Do this maths. It R Hard.
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I've been watching Common Core math videos on youtube.com lately. It's pretty fun.
They teach arithmetic as if it was a college class, using the vocabulary of (simple) modern mathematics, like 'symbol', 'expression', 'value', 'meaning', 'interpretation'. All the stuff you guys don't get, but which are so important to clear thinking.
Interestingly, they also introduce thinking in terms of variables really early on.
Most interestingly, they mainly use conceptual "algorithms" to explain the concepts. So they have a language for a number line, and expressions like
2 + 4are interpreted as sequences of instructions. "You start at two, and then you move to the right four times."So it was pretty neat when the guy explained the equals sign to first graders, and they all got it.
It's like they designed a programming language and api for doing elementary math and agreed to use it everywhere in America.
Guess what they're training the kiddos to do... and it's about time.
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TIL apparently NodeBB doesn't have any plugin enabled to support BBCode-style [spoiler]tags[/spoiler]
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@Captain said in Do this maths. It R Hard.:
I've been watching Common Core math videos on youtube.com lately. It's pretty fun.
They teach arithmetic as if it was a college class, using the vocabulary of (simple) modern mathematics, like 'symbol', 'expression', 'value', 'meaning', 'interpretation'. All the stuff you guys don't get, but which are so important to clear thinking.
Interestingly, they also introduce thinking in terms of variables really early on.
Most interestingly, they mainly use conceptual "algorithms" to explain the concepts. So they have a language for a number line, and expressions like
2 + 4are interpreted as sequences of instructions. "You start at two, and then you move to the right four times."So it was pretty neat when the guy explained the equals sign to first graders, and they all got it.
It's like they designed a programming language and api for doing elementary math and agreed to use it everywhere in America.
Guess what they're training the kiddos to do... and it's about time.
Damn it, Captain. Quit making me like you. You are a proponent for Haskell for God's sake!
This. Should not. BE!
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@Tsaukpaetra said in Do this maths. It R Hard.:
TIL apparently NodeBB doesn't have any plugin enabled to support BBCode-style [spoiler]tags[/spoiler]
I started one.
https://what.thedailywtf.com/topic/19577/composer-buttons-plugin
GitHub - NedFodder/nodebb-plugin-tdwtf-buttons at spoiler
Composer Buttons for WTDWTF. Contribute to NedFodder/nodebb-plugin-tdwtf-buttons development by creating an account on GitHub.
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@Captain said in Do this maths. It R Hard.:
They teach arithmetic as if it was a college class, using the vocabulary of (simple) modern mathematics, like 'symbol', 'expression', 'value', 'meaning', 'interpretation'. All the stuff you guys don't get, but which are so important to clear thinking.
Hmm...I thought this was the point being made by various people all along.
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@boomzilla said in Do this maths. It R Hard.:
@Captain said in Do this maths. It R Hard.:
They teach arithmetic as if it was a college class, using the vocabulary of (simple) modern mathematics, like 'symbol', 'expression', 'value', 'meaning', 'interpretation'. All the stuff you guys don't get, but which are so important to clear thinking.
Hmm...I thought this was the point being made by various people all along.
I don't know, I don't read threads. I just post in them.
But the nice thing about common core is that the kids still learn arithmetic. But they end up with a 10 year head start over us adults, like the Chinese and others did/do.
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@Captain said in Do this maths. It R Hard.:
But the nice thing about common core is that the kids still learn arithmetic
Perhaps.
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@Captain said in Do this maths. It R Hard.:
But the nice thing about common core is that the kids still learn arithmetic.
All I have to say about Common Core is represented in this single image:
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Yeah, that dad is an idiot, because counting up from a number to figure out the difference is a much simpler algorithm than carrying.
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@Captain counting up requires carrying. If you don't fucking understand carrying you can't fucking count, and conversely if you understand counting then you understand how carrying works. Carrying is just counting up from 9 to 10. That is all it fucking is. It's not difficult and it doesn't require a fucking DIAGRAM.
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@Captain said in Do this maths. It R Hard.:
Yeah, that dad is an idiot, because counting up from a number to figure out the difference is a much simpler algorithm than carrying.
if common core is simplicity, and superior, please explain to me why i can find no professional mathematician that uses common core to calculate, nor can i find any commercially available counting device used for professional purposes that uses the common core approach?
