1050: "Forgot Algebra"

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Jaywalk3r
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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Mon May 07, 2012 8:16 pm UTC

Marlayna wrote:Unless your chosen profession involves math, when was the last time you had to take a logarithm, or solve a system of linear equations, or use a trigonometric identity?


As quick examples, carpenters often use the 3 4 5 rule, which is just a special case of the Pythagorean identity (trigonometry). Roofers have to understand rise over run, which is the derivative of a linear equation (differential calculus). Most everyone who uses money uses algebra. Anyone who keeps a checking account balanced certainly uses algebra. Anyone who ever adjusts recipes to make a more appropriate number of servings uses algebra. Heck, one cannot add two and two without using algebra.

Just because most people never sit down an work a bunch of math problems in their adult lives like they had to do in school does not mean they don't use math on a regular basis. There's a big difference between learning math and using math.

mric
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Re: 1050: "Forgot Algebra"

Postby mric » Mon May 07, 2012 9:20 pm UTC

Jaywalk3r wrote:
Marlayna wrote:Unless your chosen profession involves math, when was the last time you had to take a logarithm, or solve a system of linear equations, or use a trigonometric identity?


As quick examples, carpenters often use the 3 4 5 rule, which is just a special case of the Pythagorean identity (trigonometry). Roofers have to understand rise over run, which is the derivative of a linear equation (differential calculus). Most everyone who uses money uses algebra. Anyone who keeps a checking account balanced certainly uses algebra. Anyone who ever adjusts recipes to make a more appropriate number of servings uses algebra. Heck, one cannot add two and two without using algebra.

Just because most people never sit down an work a bunch of math problems in their adult lives like they had to do in school does not mean they don't use math on a regular basis. There's a big difference between learning math and using math.

No, those are all examples of people not using algebra. The 3 4 5 rule exists precisely to avoid using Pythagoras' theory. Remarkably, the roofer can understand rise over run without ever having heard of differential calculus. Finding a ratio (roughly two thirds, say) and applying it in cooking is only algebra in a trivial and irrelevant sense.

Is your last sentence saying that people can use maths without learning it, that the roofer is using differential calculus despite never having learnt it? If so, I think you are wilfully misunderstanding the sense of the word 'use' here (or perhaps wilfully misunderstanding the word 'math').

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Re: 1050: "Forgot Algebra"

Postby cjmcjmcjmcjm » Mon May 07, 2012 9:58 pm UTC

For everyone complaining about how 7 is a bitch for arithmetic, there is a rule to determine if a number is divisible by seven. I'm not entirely sure how it works, but it is:[list=][*]Separate the last digit from the rest of the number ex: 9|2, 4|2
[*]Double the last digit
[*]If the result is divisible by 7, the number is divisible by 7 9-4=5; 94 is not divisible by 7. 4-4=0; 42 is divisible by 7[/list]

There is also a method for divisibility by 11 that involves adding and subtracting alternate digits, but I can't remember it.
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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Tue May 08, 2012 3:20 am UTC

mric wrote:
Jaywalk3r wrote:
Marlayna wrote:Unless your chosen profession involves math, when was the last time you had to take a logarithm, or solve a system of linear equations, or use a trigonometric identity?


As quick examples, carpenters often use the 3 4 5 rule, which is just a special case of the Pythagorean identity (trigonometry). Roofers have to understand rise over run, which is the derivative of a linear equation (differential calculus). Most everyone who uses money uses algebra. Anyone who keeps a checking account balanced certainly uses algebra. Anyone who ever adjusts recipes to make a more appropriate number of servings uses algebra. Heck, one cannot add two and two without using algebra.

Just because most people never sit down an work a bunch of math problems in their adult lives like they had to do in school does not mean they don't use math on a regular basis. There's a big difference between learning math and using math.

No, those are all examples of people not using algebra. The 3 4 5 rule exists precisely to avoid using Pythagoras' theory. Remarkably, the roofer can understand rise over run without ever having heard of differential calculus. Finding a ratio (roughly two thirds, say) and applying it in cooking is only algebra in a trivial and irrelevant sense.

Is your last sentence saying that people can use maths without learning it, that the roofer is using differential calculus despite never having learnt it? If so, I think you are wilfully misunderstanding the sense of the word 'use' here (or perhaps wilfully misunderstanding the word 'math').


Are you serious? The carpenter absolutely uses a special case of the Pythagorean identity when he uses the 3 4 5 rule. That he may not realize that it's the Pythagorean identity that he's using doesn't change that fact. The roofer doesn't have to realize that he is using calculus to use it. Just because it was learned in isolation, outside of a classroom, doesn't make calculating the slope of a line any less an example of taking a derivative.

Finding a ratio is no more trivial than many other aspects of algebra. I once had a Mechanics professor who explained that arithmetic was algebra. I took him at his word, but I never fully understood his point until I took Introduction to Abstract Algebra. At that point I finally realized that, except for Geometry and Trigonometry, nearly all of the math I had learned from kindergarten until I began Calculus I had been algebra. Apparently Algebra must be somewhat important, or I wouldn't have had to take thirteen years of it before being allowed to enroll in the calculus sequence. The only reason some of the algebra we've learned seems trivial is that we've been doing it for so long and we easily see their applications in our lives and the world around us; performing the operations feels second nature.

