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New Math
Topic Started: Oct 1 2014, 01:39 PM (715 Views)
Aqua Letifer
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ZOOOOOM!
I got pretty high in math myself; Multi-order diff.eq. was what I had to do for a minor.

It is absolutely true that you're going to get nowhere in mathematics—nowhere—if all you can do is get the right number.

Ask Klaus. You have to understand what it is you're actually doing.

And then there's the whole "understanding for its own sake" argument but hey, that just complicates things.
I cite irreconcilable differences.
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Horace
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HOLY CARP!!!
Mikhailoh
Oct 1 2014, 05:20 PM
Really, Aqua? Addition and subtraction? They hardly contain the plethora of possibilities that an application might have. Horrible analogy.
Word problems come to mind - as does my recollection that word problems really tripped kids up in grade school.

For instance - "you're in city A and you start down the highway. 25 miles later you pass city B, and 60 miles later you arrive in city C. How far away is city C from city B?"

Understanding the theory behind subtraction just allows the student to recognize that the problem as stated is a subtraction problem. Some rote methods of subtraction map to that theory better than others, I'd say.
As a good person, I implore you to do as I, a good person, do. Be good. Do NOT be bad. If you see bad, end bad. End it in yourself, and end it in others. By any means necessary, the good must conquer the bad. Good people know this. Do you know this? Are you good?
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Aqua Letifer
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ZOOOOOM!
I should add that I'm not for CC, and that you shouldn't have to sit through endless theory lessons before you're allowed to add and subtract. Just that you do reach a certain point—and I think you reach it quickly—where you have to know more about what you're doing before you can learn more.
I cite irreconcilable differences.
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Horace
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HOLY CARP!!!
I've more or less built a career (such that it is) by understanding simple math stuff better than others around me. I never got far in math, and was never particularly good with the rote learning thing anyway, but I'm known as a guy good with math, simply because I understand pretty basic manipulations of numbers on a theoretical level and can apply that understanding to do real things. It's consistently surprising to me how rare this is, especially in the professional company I keep.
As a good person, I implore you to do as I, a good person, do. Be good. Do NOT be bad. If you see bad, end bad. End it in yourself, and end it in others. By any means necessary, the good must conquer the bad. Good people know this. Do you know this? Are you good?
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Copper
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Shortstop
Horace
Oct 1 2014, 05:22 PM
Understanding the theory behind rote processes

Rote is nice, but Correlation is the thing

Posted Image
The Confederate soldier was peculiar in that he was ever ready to fight, but never ready to submit to the routine duty and discipline of the camp or the march. The soldiers were determined to be soldiers after their own notions, and do their duty, for the love of it, as they thought best. Carlton McCarthy
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Mikhailoh
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If you want trouble, find yourself a redhead
If you don't know what subtraction is I suppose you would not be able to work that particular problem. But figuring out that you should subtract is key. That is reading comprehension first and foremost.

My main point being that there is nothing wrong with going in depth on some subjects, but every hour you spend in school on one subject is an hour you cannot spend on another. How does one provide a broad enough education?
Once in his life, every man is entitled to fall madly in love with a gorgeous redhead - Lucille Ball
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Horace
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HOLY CARP!!!
Copper
Oct 1 2014, 05:34 PM
Horace
Oct 1 2014, 05:22 PM
Understanding the theory behind rote processes

Rote is nice, but Correlation is the thing

Posted Image
Well, I used the word "related" rather than "correlated". They'll just have to correct their pyramid. :)

Quote:
 
Understanding the theory behind rote processes allows you to use that theory to understand and perform that rote process, along with an infinite amount of other related processes
As a good person, I implore you to do as I, a good person, do. Be good. Do NOT be bad. If you see bad, end bad. End it in yourself, and end it in others. By any means necessary, the good must conquer the bad. Good people know this. Do you know this? Are you good?
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jon-nyc
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Cheers
Mikhailoh
Oct 1 2014, 05:36 PM
How does one provide a broad enough education?
Psst - you're supposed to call them 'women' these days.
In my defense, I was left unsupervised.
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Copper
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Shortstop
Horace
Oct 1 2014, 05:38 PM

Well, I used the word "related" rather than "correlated". They'll just have to correct their pyramid. :)

That's a flight instructor pyramid. While poking around for the image I noticed several variations on the theme.
The Confederate soldier was peculiar in that he was ever ready to fight, but never ready to submit to the routine duty and discipline of the camp or the march. The soldiers were determined to be soldiers after their own notions, and do their duty, for the love of it, as they thought best. Carlton McCarthy
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Horace
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HOLY CARP!!!
Mikhailoh
Oct 1 2014, 05:36 PM
If you don't know what subtraction is I suppose you would not be able to work that particular problem. But figuring out that you should subtract is key. That is reading comprehension first and foremost.