If you can explain this discrepancy to me in a way that answers the question, and explains why teaching common core in a world where common core is not used outside of primary schools is a good introduction for students to the world of mathematics, without resorting to prevarication or circumlocution, i will convert to the ranks of common core zealots and seek to convert all i see as well.
if you cannot i will continue to mock common core with all the ferocity it so richly deserves.
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@anotherusername said in Do this maths. It R Hard.:
@Captain counting up requires carrying. If you don't fucking understand carrying you can't fucking count, and conversely if you understand counting then you understand how carrying works. Carrying is just counting up from 9 to 10. That is all it fucking is. It's not difficult and it doesn't require a fucking DIAGRAM.
Diagrams make things easier. You don't need a fucking DIAGRAM to count up, but it helps teach how to do the algorithm to little kids.
That's the same reason students in Bachelor's programs in Math use diagrams for problem solving. And why they're taught with diagrams. Because some kids are visual learners, and the diagram can help them. The rest of the kids still heard the lesson.
And by the way, carrying is an artifact of a particular algorithm for performing addition. It is not an intrinsic property of numbers. In other words, you only have to carry when numbers are drawn in arrays, and are added by adding their digits together. There are other algorithms. OBVIOUSLY.
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@accalia said in Do this maths. It R Hard.:
if common core is simplicity, and superior, please explain to me why i can find no professional mathematician that uses common core to calculate, nor can i find any commercially available counting device used for professional purposes that uses the common core approach?
What are you talking about? They're teaching the concepts before the algorithms, by using simple algorithms and line drawings. Later, once the kids understand why they're pushing symbols around, they can go ahead and memorize times tables and learn the standard algorithms. This leads to more engaged mathematics learners, instead of rote learners and math/logic-phobics.
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@Captain said in Do this maths. It R Hard.:
Diagrams make things easier. You don't need a fucking DIAGRAM to count up, but it helps teach how to do the algorithm to little kids.
Then after they clearly understand it, let them graduate to the method which requires a shitton less writing already. Fuck.
I don't give a fuck if you're trying to teach Common Core math, writing
427 - 316 ----- 111to solve 427 - 316 should never be marked wrong, by any teacher, anywhere. It shows clear understanding of the concept and you don't need a fucking diagram for it. Then, if you want to test whether they understand how to borrow, you give them a problem which requires them to borrow.
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@anotherusername Math is a machine, and the kiddos need to learn that. That's why they're testing for the algorithm. To see if they understand how to apply a sequence of instructions, one after another, to produce the desired result. The kids need to know how to do that, because many of them will be software developers in the economy of the future.
I could have used Excel to do that subtraction. Or Peano arithmetic. Neither would show I understand how to apply the algorithm they taught.
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@Captain then instead of crippling them with an algorithm that requires a huge, wonky diagram, how about teaching them a nice, simple one?
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@anotherusername said in Do this maths. It R Hard.:
@Captain then instead of crippling them with an algorithm that requires a huge, wonky diagram, how about teaching them a nice, simple one?
Really? The algorithm requires a diagram?
You can't subtract 99 from 100 by counting up without a diagram?
How about 91?
How about 81? (Hmm, if I go up 9, i'll be at 90, and if I go up another 10 I'll be at 100).
The algorithm they taught us is an unmotivated optimization, based on operations on digits instead of numbers. It's not simpler. It's significantly more complex. And worse yet, unmotivated.
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@Captain said in Do this maths. It R Hard.:
Neither would show I understand how to apply the algorithm they taught.
Based on the diagram, I have no idea what they're teaching.
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@boomzilla subtraction by adding up. The reason for the groupings is that there are "easy" additions that make the subtraction easier to do in your head.
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@Captain how do you do it on paper without the godawful diagram?
So your choices are, the godawful fucking diagram on paper, or counting it in your head?
Now what happens when you have big numbers? Either you use a huge fucking diagram on paper or you try to do it in your head and probably screw up in the middle because there's nothing on paper to keep you on track.
OR you shrug your shoulders and punch it into your computer and it gives you the answer, because once you understand how it works it's a total waste of your time to actually solve the problems, I guess.
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@Captain I can understand that. I guess it's the fact that the fictitious kid who did that was shown to intentionally make an error. Which was apparently that he forgot what numbers he was using.
Counting on a number line is a poor example of common core, though. I'm sure there's a better example somewhere up thread, where they talk about "make a z from x and y." All numbers that have no simple arithmetic relationship.
They're trying to teach shortcuts (and I'm not talking about counting up to learn subtraction) before they get the basics down.