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Re: 1050: "Forgot Algebra"

Postby mric » Tue May 08, 2012 5:20 am UTC

Jaywalk3r wrote:Are you serious? The carpenter absolutely uses a special case of the Pythagorean identity when he uses the 3 4 5 rule. That he may not realize that it's the Pythagorean identity that he's using doesn't change that fact. The roofer doesn't have to realize that he is using calculus to use it. Just because it was learned in isolation, outside of a classroom, doesn't make calculating the slope of a line any less an example of taking a derivative.

Yep, it's the word 'use' you don't understand here.

Jaywalk3r
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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Tue May 08, 2012 5:37 am UTC

mric wrote:Yep, it's the word 'use' you don't understand here.


I understand the word 'use' perfectly, though I'm not sure that you do. Full and complete knowledge is not required for something to be used.

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Re: 1050: "Forgot Algebra"

Postby HungryHobo » Tue May 08, 2012 8:43 am UTC

Jaywalk3r wrote:As quick examples, carpenters often use the 3 4 5 rule, which is just a special case of the Pythagorean identity (trigonometry). Roofers have to understand rise over run, which is the derivative of a linear equation (differential calculus). Most everyone who uses money uses algebra. Anyone who keeps a checking account balanced certainly uses algebra. Anyone who ever adjusts recipes to make a more appropriate number of servings uses algebra. Heck, one cannot add two and two without using algebra.

Just because most people never sit down an work a bunch of math problems in their adult lives like they had to do in school does not mean they don't use math on a regular basis. There's a big difference between learning math and using math.


You didn't even read the topic did you?

You don't have to know anything whatsoever about trigonometry to simply use the 3 4 5 rule.
Someone who has never heard of trigonometry can use it. someone who has no idea what sin cos or tan means can use it.
they are not using trigonometry.

rise over run may be a derivative of a linear equation but you don't have to actually do any differential calculus.

Most everyone who uses money uses addition, subtraction, multiplication and division. not algebra.

Anyone who keeps a checking account balanced certainly usesuses addition, subtraction, multiplication and division. not algebra.

unless you redefine what they're doing in some convoluted way. people can and do handle those tasks even if they've never heard of algebra.

Anyone who ever adjusts recipes to make a more appropriate number of servings uses multiplication and division. not algebra.

Heck, one cannot add two and two without using addition or multiplication.


lots of people use basic arithmetic.
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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Tue May 08, 2012 3:36 pm UTC

HungryHobo wrote:You don't have to know anything whatsoever about trigonometry to simply use the 3 4 5 rule.
Someone who has never heard of trigonometry can use it. someone who has no idea what sin cos or tan means can use it.
they are not using trigonometry.


Knowing the 3 4 5 rule implies some knowledge of trigonometry, because the 3 4 5 rule is trigonometry. That it is often learned in the context of carpentry doesn't change that any.

rise over run may be a derivative of a linear equation but you don't have to actually do any differential calculus.


Yes, you're doing calculus, even if it wasn't learned as such. Math that ordinary people use in the real world often comes without intimidating labels. That doesn't mean the label are inapplicable; it means that they aren't essential for doing the math.

Most everyone who uses money uses addition, subtraction, multiplication and division. not algebra. Anyone who keeps a checking account balanced certainly usesuses addition, subtraction, multiplication and division. not algebra.

unless you redefine what they're doing in some convoluted way. people can and do handle those tasks even if they've never heard of algebra.

Anyone who ever adjusts recipes to make a more appropriate number of servings uses multiplication and division. not algebra.

lots of people use basic arithmetic.


Performing addition, subtraction, multiplication, and division operations on the real numbers is algebra. Arithmetic may sound less intimidating, but, make no mistake, arithmetic is algebra. Not knowing that fact doesn't mean that people aren't doing algebra when they perform arithmetic.

My niece, in second grade, is learning algebra in school. It's exactly the same math I learned at her age. Where I saw problems such as 5 + 3 = ___ , she sees them as 5 + 3 = x. Presumably, they are teaching the students this way instead of perpetuating the artificial distinction between arithmetic and algebra so that students will become comfortable with letters being used as variables. All too often, people become intimidated when they see letters in their math, because they don't realize that it's no different from the "basic arithmetic" they are used to doing. It's the addition, subtraction, multiplication, and division operations that make it algebra, not the variables.

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Re: 1050: "Forgot Algebra"

Postby HungryHobo » Tue May 08, 2012 3:48 pm UTC

Jaywalk3r wrote:Knowing the 3 4 5 rule implies some knowledge of trigonometry


No it does not any more than driving a car implies some knowledge of oil drilling.
It implies that someone, somewhere, had to have that knowledge but th individual doesn't need it at all.

Yes, you're doing calculus, even if it wasn't learned as such.


again, no, not unless you radically redefine "doing calculus"

you look up 1 in 20 in a table.
You're no more "doing calculus" than someone reading a history book is doing archaeology.

Jaywalk3r wrote:It's the addition, subtraction, multiplication, and division operations that make it algebra, not the variables.


No. just no.


al·ge·bra/ˈaljəbrə/Noun:

1.The part of mathematics in which letters and other symbols are used to represent numbers and quantities in formulae and equations.


it is not the the addition, subtraction, multiplication, and division operations that make it algebra.

it's the variables

Without those it's not algebra.

no matter how much you want it to be it's not algebra.

the step to algebra may be small- the addition of letters and other symbols to represent numbers and quantities - but without that addition it simply is not algebra.



