Are you smarter than a 4th grader?

Siddar · Oct 28, 2019

Chris said:
Is anyone actually saying no memorization?

When it's done well kids do both, they know they can add up 9 elevens to get 99 and also know that 9 x 11 = 99 which is faster.

Show me anyone saying that common core methods should be used in High School or as an adult. These methods are just designed to teach conceptual understanding, not be workable methods.

The questions on that homework showed the situation that is being described.

It indicates that students are skipping past multiplication tables and being asked to solve problem using unknown variables.

No body here was taught that way including you.

Siddar · Oct 28, 2019

duplicate post

Szlia · Oct 28, 2019

Aren't these just factorization exercises ? Like 72 / 4 = n * 9 is (9 * 4 * 2) / 4 = n * 9 so you can remove the 9s on both sides and remove the 4s on the left and you get 2 = n ?

Sanrith Descartes · Oct 28, 2019

Gravel said:
I think this is the crux of it. Let's be honest here, most people are fucking retarded.

Ding, ding, ding! We have a winner.

Lendarios · Oct 28, 2019

I think that restricting the answer to the method provided is less useful than memorizing the result.

Some kids can see the pattern, some kids can memorize better.

Memorization gets a bad rep, because people without it has stigmatize it. Memorization is what you want, rationalization is second best.

Mist · Oct 28, 2019

Chris said:
Is anyone actually saying no memorization?

When it's done well kids do both, they know they can add up 9 elevens to get 99 and also know that 9 x 11 = 99 which is faster.

Show me anyone saying that common core methods should be used in High School or as an adult. These methods are just designed to teach conceptual understanding, not be workable methods.

NEVAR FORGET 9 11s.

Mist · Oct 28, 2019

Void said:
But at some point, memorization is such a time saver that it is essential.

Let's look at what "understanding numbers" would entail for someone that has ZERO multiplication memorized.

9 x 11 = ?

If you are not allowed to memorize anything, how do you solve this problem? You essentially have to add 11+11+11+11+11+11+11+11+11 to get 99.

Now imagine that you have to do this EVERY time you see a multiplication problem. Every time. That's what you are taking away by saying no to memorization.

At some point, the average person says, "Hey, I've multiplied 9 x 11 enough times that I'm just gonna go ahead and remember that it is 99." And from there it becomes obvious that after learning how to "understand" how multiplication works, you adopt a shortcut for numbers up to a certain point. 10 x 10 is a logical point because it allows you to break larger numbers down into smaller sub-problems (which is exactly what "carry the 4" and such involves), but for whatever reason most go to 12.

Pushing for memorization doesn't mean you just completely skip the part where you add 11 to itself 9 times. That's essential and, at least when I was in school decades ago, was the first thing they taught us. But after you understand how that works, fuck yes you should memorize those tables instead of doing it the long way every time. Can you imagine if every adult stopped what they were doing and ticked off "11, 22, 33,..." while they raised 9 fingers, every time they had to do multiplication?

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.

Mist · Oct 28, 2019

I was actually listening to this when I saw this thread:

America’s Math Curriculum Doesn’t Add Up - Freakonomics

freakonomics.com

Borzak · Oct 29, 2019

I never really thought about how I got the answer. There was a guy who was an operator and I would run into him from time to time. He could do trig and find sin, tan and such quicker and to 4 digits faster than I could using my calculater that's made for that. He didn't know either how he did it. He was great to have around when trying to work a lot of right triangles to figure out something in the field. His job didn't have anything to do with math either.

iannis · Oct 29, 2019

Borzak said:
I never really thought about how I got the answer. There was a guy who was an operator and I would run into him from time to time. He could do trig and find sin, tan and such quicker and to 4 digits faster than I could using my calculater that's made for that. He didn't know either how he did it. He was great to have around when trying to work a lot of right triangles to figure out something in the field. His job didn't have anything to do with math either.