After many years of math and having helped my daughter up to 9th grade (so far), my conclusion is that to learn math you start with rote. Whether it's memorizing a multiplication table or a sequence of steps to do a particular type of problem, you follow a recipe. And you don't worry too much about it. You just do it. After repetition, some understanding begins to dawn and ideally you really understand it and can see how it relates to other stuff.
Skipping stuff like this is like getting thrown into a rails project and being told about the magic and never understanding because you've skipped steps.
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@Captain said in Do this maths. It R Hard.:
This leads to more engaged mathematics learners, instead of rote learners and math/logic-phobics.
There's no real evidence this is true with Common Core. If anything, like New Math, it seems to do the exact opposite.
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@boomzilla said in Do this maths. It R Hard.:
After repetition, some understanding begins to dawn and ideally you really understand it and can see how it relates to other stuff.
Amen. In HS, I wound up studying physics and calculus at the same time. Up to that point, math had gotten boring--although I was good at it--because there was no real worldly context for it. Until one day we started to learn the power rule and the stuff that leads up to it in math, in the same week we started learning the relationship between distance, velocity, and acceleration in physics. I had a literal Eureka moment as it all came together for me.
Common Core teaching is so backwards that I bet it's going to cause a lot fewer people to hang on long enough to have the potential for that.
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@Captain Could you explain what is the suggested algorithm in the picture? I would like to understand it, but the contrived form of the task (algorithm+error) makes it hard to recover the proper algorithm.
expressions like 2 + 4 are interpreted as sequences of instructions
Haven't they always been teaching like this? "You have N apples, then you are given M apples, now you have N+M apples"
An interesting approach to view this as a programming API.On the other hand, I noticed that many notions in math are best understood as 2 objects being the same thing.
Equations: 2+x = 4 IS 4+x=6 IS x=2
Rational numbers: a/b IS 2a/2b IS Na/Nb
Algebra: matrix IS a linear function
Thinking of it this way is not easy, but it helps understanding. Probably because a lot of math progress looks like: "i have a solution for A. I can prove problem B is equivalent A, let's use the method for A".So can we express those ideas in the programmatic "procedural" way?
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Simplifying fractions by cancelling, made easy:
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@da-Doctah
$\frac{21}{16}\neq\frac{2}{6}$
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@Adynathos said in Do this maths. It R Hard.:
Could you explain what is the suggested algorithm in the picture?
Subtract 316 from 427. Start at 427. Subtract 100 three times. Subtract 10 once. Subtract 1 six times. Draw a big fucking diagram and label all the numbers. The number at the end is the answer:
So to work the problem as instructed, "write a letter to Jack telling him what he did right, and what he should do to fix his mistake":
"Dear Jack, you got three 100s and 6 ones in 316, but you fucking forgot the 10 you little waste of ectoplasm and it would've been fucking obvious if you'd just done the nice simple little diagram instead of that fucking atrocity."
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@anotherusername Thanks, I thought the algorithm was "how much do I have to move from 316 to arrive at 427", now I see.
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@anotherusername said in Do this maths. It R Hard.:
So to work the problem as instructed, "write a letter to Jack telling him what he did right, and what he should do to fix his mistake":
Dear Jack,
You did nothing right, but that's not your fault; the fault lies entirely with the truly fucking retarded method you were taught. To avoid this mistake in future, you should use the method that has served humanity well for hundreds of years, takes just a few seconds, and doesn't use a fucking mile of paper for what is, let's be honest, the second simplest mathematical operation there is.
Yours,
Someone who was taught maths properly.
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You know what? I theorize common core is actually a hidden measure to bring equality to students.
Think about it. Normally, some children receive help understanding maths from parents, guardians, etc, which gives them an advantage over children who have to make do with the teacher alone.
Because nobody actually understands common core, this unfairness is removed - everyone has to learn from the teacher alone, and thus everyone gets an equal fair chance to learn maths.
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@PleegWat
In soviet math class, algorithm teaches you!
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@Adynathos said in Do this maths. It R Hard.:
@anotherusername Thanks, I thought the algorithm was "how much do I have to move from 316 to arrive at 427", now I see.
The dad trying to label the 1s jumps as 10s to make sense of it was wrong, and made it really confusing. If you recognize that they were supposed to be 1s instead of 10s and ignore his numbers, it becomes ... slightly ... easier to understand.
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@anotherusername Now that I know what they are doing, the algorithm is trivial.