This, what is it about this is the kind of desperate, pleading desire some people seem to have, this insatiable need to redefine everything as math.
There's lots of uses of math, there's lots of professions in which the various advanced forms of math have lots of uses. Math even has it's own value and it's own beauty beyond what it can actually be used for.

yet for the vast vast majority of the population all they'll ever need is addition, subtraction, multiplication and division. indeed those 4 are exceptionally useful to the majority yet instead of getting people really good at those basics there seems to be people who feel some kind of perverse compulsion to inflict effectively useless material on that majority and apparently it's not enough for them to merely do that but they also have to justify it to themselves by redefining everthing, even that which would be far better handled with basic arithmetic in terms of more advanced math.
Last edited by HungryHobo on Tue May 08, 2012 4:07 pm UTC, edited 1 time in total.
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Re: 1050: "Forgot Algebra"

Postby Роберт » Tue May 08, 2012 3:59 pm UTC

HungryHobo wrote:the step to algebra may be small- the addition of letters and other symbols to represent numbers and quantities - but without that addition it simply is not algebra.

I'd argue that whether the symbol used is an x or just a blank underline ________ it's algebra.

It's not the fact that the variable is an x that makes it algebra, if the variable is a question mark it's still algebra.
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Re: 1050: "Forgot Algebra"

Postby HungryHobo » Tue May 08, 2012 4:16 pm UTC

Роберт wrote:I'd argue that whether the symbol used is an x or just a blank underline ________ it's algebra.

It's not the fact that the variable is an x that makes it algebra, if the variable is a question mark it's still algebra.


Blank is not a symbol.

algebra only gains any use as algebra when there's more than one unknown. and while it's perfectly valid to have an expression with a blank ____ that is not the same as ____ being a symbol.

____ is not a symbol

Simple (dis)proof

a != a

is a contradiction but

____ != ____

is not.

You're reaching. you're desperatly trying to redefine everything as algebra but it's foolish and it's just not the case.

algebra is perfectly fine on it's own, it doesn't need you pretending that all forms of calculation are algebra.
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Re: 1050: "Forgot Algebra"

Postby Роберт » Tue May 08, 2012 4:32 pm UTC

HungryHobo wrote:You're reaching. you're desperately trying to redefine everything as algebra but it's foolish and it's just not the case.
I'm not, actually. Perhaps you have me confused with someone else?
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Re: 1050: "Forgot Algebra"

Postby Nic » Tue May 08, 2012 5:30 pm UTC

I'm with Po6ept so far that arithmetic is a subset of algebra. You have a very specific ground field in mind, and the vanilla operations of addition and multiplication are being performed over them. But for the sake of comparison, the integers are a subset of the real numbers, and solving [imath]x^3+y^3=z^3[/imath] over the reals is nothing like solving over the integers. Similarly, if you're only allowed constants on one side of the equation and you're required to have the unknown by itself on the other, then there will be a large class of practical problems which you will be unable to solve. More importantly, the problems you can solve are more complicated, take far longer to set up, and the setup would rely on rote memorization.

Frinstance, people were making the same distinction when that question was posed five pages ago. Someone brought up an example "I go to the store with two dollars and broccoli is 39c a pound. How many pounds can I buy?" You would let the number of pounds be the unknown, and then number of pounds, times the money you pay per pound, equals the total money. Once you have (#pounds)*(price per pound)=(money) you can plug in .39, X, and 2 to find the answer. The rebuttal was "the answer's just 2/.39 so it's arithmetic." Sure that's the answer, but how did you get it? Everybody here, even the ones complaining, all know how to do algebra at an automatic level for something this simple, so you don't have a conception of what life would be like without it.
Last edited by Nic on Tue May 08, 2012 5:51 pm UTC, edited 1 time in total.

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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Tue May 08, 2012 5:32 pm UTC

HungryHobo wrote:
Jaywalk3r wrote:It's the addition, subtraction, multiplication, and division operations that make it algebra, not the variables.


No. just no.


al·ge·bra/ˈaljəbrə/Noun:

1.The part of mathematics in which letters and other symbols are used to represent numbers and quantities in formulae and equations.


it is not the the addition, subtraction, multiplication, and division operations that make it algebra.

it's the variables

Without those it's not algebra.

no matter how much you want it to be it's not algebra.

the step to algebra may be small- the addition of letters and other symbols to represent numbers and quantities - but without that addition it simply is not algebra.


Yes, it is algebra. No matter how much you wish it wasn't. The definition of algebra that you posted is neither formal nor complete.

A more formal, accurate definition:
"An algebraic system is an ordered pair (A,O), where A is a set, called the underlying set of the algebraic system, and O is a set, called the operator set, of finitary operations on A.
We usually write A, instead of (A,O) , for brevity."
Note: "An algebraic system is also called an algebra for short."
(Cite: Chi Woo, Raymond Puzio, J. Pahikkala, yark. "algebraic system" (version 47). PlanetMath.org. Freely available at http://planetmath.org/AlgebraicSystem.html)

Now, let A = ℝ and O = {0, 1, -, +, ⁻¹, ·}, where ℝ is the set of real numbers, 0 is the additive identity, 1 is the multiplicative identity, - is the unary additive inverse, + is the binary addition operator, ⁻¹ is the unary multiplicative inverse, and · is the binary multiplication operator. This is an algebraic field. This ordered pair of sets (or an ordered pair of special subsets of these sets) is required for arithmetic. We can't perform 1 + 1 without it. Of course, we don't need to teach young elementary students all of the formalities of this algebraic field. It is sufficient to teach them how to perform the algebraic operations. Of course, even though they don't know it, they are still working with an algebraic field; even as they do simple sums they are doing algebra.