I've known guys who could do similar and could explain it.

They found patterns and memorized them. That might not be the best way to say it. For us to do it, we'd have to memorize them. But doing that we will always face a pay in accessing the memory. It'll make us quicker, but not as quick or versatile as one of those guys. For them those patterns are self evident and they don't need to memorize, just observe.

People try to seed that in their children. Sometimes it works, sometimes not, and sometimes it emerges without the seeding.

Some small part of their cognition is just different.

Borzak · Oct 29, 2019

My dad is almost like that in some ways. In his engineering type work he spouts out a lot of answers before anyone even gets it written down or punched into a calculater or computer. I think most of it comes from when he started in the business it was all done by hand and the only calculaters were mechanical (like old cash registers) machines that did feet and inches. They weighed about 50 pounds and I sitll have one. I think it grew out of just saving time and the hassle of punching all that shit in, plus years and repitition. I grew up with calculaters made specifically for that.

Aldarion · Oct 29, 2019

Mist said:
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.

No, seriously - you and a couple others have denigrated the idea of being math competent as being "human calculators". "Just use your phone dude!"

I feel like I'm taking crazy pills.jpeg

Yes, that was precisely the point. Somewhere in elementary school we used to train people to do math in their heads. Because its easy, we covered it in elementary school. And it allowed people to spend the rest of their lives with this built in incredible ability to do math in their heads. Like a friggin superpower. Like having a computer built in to their brains.

Not just academics. Carpenters, plumbers, even cashiers. They all had this sci-fi ability, practically Mentats out of Herbert's Dune, to do arithmetic in their heads.

THEN some educators decided to "fundamentally rethink math education" and now we have people seriously proposing that the human brain is too good to waste on basic math, and we should all just thumb our phones like illiterate retards until The Computer tells us the right answer.

If you don't see the practical value of being able to do basic math (*and this REQUIRES memorization of multiplication tables), at least acknowledge the social value. Everyone who whips out a phone to do basic math brands themselves an idiot, irrevocably. Surely its worth memorizing some easy shit in grade school if only to avoid that?

--

On topic, the way this is used at my kids school is largely supplementary like Chris described, and not actually a problem. But I have seen how trends sweep education. A few people noted minor issues with the lecture-only format and we now have idiots seriously running around saying "lectures don't work" and "flip the classroom". It wouldnt surprise me at all if there are schools where this is the bulk of the course, and theyre actually skipping the tables.

Borzak · Oct 29, 2019

When I was in college 20 years ago we weren't allowed to use calculaters in a 2 hour exam on projecting out management plans and the statistical analysis. If you needed to know the standard deviation you raised your hand and the prof came by and looked at your sheet and let you look at the SD on his paper and that was it. All done by hand. Pretty sure that is now smart phones now, if they even require 12 hours of statistics for forest and wildlife management anymore.

They were fond of saying "When you know what you are doing you can use a calcuater or hire an assistant to do all that stuff".

Apparently I learned very little math in middle and high school. I suck at certain types of math and failed a course or two. Geometry and trig worked well for me. I always needed to see something I was calculating rather than an abstract.

wormie · Oct 29, 2019

Thre problems posted here seem like half assed intro to abstract algebra exercises. This would be good to understand as this can lead to a rigorous explanation to the arithmetic we do daily. But the problem is that people who designed these problems and people trying to explain and teach these concepts don't know fuck all about it.

maskedmelon · Oct 29, 2019

Aldarion said:
No, seriously - you and a couple others have denigrated the idea of being math competent as being "human calculators". "Just use your phone dude!"

I feel like I'm taking crazy pills.jpeg

Yes, that was precisely the point. Somewhere in elementary school we used to train people to do math in their heads. Because its easy, we covered it in elementary school. And it allowed people to spend the rest of their lives with this built in incredible ability to do math in their heads. Like a friggin superpower. Like having a computer built in to their brains.

