without a gps, can't compute 12x5 without their phone, haven't learnt any history, because they can check on wikipedia. We make them believe (or convince ourselves) that we don't need the foundations and we can just move on the more gratifying and complex stuff, but the reality is we cannot. Anyone that has actually worked in any, even semi-technical field, knows that millenials are just, as a whole, horrible at it. And they are the Incarnation of that belief, you don't need to memorize, it's on the Internet.

You don't need to just "understand" multiplications", you need to be able to be able to compute them very quickly if you are to do any maths. And that require, for 99% of the kids, to learn the godamn table, even if they're super smart.
Click to expand...
smart kids understand they have to master the tools.
 
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iannis

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wormie said:
You dont master those topics by memorizing them. You master them by understanding what and why.
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memorization plays a crucial role in being able to do that though.

I suppose you could work through from base principles every time, and that is legit a type of mastery. It's unnecessary though and no one should want to do that. They should be ABLE to at need.

Memorization doesn't interfere with that ability. It doesn't replace it either.
 
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wormie

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iannis said:
memorization plays a crucial role in being able to do that though.

I suppose you could work through from base principles every time, and that is legit a type of mastery. It's unnecessary though and no one should want to do that. They should be ABLE to at need.

Memorization doesn't interfere with that ability. It doesn't replace it either.
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What I am saying is that his claim that kids are spending 20 hours a week memorizing math exercises is wrong. You do exercises to understand why the thing you are studying works one way or another. No one is memorizing the exercises in that linear algebra thing he just linked.
 
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maskedmelon

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wormie said:
What I am saying is that his claim that kids are spending 20 hours a week memorizing math exercises is wrong. You do exercises to understand why the thing you are studying works one way or another. No one is memorizing the exercises in that linear algebra thing he just linked.
Click to expand...

whether they are memorizing those specific things or are not, his general point was that memorizing stuff is useful even for intelligent people and it is, because then we can devote more thought to other considerations. Machines do the same thing for us, but there does remain a tremendous advantage to storing that stuff in your head: it provides a robust resource base for creative expression. Knowledge does not make a man innovative, but it does allow an innovative man to innovate more broadly.
 
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Siddar

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I expect will get the clear answer to this topic in about five years. As to weather new are old methods worked best. These changes have been going on for three to five years now and are being implemented in elementary school. The first waves of it should just be starting to wash up in middle school about now. Its very unlikely that the establishment will be able to alter testing fast enough in order to not show a rapid decline in middle school math scores.

It's also being pushed by the same people that want to transition children into sex they're not.
 
zombiewizardhawk

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The school system has been lowering standards for decades to make it seem like shit teachers and shit school policies aren't having a negative impact. I graduated high school in 2003, took the FCAT in 2000 or 2001 don't remember for sure, but it was the last year that it was required to graduate in Florida. They phased it out because it was "too hard" (for the kids who fucked off in school/slept/didn't want to learn cause they were too busy being 'cool'). All the different sources we've gotten on this site have proved that the shit hasn't slowed down or stopped recently, so why would it magically stop in the future?

Tests are too hard, these new methods are great tho so we're just gonna relax standards even more!
 
Mist

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Void said:
No, and fuck you, no. You're saying that those of us that memorized the tables aren't smart enough to visualize 4 rows of 6 rabbits, so we have to "fall back" on memorization?
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No, that's the exact opposite of what I'm saying.

What I'm saying is that by forcing you to memorize them by default you were robbed of the chance to learn to think about multiplication in a more intuitive way.
 
LachiusTZ

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Mist said:
It's a fundamental rethink of what the purpose of teaching kids math is.

If you want to train future cashiers then doing it the old way is definitely the best way to do it.

However, by the time kids in elementary school get into the workforce there's probably going to be about 50 cashiers left in the country that haven't been automated and 10 years after that they'll all have smartphones implanted in their skulls.

The point is to get kids to think about numbers the way mathematicians and programmers and other people do, from as young of an age as possible. Yes, it might be pointless for 70% of students but old math was also pointless for those students beyond the basics. Most of the content school is useless for most people, it's just 13 years of training you to do what you're told and behave in classroom for long enough to not get kicked out. Training those kids to do shit the new math way fills the same void as training them to do math the old way, basically.