I can't help but feel a perverse joy knowing that I am the one who let you in on the dirty little secret, that your teachers tricked you into learning algebra without you realizing it. Morever, you use algebra often!
Last edited by Jaywalk3r on Tue May 08, 2012 7:30 pm UTC, edited 3 times in total.

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Re: 1050: "Forgot Algebra"

Postby goomba25 » Tue May 08, 2012 5:49 pm UTC

Jaywalk3r wrote:
rise over run may be a derivative of a linear equation but you don't have to actually do any differential calculus.


Yes, you're doing calculus, even if it wasn't learned as such. Math that ordinary people use in the real world often comes without intimidating labels. That doesn't mean the label are inapplicable; it means that they aren't essential for doing the math.


You seem to be arguing that because the slope is technically defined in differential calculus with a limit that algebra/arithmetic is an extension of calculus. That is valid, but it is also backward, both in common understanding and in historical context. Most of the students who take their first calculus course struggle to make the leap between slope/area of linear shapes and derivative/integral of curvy shapes because the methods sound so different as to be unrecognizable.

Early math: find the length and width of this box. Multiply them together and you have the area.
Calculus: Set the box on an x-y axis. Find the length of this box. Cut up the box into infinitely many pieces and find the width of each piece. Add them together to find the area of the box. Subtract any area below the x-axis, unless you're differentiating with respect to y.

In this case, early math is just a special case of calculus, where people can get away with using a simpler method to accomplish the same thing. Sure, you could integrate the area of the box instead of multiplying length and width. You could also drive backwards all day. It's certainly possible, but unless you need to, why would you? When you want to find the area of a sphere, do you use the formula? Or do you picture a 2-D shape, rotate it 360 degrees and integrate the disk with respect to y?

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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Tue May 08, 2012 6:25 pm UTC

goomba25 wrote:You seem to be arguing that because the slope is technically defined in differential calculus with a limit that algebra/arithmetic is an extension of calculus.


No. I'm asserting that just because a particular procedure from calculus (or trigonometry, etc.) is learned informally outside of the context of mathematics does not make it any less calculus (or trig, etc.). Most roofers probably don't have any need to know the formal definition of a derivative, but calculating the derivative of a line defined by two given points is very useful, so they know how to do that. In the real world, lots of mathematical properties and procedures are learned in isolation. Those properties and procedures aren't then excluded from the area of mathematics from which they came just because someone uses them without understanding their mathematical context.

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Re: 1050: "Forgot Algebra"

Postby Adam H » Tue May 08, 2012 7:28 pm UTC

Rather than asking "How often do I use higher math in my daily life?" I think a better question would be "Is my life better because I took higher math?" You are fooling yourself if you think the answer is no (I don't think anyone here would say that). While I don't do calculus problems anymore, I think about calculus daily and my life is richer for it.

We are probably just generally incapable of separating our general knowledge with what we learned in each of our different classes, with the exception of trivia. Math has very little trivia, so it gets picked on the most.


Oh, and memorizing multiplication tables is about the most useful thing I've ever done. Pro-tip: 56=7*8. 56=7*8... It's the easiest one there is!
-Adam

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Re: 1050: "Forgot Algebra"

Postby goomba25 » Tue May 08, 2012 7:50 pm UTC

Adam H wrote:Rather than asking "How often do I use higher math in my daily life?" I think a better question would be "Is my life better because I took higher math?" You are fooling yourself if you think the answer is no (I don't think anyone here would say that). While I don't do calculus problems anymore, I think about calculus daily and my life is richer for it.


I've taken calculus 7 times (not 8 as I earlier said, I dropped one early on). I've had good professors and bad professors. I've taken lectures in small groups of a dozen and in lectures halls of 400. I've taken the classes at both local community colleges and a top 25 institution. I've had outstanding TAs, apathetic TAs, and TAs who could barely speak English. After I got a D- by skipping half the semester, I got a D after doing every other odd problem in the book. In all of those scenarios, I was never able to earn anything above a C except for the times when a pro-active TA dragged me through the class. I threw everything I had at that class, and all I did was waste energy and notebook paper.

The only thing that I learned from calculus was that my best wasn't good enough. Trust me, I already knew that! Every math class from 1+1 to trigonometry had already drummed that lesson into my head. I wasn't naive. I didn't have a choice in what math class I could take. I knew it was going to be hard. For goodness's sake, I just wanted a pair of C's! Instead, I faced off against classrooms where 95% (an estimate by the tutoring center) had already taken the subject before, whereas I went in nearly blind. In hindsight, the result was inevitable.

"Is my life better because I took higher math?" Calculus poisoned my first 2 years of college, turning what should have been a hard but necessary struggle into something worthy of Moby Dick. Maybe calculus taught me a lesson: knowing when to give up. Tell me, is that a lesson worth learning?

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Re: 1050: "Forgot Algebra"

Postby Adam H » Tue May 08, 2012 8:12 pm UTC

1) That's a sad story. :(
2) OK, let's try this "Is my life better because I took know higher math?"
3) Your experience could have happened with any subject.
-Adam

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Re: 1050: "Forgot Algebra"

Postby mric » Tue May 08, 2012 8:14 pm UTC

Jaywalk3r wrote:
goomba25 wrote:You seem to be arguing that because the slope is technically defined in differential calculus with a limit that algebra/arithmetic is an extension of calculus.