My main point being that there is nothing wrong with going in depth on some subjects, but every hour you spend in school on one subject is an hour you cannot spend on another. How does one provide a broad enough education?
I would say that an attempt to teach "theory" relates to breadth directly, while teaching rote relates to the concept of "academic".

Then again, math yields itself to theory because ultimately it's the teaching of things about which there can be no argument. Teaching theory in other subjects seems much more dicey.
As a good person, I implore you to do as I, a good person, do. Be good. Do NOT be bad. If you see bad, end bad. End it in yourself, and end it in others. By any means necessary, the good must conquer the bad. Good people know this. Do you know this? Are you good?
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Aqua Letifer
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ZOOOOOM!
Mikhailoh
Oct 1 2014, 05:36 PM
How does one provide a broad enough education?
By not having kids in Brooklyn and the Badlands doing the exact same stuff.

Education's a perfect example of an absurdly large entity screwing up most of what they do because of their size.

It's absurd to believe kids in inner cities and rural areas should receive identical educations. Get them to a place where they're curious and they know how to go about answering their own questions by age 18. That's broad enough for me.
I cite irreconcilable differences.
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JBryan
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I am the grey one
George K
Oct 1 2014, 02:36 PM
I've read (and I have no independent verification of this) that one is now allowed to bring a calculator into your testing room for things like placement, SAT, etc. No need to learn method, let the computer do it for you. Can anyone confirm?

That said, I remember taking physics in college and being confused by the formulas, etc. I found it much easier to remember the theory behind the formula, and deriving the formulas for my tests. I actually understood the *why*.
:uparrow:
"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne


There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it".


Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody.

Eleanor: At my age there's not much traffic anymore.

From The Lion in Winter.
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Copper
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Shortstop

I think we used to have a common core that consisted of basics like reading, writing, arithmetic and in high school things like the sciences and home economics, civics and shop.

The problem with those things is that they don't have much room for political indoctrination except maybe civics.

If everyone gets a good education and a good job there are no more poor people. If there are no more poor people the democrats are out of work. Common core can insure a good supply of democrats for years to come.
The Confederate soldier was peculiar in that he was ever ready to fight, but never ready to submit to the routine duty and discipline of the camp or the march. The soldiers were determined to be soldiers after their own notions, and do their duty, for the love of it, as they thought best. Carlton McCarthy
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John D'Oh
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MAMIL
Copper
Oct 1 2014, 06:14 PM
If there are no more poor people the democrats are out of work. Common core can insure a good supply of democrats for years to come.
I get the distinct impression that ill-educated ignorance is a bit of a gold-mine for the GOP voter base, so it's really a win-win for both parties.
What do you mean "we", have you got a mouse in your pocket?
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Lisa
Junior Carp
I am 43 and learned the rote method for all of this stuff in school. I could add, subtract, multiply and divide following the method I was taught, but for all but the simplest problems, I needed a piece of paper so I could hand write the problem and write out the borrowing/carrying/etc.