Not just academics. Carpenters, plumbers, even cashiers. They all had this sci-fi ability, practically Mentats out of Herbert's Dune, to do arithmetic in their heads.

THEN some educators decided to "fundamentally rethink math education" and now we have people seriously proposing that the human brain is too good to waste on basic math, and we should all just thumb our phones like illiterate retards until The Computer tells us the right answer.

If you don't see the practical value of being able to do basic math (*and this REQUIRES memorization of multiplication tables), at least acknowledge the social value. Everyone who whips out a phone to do basic math brands themselves an idiot, irrevocably. Surely its worth memorizing some easy shit in grade school if only to avoid that?

--

On topic, the way this is used at my kids school is largely supplementary like Chris described, and not actually a problem. But I have seen how trends sweep education. A few people noted minor issues with the lecture-only format and we now have idiots seriously running around saying "lectures don't work" and "flip the classroom". It wouldnt surprise me at all if there are schools where this is the bulk of the course, and theyre actually skipping the tables.

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.

Chris · Oct 29, 2019

Siddar said:
The questions on that homework showed the situation that is being described.

It indicates that students are skipping past multiplication tables and being asked to solve problem using unknown variables.

No body here was taught that way including you.

Was that a teaching aid for multiplication tables or for common factors and algebra though? It was definitely way too complicated for teaching times tables, I agree. I don't know how the US system works but in the UK we have exams at 16 and students can use any method that works.

Here's what is going on:

We were all taught properly how time tables are derived and to memorise them. Great. But some kids can't do it or some teachers can't teach it, how do you fix that?

Well people in charge of education look for solutions and end up with something good teachers do anyway but given a fancy name e.g. Common Core, paying a consultant a bunch of money for it and for related textbooks.

Then the shit teachers take those materials to heart and make it the entire point of their teaching. Then you see memes of correct answers being marked incorrectly or overcomplicated teaching aids like we saw in this thread.

The good teachers still teach it properly and use the materials as an aid to learning the content and not as the content itself.

Mist · Oct 29, 2019

Borzak said:
I never really thought about how I got the answer. There was a guy who was an operator and I would run into him from time to time. He could do trig and find sin, tan and such quicker and to 4 digits faster than I could using my calculater that's made for that. He didn't know either how he did it. He was great to have around when trying to work a lot of right triangles to figure out something in the field. His job didn't have anything to do with math either.

In Kindergarten we would get counting exercises that asked you to count things up in rows. Before I even knew what multiplication was I could tell you that 4 rows of 6 rabbits is 24 rabbits and 2 extra rabbits is 26 rabbits. This pissed off my Kindergarten teacher to no end.

I never had to memorize anything other than the 7s of the multiplication table because I guess my brain just didn't like visualizing 7s quick enough to satisfactorily pass a verbal multiplication quiz.

But in general I do not believe that memorization of the multiplication tables is required for all kids. It is far better to teach kids to visualize or otherwise intuitively think about numbers from a young age, and it's probably better to save the memorization as a fallback crutch for those that just aren't smart enough to do it intuitively. Going straight to memorization as the default, as in our previous curriculum, seems like something to be avoided because you are robbing kids that could learn to think about numbers more intuitively from doing so. Given how fundamental this is you might even be making those kids dumber in the long run by teaching them to memorize instead of to think.

So you've got 3 tranches of of kids:

Kids who think intuitively about numbers without needing being taught.
Kids who could be taught to think intuitively about numbers but don't do this naturally on their own.
Kids who will only be able to memorize multiplication tables if they ever want to be good at basic arithmetic.

Void · Oct 29, 2019

Mist said:
and it's probably better to save the memorization as a fallback crutch for those that just aren't smart enough to do it intuitively.

So you've got 3 tranches of of kids:

Kids who think intuitively about numbers without needing being taught.
Kids who could be taught to think intuitively about numbers but don't do this naturally on their own.
Kids who will only be able to memorize multiplication tables if they ever want to be good at basic arithmetic.