No. I'm asserting that just because a particular procedure from calculus (or trigonometry, etc.) is learned informally outside of the context of mathematics does not make it any less calculus (or trig, etc.). Most roofers probably don't have any need to know the formal definition of a derivative, but calculating the derivative of a line defined by two given points is very useful, so they know how to do that. In the real world, lots of mathematical properties and procedures are learned in isolation. Those properties and procedures aren't then excluded from the area of mathematics from which they came just because someone uses them without understanding their mathematical context.

But the fact that the procedures aren't what people learnt in school means that what they learnt in school isn't what they use. So, to the extent that the protagonist in the comic is saying "I didn't use what you taught me" to the teacher, they may be right. The proposition that they are using something that is formally related to the thing they studied doesn't mean that they used the thing they studied - it is a coincidence, and irrelevant to the situation in the comic.

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Re: 1050: "Forgot Algebra"

Postby goomba25 » Tue May 08, 2012 8:32 pm UTC

Adam H wrote:2) OK, let's try this "Is my life better because I took know higher math?"

Still no. Not only does my field not use it at all, I believe that a vast majority of its members aren't even aware that it underlies many of the formulas and tools that are used because that level of understanding is simply unnecessary. The only thing from calculus that's proved to be even remotely useful was using power rule and reverse power rule to switch between the kinematic equations in physics class. I can't even say that Epsilon-Delta proofs and proving convergence/divergence of series made me think more clearly, because I plugged-and-chugged without actually thinking.

1 instance in the 7 years since my first encounter. I could've mastered power rule myself in 1 hour, and I would been able to skip the infinitely useless drecks that were the formal definition of a derivative and Riemann sums. "We just spent 2-3 weeks learning to do it the hard way! Now that you've mastered the concepts, let's throw that all out and use a much simpler shortcut that only requires arithmetic!"

Adam H wrote:3) Your experience could have happened with any subject.

Absolutely, and if had happened in another subject, say biology or history, I wouldn't be on this message board because the original comic was about math, and because the threads in this forum have mostly revolved around math.

Again, I have no problem with people saying they excel at math, or that they find it fun, or that they specifically use it in their lives. That's their thing, and I'm OK with that. Grudgingly, I'll admit that our world _is_ better off with calculus than without. But that doesn't explain why I had to learn it to the depth that I did, and it still doesn't excuse the fact that I had to take engineer-level calculus to stay in my major.

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Re: 1050: "Forgot Algebra"

Postby J Thomas » Tue May 08, 2012 8:44 pm UTC

goomba25 wrote:I've taken calculus 7 times (not 8 as I earlier said, I dropped one early on). I've had good professors and bad professors. I've taken lectures in small groups of a dozen and in lectures halls of 400. I've taken the classes at both local community colleges and a top 25 institution. I've had outstanding TAs, apathetic TAs, and TAs who could barely speak English. After I got a D- by skipping half the semester, I got a D after doing every other odd problem in the book. In all of those scenarios, I was never able to earn anything above a C except for the times when a pro-active TA dragged me through the class. I threw everything I had at that class, and all I did was waste energy and notebook paper.

The only thing that I learned from calculus was that my best wasn't good enough. Trust me, I already knew that! Every math class from 1+1 to trigonometry had already drummed that lesson into my head. I wasn't naive. I didn't have a choice in what math class I could take. I knew it was going to be hard. For goodness's sake, I just wanted a pair of C's! Instead, I faced off against classrooms where 95% (an estimate by the tutoring center) had already taken the subject before, whereas I went in nearly blind. In hindsight, the result was inevitable.

"Is my life better because I took higher math?" Calculus poisoned my first 2 years of college, turning what should have been a hard but necessary struggle into something worthy of Moby Dick. Maybe calculus taught me a lesson: knowing when to give up. Tell me, is that a lesson worth learning?


It's possible that you have some sort of organic brain disfunction that makes it hard for you to learn calculus. Things that other people see instinctively, you would need to apply tedious workarounds for.

But likely not. Math is kind of like an upside-down pyramid. You start with the little sharp base at the bottom, and you build on top of that wider and higher. If you miss something basic, then none of the things that are supposed to be built on top of the missing piece will fit.

If you got sick and missed a week of class in first grade, and you never really got that material straight later, then you'll be crippled at all the math that needs that stuff. None of it will work until you go back and learn the missing piece.

If you miss a week of english literature and don't fill it in, it won't hurt you that much. "Byron? Don Byron is OK, but there are better jazz musicians." It leaves a hole. If you miss a week of math you lose everything that gets built over that hole.

So if it doesn't make sense, you go back to something earlier, and see if that makes sense. And you go back until you get to the first thing you don't quite understand, and figure it out. After you get it, it will look easy. The math that gets taught a lot is designed that way -- it's all supposed to be small easy steps. When for any reason a step isn't easy, it looks real real hard because you don't understand it. After you get it, you find out that all the hard stuff was ideas in your head for what it might be. The reality was simple and easy.

All the people who gave you the idea you weren't any good at it? They just psyched you out. All of it including calculus is simple and easy if you do it in the right order and you don't skip any steps. Unless perhaps you do have organic brain damage; that makes it harder.