My kids are now 13 and 10 and we've been through a curriculum called "Everyday Math" -- from the screen shot of that math book, I suspect it's the same thing. Some of the Everyday Math stuff is kind of crazytown -- they do this ridiculously complicated thing called lattice method when learning to multiply that involves drawing this big grid and multiplying individual parts of the numbers together. When they first covered it with my daughter, I was baffled and, much like the people who wrote that initial email, pretty much of the "WTF is this crap?!" mindset. But when I actually had to learn it (along with a few other multiplication strategies that they teach before teaching the "rote" method that I learned) in order to help my kids with their homework....well, I still think its a ridiculously cumbersome approach to multiplying 2 2-digit numbers together, but honestly, it gave me a better understanding of just how multiplication works. And the other strategy they teach (called partial products -- you can google it) was even better for me from a theoretical standpoint. Thanks to partial products, I can now multiply much better in my head because I understand how multiplication works -- when I learned the rote method in school, I never realized that if you are trying to multiply 76 x 32 it's the same as multiplying 70 x 30, 70 x 2, 6 x 2 and 6 x 30 and adding them all together. That's the kind of theoretical understanding that totally passed me by while I was dutifully learning to carry my 1's and borrow and all the other rote steps we learned in elementary school. Will my kids ever use the lattice method again to multiply -- no, of course not. But does it help them understand the workings behind multiplication instead of just a rote process? I would say yes, definitely. When I can say that at 40 years old with several college degrees under my belt, I learned something new about multiplying from my kid's 4th grade math book, that's saying something.
Edited by Lisa, Oct 2 2014, 03:56 AM.
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jon-nyc
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Cheers
Good to know. My son's school was traditionally an Everyday Math school but switched over to Singapore Math a few years ago. I think they still use Everyday math until 3rd or 4th grade though.
In my defense, I was left unsupervised.
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Mikhailoh
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If you want trouble, find yourself a redhead
Now see, I'm a lot older than Lisa and I DID learn that multiplying 76 x 32 is the same as multiplying 70 x 30, 70 x 2, 6 x 2 and 6 x 30 and adding them all together. I use that method a lot when multiplying in my head.
Once in his life, every man is entitled to fall madly in love with a gorgeous redhead - Lucille Ball
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JBryan
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I am the grey one
You are really using that method when you multiply the old fashioned way.
"Any man who would make an X rated movie should be forced to take his daughter to see it". - John Wayne


There is a line we cross when we go from "I will believe it when I see it" to "I will see it when I believe it".


Henry II: I marvel at you after all these years. Still like a democratic drawbridge: going down for everybody.

Eleanor: At my age there's not much traffic anymore.

From The Lion in Winter.
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John D'Oh
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MAMIL
The problem with the old way isn't that it's old, or that it doesn't work, it's that learning the method by rote obscured the reasoning behind it.

If you're only going to teach someone a method without any understanding of why they're doing what they're doing, you might as well just give them a calculator and save everybody a lot of time.
What do you mean "we", have you got a mouse in your pocket?
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Horace
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HOLY CARP!!!
It's all geometry. Addition and subtraction is the distance (visual! You could put it on a slide!) between two points. Multiplication and division is that same distance, but a certain number of them - maybe 10, maybe only a tenth.

I think it's important to make the visualization of the thing the most important part of the teaching of the thing.
As a good person, I implore you to do as I, a good person, do. Be good. Do NOT be bad. If you see bad, end bad. End it in yourself, and end it in others. By any means necessary, the good must conquer the bad. Good people know this. Do you know this? Are you good?
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John D'Oh
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MAMIL
When I did teacher training, we used the number line a lot as a way of visualising it. Pictures are great - I struggled with imaginary numbers until somebody showed them as points on 2-axis curve, then suddenly it all made perfect sense. In fact, they'd have been better off never calling them imaginary numbers in the first place - very misleading.
What do you mean "we", have you got a mouse in your pocket?
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Mikhailoh
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If you want trouble, find yourself a redhead
Horace
Oct 2 2014, 11:13 AM
It's all geometry. Addition and subtraction is the distance (visual! You could put it on a slide!) between two points. Multiplication and division is that same distance, but a certain number of them - maybe 10, maybe only a tenth.

I think it's important to make the visualization of the thing the most important part of the teaching of the thing.
For people like me who are visually oriented that works well and I agree. Not sure about those who are otherwise.
Once in his life, every man is entitled to fall madly in love with a gorgeous redhead - Lucille Ball
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jon-nyc
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Cheers
John D'Oh
Oct 2 2014, 11:55 AM
When I did teacher training,
Oh my. Tell me you never actually taught children.
In my defense, I was left unsupervised.
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John D'Oh
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MAMIL
jon-nyc
Oct 2 2014, 01:57 PM
John D'Oh
Oct 2 2014, 11:55 AM
When I did teacher training,
Oh my. Tell me you never actually taught children.
What else would I do with the little buggers?

I think it's fair to say that I wasn't very good at it. I managed to get through the teaching practice, went on holiday to Europe for a month, and decided to do something else instead. Actually, to be more accurate, to do anything else instead.
What do you mean "we", have you got a mouse in your pocket?
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jon-nyc
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Cheers
Looks like some kids really dodged a bullet.
In my defense, I was left unsupervised.
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