But if you can just maybe get your 115 IQ kids into thinking about numbers in the same way that 130 IQ kids inherently think about numbers and at a young age, then you've just doubled your pool of potential data scientists, engineers and programmers.

Is it a good plan? No one knows, but training kids to be basic calculators wasn't doing a heck of a lot of good either.
Click to expand...

You are a powerful kind of stupid.

But a great gauge of what's right and wrong.
 
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Borzak

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If you are in a conference about something that has to be fixed right now to stop further damage or catastrophe you would be amazed (or maybe not) the engineers and PM's when someone is talking the looks in their eye doing math and a few of them moving their fingers up and down counting and hoping someone doesn't notice. Personally I don't care if they take off their shoes and count to themselves using fingers and toes as long as they end up in the right spot.

Hell I've done it at the end of a 16 hour work day in the fiel to make sure I didn't just skip something lol.

This was a big thing when I was young.

en.wikipedia.org

Chisanbop - Wikipedia

en.wikipedia.org en.wikipedia.org

A big issue now is some in schools (teachers administrators) downplaying the need to learn any math regardless of how you get there. I mean come on, even McDonalds counts change for you now. I think a fair number of teachers can't give a real world of example for certain things used in math. I liked real world examples. I guess that's why I stuck to geometry and trig. Past that the teachers normally were "It's a good thing to know one day". Couldn't explain how you would use it in the real world.
 
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Aldarion

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Mist said:
What I'm saying is that by forcing you to memorize them by default you were robbed of the chance to learn to think about multiplication in a more intuitive way.
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See, this is a good example of what I mean by vague, fuzzy, subjective standards being brought into education.

How exacty does one measure the extent to which a student "thinks about multiplication in a more intuitive way"? Is this binary? Do we attach a score to it somehow? What test do we give the student to measure the intuitiveness of their thinking?

At their core statements like this are subjective bullshit. Feels. (At least you were creative and didnt just say "understanding numbers" or "think quantitatively", those other favorite vague immeasurable quantities educators love to talk about)

You know what you can test? Whether the student gets the right answer. Make it a quick test, and it has to be done by memorization.

Voila - just like that, by focusing on what can actually be tested, we are back to training people to use their brains. And people won't have to rely on a thousand dollar gadget to do a second grade calculation.
 
Aldarion

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maskedmelon said:
Sorry your super power has been irrevocably supplanted by a smart phone app, dude.

You are right though, the ability was and still is useful. Unfortunately, the sun is setting on that utility. You can't make smart so I don't have much hope for these alternative teaching methods, but if they manage salvage even some of the billions of minds rendered obsolete by innovation then I think they are worth entertaining.
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Well, until the devices goddamn RIDICULOUSLY short battery life runs out. Then, its Flowers for Algernon time and we can sit around drooling on ourselves until it recharges. (Seriously, I don't do smartphones but I use one as a camera sometimes. I don't know whats funnier about smartphone users - that they've accepted wtaching videos on a screen the size of a postage stamp or that theyve accepted battery life thats measured in hours).

Or if you drop it in the water. Or your finger is a little too wet, or a little too dry, so the screen doesnt respond when you touch it.

Or you're in a situation where only a total asshole whips out their phone (dinner, a classroom, the middle of a conversation) but would still like to retain the ability to do second grade math.

In any case, I see no evidence these "new" methods will help produce math literacy and a lifetime of evidence that the old methods worked.
 
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Lendarios

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Let me give you two examples.

I memorized that 12x12 is 144.
I also know how to get to it, what it means and the simple steps to get to it.

I also memorized that pi is 3.1415267... ,no google so I may be off a decimal; but I have NO clue how to get to the number. There are probably 10 different ways of computing pi as a series, as an integral, and they are all right, but for geometry just knowing the value is enough. I probably computed PI as a limit but I cant remember.

The same way with square root, I dont know how to compute them save by dividing and approximating same as COS SIN TAN. All I know is sohcahtoa boom done for most trivial cases.
 
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