Is it worth doing? It provides a way to see the world that you probably didn't have before. That can be useful sometimes. You can use that sense of things to communicate with other people who have it. Sometimes it makes it easier to solve some kinds of problems. But our society has been carefully designed so you won't actually need it. Just get a job and figure out what they want you to do and do it. Watch the ads on TV and do what they say. Avoid credit card debt and get expert advice if you get a mortgage. You can expect average results.
The Law of Fives is true. I see it everywhere I look for it.

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Re: 1050: "Forgot Algebra"

Postby mric » Tue May 08, 2012 9:01 pm UTC

J Thomas wrote:So if it doesn't make sense, you go back to something earlier, and see if that makes sense. And you go back until you get to the first thing you don't quite understand, and figure it out. After you get it, it will look easy. The math that gets taught a lot is designed that way -- it's all supposed to be small easy steps. When for any reason a step isn't easy, it looks real real hard because you don't understand it. After you get it, you find out that all the hard stuff was ideas in your head for what it might be. The reality was simple and easy.

All the people who gave you the idea you weren't any good at it? They just psyched you out. All of it including calculus is simple and easy if you do it in the right order and you don't skip any steps. Unless perhaps you do have organic brain damage; that makes it harder.

I don't think the evidence supports that view. There is a largish minority of the population who never get even the simplest things in maths. I have a brother for whom the connection between 6x7 and 7x6 remains a mystery, despite significant help with remedial maths. There are no signs of brain damage, and the shape of the graph on maths ability suggest that would be an improbable cause for the bottom end of capability - I would expect a discontinuity in the curve that just isn't present.

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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Tue May 08, 2012 9:03 pm UTC

mric wrote:The proposition that they are using something that is formally related to the thing they studied doesn't mean that they used the thing they studied - it is a coincidence, and irrelevant to the situation in the comic.


That's an interesting straw man argument, but unrelated to my point that trig, calculus, algebra, etc. are commonly used by ordinary people who don't work in fields associated with mathematics.

As has been pointed out previously in the thread, if she (in the comic) was able to calculate how long she had been out of school, that would be sufficient proof that she has not forgotten everything she learned about algebra and has solved an algebraic equation since high school algebra. It could be debated whether or not it's Miss Lenhart's fault that she didn't realize she has, in fact, used algebra since high school, but I have no interest in that debate.

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Re: 1050: "Forgot Algebra"

Postby Adam H » Tue May 08, 2012 9:15 pm UTC

goomba25 wrote:
Adam H wrote:2) OK, let's try this "Is my life better because I took know higher math?"

Still no. Not only does my field not use it at all, I believe that a vast majority of its members aren't even aware that it underlies many of the formulas and tools that are used because that level of understanding is simply unnecessary. The only thing from calculus that's proved to be even remotely useful was using power rule and reverse power rule to switch between the kinematic equations in physics class. I can't even say that Epsilon-Delta proofs and proving convergence/divergence of series made me think more clearly, because I plugged-and-chugged without actually thinking.
OK, but are you an engineer? Or are you a human? (Or are we dancer!) I really do think you are fooling yourself. You would be INCAPABLE of having this discussion without your knowledge of calculus. I suppose ignorance can be bliss but I don't think it is in this case.

Every time I accelerate or brake in a car, I think "heh, the derivative of acceleration is jerk." And every time I throw something into the wind I think "roughly 35 degrees for maximum distance!" And every time someone tries to prove something logically, I think "proof?!? That's no proof!" So while I don't remember any of the stuff you talk about, I still feel better off for learning calculus.
-Adam

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Re: 1050: "Forgot Algebra"

Postby mric » Tue May 08, 2012 9:36 pm UTC

Jaywalk3r wrote:
mric wrote:The proposition that they are using something that is formally related to the thing they studied doesn't mean that they used the thing they studied - it is a coincidence, and irrelevant to the situation in the comic.


That's an interesting straw man argument, but unrelated to my point that trig, calculus, algebra, etc. are commonly used by ordinary people who don't work in fields associated with mathematics.

As has been pointed out previously in the thread, if she (in the comic) was able to calculate how long she had been out of school, that would be sufficient proof that she has not forgotten everything she learned about algebra and has solved an algebraic equation since high school algebra. It could be debated whether or not it's Miss Lenhart's fault that she didn't realize she has, in fact, used algebra since high school, but I have no interest in that debate.

No, it wouldn't be sufficient proof. Had she not attended high school, is it plausible that she could know that her peers had attended high school twenty years earlier? If so, then she would, in your distorted terms, have 'solved an algebraic equation' despite having never been taught algebra. The clue to the fact you know how thin the ice you are on is comes from the clumsy post hoc, ergo propter hoc implied in 'has solved an algebraic equation since high school algebra'.

Jaywalk3r suggests the following syllogism: X uses maths. X was taught maths in school. Therefore X uses the maths they were taught in school.

The only thing I can deduce from that syllogism is that Jaywalk3r was never taught formal logic sufficiently well to avoid repeatedly making simple errors.

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Re: 1050: "Forgot Algebra"

Postby goomba25 » Tue May 08, 2012 9:56 pm UTC

Adam H wrote:OK, but are you an engineer? Or are you a human? (Or are we dancer!) I really do think you are fooling yourself. You would be INCAPABLE of having this discussion without your knowledge of calculus. I suppose ignorance can be bliss but I don't think it is in this case.