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? Aside from how ridiculous that statement is, are you really telling me that you picture those rabbits every time you have to multiply two numbers? Or did you perhaps do it enough times that you instinctively knew that the answer to 4 x 6 was 24? Did you, perhaps, FUCKING MEMORIZE it??

You're literally saying that those of us that memorized them never got taught how to "think intuitively" about numbers, and/or we aren't capable of understanding it. Maybe you should have added a 4.

4) Kids who grasp how to think about numbers intuitively (whether on their own or taught) and then realize how much more useful it is to memorize their times tables so they don't have to count rows of fucking rabbits every time.

a c i d.f l y · Oct 29, 2019

Animale said:
Because multiplication tables don’t teach kids how to understand numbers, but how to memorize tables.

You learn words and the alphabet before you learn to speak and understand what the fuck you're saying. You're going to have a really hard time trying to do algebra when you can't do simple multiplication without using a calculator. You learn how multiplication works, then you memorize what you can to speed up learning and doing higher level math. We learn how to do long division to understand how it works, but I'm not going to not use a calculator because I need to understand division better. That's stupid.

You can't teach intuition. That's something you have or you don't. The definition of intuition is to understand something immediately without conscious thought. It's a feeling, and teaching feelings is stupid. The kid who lacks intuition and does math wrong, won't know they've done it wrong until they get their paper back and wonders why they're failing math when they studied oh so hard, but they certainly felt really good about studying.

This lesson is stupid, or at best stupidly presented.

Math always irritated me because I was always like, "Get to the point." Yeah, yeah, I can take the double derivative of blah blah in my fucking sleep, where and when do I get to apply this? Because the teachers had to spend so much god damn time coddling or restating the same information over and over for the several idiots in the class that couldn't comprehend how to reduce or whatever lesson it was. I could have covered a years worth of calculus in 6-8 weeks, and proved it in college.

I don't get why we even bother teaching kids higher level math when they're literally not going to use it in any way, and whatever understanding a person would ever need in life stops after multiplication. You know who is going to grow up and do something with math by the time they're in the 3rd grade. Jimmy Two Dicks or the kid that's helping teach his friends fractions?

Lendarios · Oct 29, 2019

a c i d.f l y said:
You learn words and the alphabet before you learn to speak and understand what the fuck you're saying. You're going to have a really hard time trying to do algebra when you can't do simple multiplication without using a calculator. You learn how multiplication works, then you memorize what you can to speed up learning and doing higher level math. We learn how to do long division to understand how it works, but I'm not going to not use a calculator because I need to understand division better. That's stupid.

You can't teach intuition. That's something you have or you don't. The definition of intuition is to understand something immediately without conscious thought. It's a feeling, and teaching feelings is stupid. The kid who lacks intuition and does math wrong, won't know they've done it wrong until they get their paper back and wonders why they're failing math when they studied oh so hard, but they certainly felt really good about studying.

This lesson is stupid, or at best stupidly presented.

Math always irritated me because I was always like, "Get to the point." Yeah, yeah, I can take the double derivative of blah blah in my fucking sleep, where and when do I get to apply this? Because the teachers had to spend so much god damn time coddling or restating the same information over and over for the several idiots in the class that couldn't comprehend how to reduce or whatever lesson it was. I could have covered a years worth of calculus in 6-8 weeks, and proved it in college.

I don't get why we even bother teaching kids higher level math when they're literally not going to use it in any way, and whatever understanding a person would ever need in life stops after multiplication. You know who is going to grow up and do something with math by the time they're in the 3rd grade. Jimmy Two Dicks or the kids that's helping teach his friends fractions?

My mind was blown when teachers showed me how to use integrals to compute the volume of irregularly shaped solids,

I was like no way... wait oh shit it works.

Are you smarter than a 4th grader?

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