I remember the "number line" exercises in elementary school, but we mostly used them for inequalities: "mark x such that x > A", "mark y such that y < B", "intersect to get conjunction".
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I don't know anything about common core. Not even sure if there's an equivalent being taught in English schools at the moment. But I do know that the current way maths is taught is hideously inneffective for a huge number of kids. It leads to people thinking maths is some esoteric magic that they just don't understand, switching off and not listening whenever anything slightly mathematical comes up in their lives
I doubt that common core is evidence based. Precious little teaching ever is. But it's an attempt at a different way of engaging kids and the main complaint I've seen about it is "that ain't the way I learned maths and it ain't the way ma pappa learned maths so it's wrong and evil". If my daughter has some new way of being taught when she starts school I'll look into the methods so I understand enough to help her, and go along with that unless she's having trouble, at which point I'll try other methods.
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@PleegWat said in Do this maths. It R Hard.:
You know what? I theorize common core is actually a hidden measure to bring equality to students.
Yep. Fucking over the smart students so they'll be as awful at math as the idiots. Glad I don't live in a common core state.
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@PleegWat said in Do this maths. It R Hard.:
@da-Doctah
$\frac{21}{16}\neq\frac{2}{6}$You kiss your mother with that mouth?
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@anotherusername said in Do this maths. It R Hard.:
Subtract 316 from 427. Start at 427. Subtract 100 three times. Subtract 10 once. Subtract 1 six times.
Oh, so Common Core subtraction is like regular column subtraction, except backwards... (or rather, forwards)?
Anyway, back on topic. This math. It be hard.
Calculate the black area.
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@algorythmics The answer is that Cheryl is trying to be a Special Snowflake and you don't get her anything for her birthday.
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@Maciejasjmj total area 400, circle area 20pi. Subtract and halve
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@Jaloopa You're missing that white nub in the lower-left corner.
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@Maciejasjmj ah, shit. Need some truth to work out the chords then I guess
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I wish I had one of the partial differential proofs I used to do (without using complex mathematics) it like is copy and pasting 800 line code that you kinda worked out once before and sticking it function and then never fucking changing it because you don't understand it anymore.
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@Jaloopa said in Do this maths. It R Hard.:
total area 400
Nope
@Jaloopa said in Do this maths. It R Hard.:
circle area 20pi
Also nope.
You seem to be suffering from caffeine withdrawal. :)
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@Maciejasjmj I was expecting a "nice" result, but if I calculated correctly, the result is pretty ugly.
Solution.
3/4 * (100 - 25π) + 25 - 12.5π + 12.5 * (α - sin(α))
α = π - 2 * atan(0.5)
I could try to simplify the formula, but it would still be ugly.
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- total area = (10 * 20) = 200
- area of circles = 2* pi * 25 = 50 pi
- total area of negative circles = 200 - 50pi
- total are of complete black areas = 3 / 8 * (200 - 50pi)
now the last bit is a bit harder.
The top right and where the circles met make a right angled triangle.
The right angled triangle area in back is
(50 - (5pi / 2)) - (1/8 * (200 - 50pi))
So if someone can simplify that for me that would be great.
EDIT:
3 / 8 * (200 - 50pi) - (50 - (5pi / 2)) - (1/8 * (200 - 50pi))
2 / 8 * (200 - 50pi) - (50 - (5pi / 2))
16 * (200 - 50pi) - (100 - 5p )
16 * (100 - 45 pi)
100 - 45pi
ERR I dunno now.
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@lucas1 said in Do this maths. It R Hard.:
The right angled triangle area in back is
(50 - (5pi / 2)) - (1/8 * (200 - 50pi)You sure? That looks different from my solution. The remaining black area is the area of the small triangle (25) - half a circle (12.5π) + area of the sector (12.5 * (α - sin(α))).
Edit: Removed incorrect π. Additional explanation for the angle: If you see the triangle in the top right, you'll also immediately see that the angle of the circle sector in the top right is 180 degrees (π) minus two times the bottom left angle of the big triangle, which is atan(10 / 20).
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@asdf no I am not. I haven't done this shit in like 16 years.
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@asdf argh fuck it you are probably right, I didn't take into account the angle between the racial divide.
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@asdf Yeah I just worked out the other 1/8 again, I thought the numbers were a bit too nice.
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@lucas1 said in Do this maths. It R Hard.:
I didn't take into account the angle between the racial divide.
Which is why brexit won?