If I hadn't been retaking calculus in this past year to appease an admittance committee, I wouldn't be able to use specific terms like "Taylor Inequality". I can assure you that aside from simple ideas, everything was brand new, and I sure didn't remember the phrase "Epsilon-Delta proof". Moreover, after this class, I'm going to do my best to forget all of these again, because fnInt.

And no, I'm not an engineer, so why did I have to learn engineer-level calculus instead of life-science caliber calculus? After I graduated, the department created its own custom calculus class designed for biology majors.
Adam H wrote:And every time I throw something into the wind I think "roughly 35 degrees for maximum distance!"

Why 35 degrees? Shouldn't it be 45 degrees?
Adam H wrote:So while I don't remember any of the stuff you talk about, I still feel better off for learning calculus.

More power to you. Wait, if you don't remember any of the topics I've mentioned, how can you say that you think of calculus daily and that it has enriched your life? I'm not trying to be provocative, but I would like a clarification.

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Re: 1050: "Forgot Algebra"

Postby Adam H » Tue May 08, 2012 10:03 pm UTC

mric wrote:Jaywalk3r suggests the following syllogism: X uses maths. X was taught maths in school. Therefore X uses the maths they were taught in school.

The only thing I can deduce from that syllogism is that Jaywalk3r was never taught formal logic sufficiently well to avoid repeatedly making simple errors.
Well, comic girl says "I forgot everything about algebra the moment I graduated", so she technically isn't talking about the algebra she learned in school. She's including the algebra you can figure out on your own by having an IQ>60.

Also, if I can point out, you are saying that higher math is useful (to avoid repeatedly making simple errors).

goomba25 wrote:
Adam H wrote:And every time I throw something into the wind I think "roughly 35 degrees for maximum distance!"

Why 35 degrees? Shouldn't it be 45 degrees?
Wind resistance. See, I'd win every snowball fight, all thanks to calculus! :D

goomba25 wrote:Wait, if you don't remember any of the topics I've mentioned, how can you say that you think of calculus daily and that it has enriched your life? I'm not trying to be provocative, but I would like a clarification.
Uh... for example:
Adam H wrote:Every time I accelerate or brake in a car, I think "heh, the derivative of acceleration is jerk."
-Adam

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Re: 1050: "Forgot Algebra"

Postby goomba25 » Tue May 08, 2012 11:43 pm UTC

Adam H wrote:
goomba25 wrote:
Adam H wrote:And every time I throw something into the wind I think "roughly 35 degrees for maximum distance!"

Why 35 degrees? Shouldn't it be 45 degrees?
Wind resistance. See, I'd win every snowball fight, all thanks to calculus! :D

You're lucky you're not a physicist: http://www.gocomics.com/foxtrot/2006/01/08

Adam H wrote:
goomba25 wrote:Wait, if you don't remember any of the topics I've mentioned, how can you say that you think of calculus daily and that it has enriched your life? I'm not trying to be provocative, but I would like a clarification.
Uh... for example:
Adam H wrote:Every time I accelerate or brake in a car, I think "heh, the derivative of acceleration is jerk."

Hmm. That's not a way I would have thought of. I pictured scenarios more along the lines of "I see this curvy object and I can integrate that using calculus." To each their own.

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Re: 1050: "Forgot Algebra"

Postby Fat Tony » Tue May 08, 2012 11:47 pm UTC

If I might object: the pride seems less in her having forgotten everything and more in the affirmation of her insistence that she would never have any use for that stuff outside of school, a point that her math teachers/other adults/you guys likely argued against throughout her entire school career. That she would forget all that she "learned" in that class was inevitable; the joy comes from her beliefs being confirmed by the Real World.
If it were pride in her lack of learning, she could have said the same thing to her teacher a month after her final exam rather than years later.
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Re: 1050: "Forgot Algebra"

Postby Mattyboy » Tue May 08, 2012 11:59 pm UTC

If you say using the 345 rule is using trig, you might as well say we're all physicists because we use matter when we walk around.

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Re: 1050: "Forgot Algebra"

Postby J Thomas » Wed May 09, 2012 3:46 am UTC

mric wrote:
J Thomas wrote:So if it doesn't make sense, you go back to something earlier, and see if that makes sense. And you go back until you get to the first thing you don't quite understand, and figure it out. After you get it, it will look easy. The math that gets taught a lot is designed that way -- it's all supposed to be small easy steps. When for any reason a step isn't easy, it looks real real hard because you don't understand it. After you get it, you find out that all the hard stuff was ideas in your head for what it might be. The reality was simple and easy.

All the people who gave you the idea you weren't any good at it? They just psyched you out. All of it including calculus is simple and easy if you do it in the right order and you don't skip any steps. Unless perhaps you do have organic brain damage; that makes it harder.

I don't think the evidence supports that view. There is a largish minority of the population who never get even the simplest things in maths. I have a brother for whom the connection between 6x7 and 7x6 remains a mystery, despite significant help with remedial maths. There are no signs of brain damage, and the shape of the graph on maths ability suggest that would be an improbable cause for the bottom end of capability - I would expect a discontinuity in the curve that just isn't present.


What view does the evidence support? I agree that the largish minority who never get the first thing, is much larger than I'd expect for brain damage.

So I think a giant psych out is the better explanation. People get used to the idea that they're stupid, that they can't learn it, and they don't try. Without understanding the basics they never get anywhere with any of the rest of it.

It's easier to accept that they can't do math than it is to actually find out what they've missed and then play catch-up. And there are plenty of role models who say they can't understand math either and they're doing fine, so don't worry about it.
The Law of Fives is true. I see it everywhere I look for it.

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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Wed May 09, 2012 3:55 am UTC

mric wrote:No, it wouldn't be sufficient proof. Had she not attended high school, is it plausible that she could know that her peers had attended high school twenty years earlier? If so, then she would, in your distorted terms, have 'solved an algebraic equation' despite having never been taught algebra.


Your scenario doesn't satisfy the antecedent of my statement. Further, most kids begin learning algebra in early elementary school with simple sums.


mric wrote:Jaywalk3r suggests the following syllogism: X uses maths. X was taught maths in school. Therefore X uses the maths they were taught in school. The only thing I can deduce from that syllogism is that Jaywalk3r was never taught formal logic sufficiently well to avoid repeatedly making simple errors.


You've missed the point. Simple addition and subtraction is algebra. What is colloquially referred to as arithmetic is, in fact, algebra. Therefore, if one does "arithmetic" after high school, that person does algebra after high school.

You are correct in that I have assumed that she learned to do at least simple addition and subtraction in school prior to taking her high school algebra class. You're right; that assumption is wholly unwarranted. There are probably millions of students across the nation who are enrolled in high school algebra but cannot perform simple addition and subtraction. [sarcasm]I humbly bow to your superior application of logic.[/sarcasm]

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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Wed May 09, 2012 4:44 am UTC

Mattyboy wrote:If you say using the 345 rule is using trig, you might as well say we're all physicists because we use matter when we walk around.


You might have a point if I were claiming that all carpenters were mathematicians simply because they used the 3 4 5 rule, but that's not what I've said. I've said that the 3 4 5 rule is a special case of the Pythagorean identity, which can be easily shown to be true by showing that (3,4,5) is a Pythagorean triple.

3² + 4² = 5²
3·3 + 4·4 = 5²
9 + 16 = 5²
25 = 5²
√(25)·√(25) = 5²
5·5 = 5²
5² = 5²

A carpenter wants to verify that an angle is square. He knows that the special case of the Pythagorean identity holds for right triangles with side lengths 3, 4, and 5. He measures a side of length 3 units and a side of length 4 units. He then measures the distance between the endpoints of those two sides. He knows his angle is square if and only if that distance is 5 units.

It requires a pretty big imagination to rationalize how using the 3 4 5 rule is somehow not using trigonometry. I suspect that a pretty significant portion of carpenters even understand why it works, though they might recite the identity in the form of the Pythagorean theorem, A² + B² = C².

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Re: 1050: "Forgot Algebra"

Postby goomba25 » Wed May 09, 2012 5:12 am UTC

Jaywalk3r wrote:There are probably millions of students across the nation who are enrolled in high school algebra but cannot perform simple addition and subtraction.

Given the horrors I hear about the US education system and the difficulties that high school seniors have in passing exit exams based on 8th grade material, I wouldn't be too surprised if this was true.

At my school district, Algebra was the most drawn out course: pre-Algebra, Algebra 1A/1B, Algebra 1, Algebra 1-Honors, Algebra 2, with students being placed based on their standardized test scores. The first two were designed to be taken in middle school, but were also offered in high school. I'd wager that a small but significant portion of my graduating class earned their diplomas without ever taking Trigonometry.

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Re: 1050: "Forgot Algebra"

Postby Jaywalk3r » Wed May 09, 2012 6:13 am UTC

goomba25 wrote:
Jaywalk3r wrote:There are probably millions of students across the nation who are enrolled in high school algebra but cannot perform simple addition and subtraction.

Given the horrors I hear about the US education system and the difficulties that high school seniors have in passing exit exams based on 8th grade material, I wouldn't be too surprised if this was true.

At my school district, Algebra was the most drawn out course: pre-Algebra, Algebra 1A/1B, Algebra 1, Algebra 1-Honors, Algebra 2, with students being placed based on their standardized test scores. The first two were designed to be taken in middle school, but were also offered in high school. I'd wager that a small but significant portion of my graduating class earned their diplomas without ever taking Trigonometry.


While high school level algebra and trigonometry are very basic maths, they are far more advanced than the simple addition and subtraction to which I was referring, which would have been taught around third or fourth grade.

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Re: 1050: "Forgot Algebra"

Postby HungryHobo » Wed May 09, 2012 8:36 am UTC

Nic wrote: "the answer's just 2/.39 so it's arithmetic." Sure that's the answer, but how did you get it?




BY DIVISION



You have 2 oranges, someone gives you 2 more how many oranges do you have?
2+2=4

that's addition. not algebra.
the mere fact that you can write it in an awkward, unintuitive way as 2+2=x, find x does not make it algebra. it does not require you to know algebra on any level whatsoever

Someone who has never ever heard of algebra in their lives, who has never done any form of algebra, who has never solved for x, has only ever done basic arithmetic can still figure out how many 39 cent items they can get for 2 dollars or how many oranges they will have if they have 2 then someone gives them 2 more.

Yes you absolutely can define it in terms of an algebraic system, you can also define such things with set theory but that doesn't make basic arithmetic set theory.

You're confusing
"X can be defined using Y"
with
"X can ONLY be defined with Y"
or possibly even worse the blatant falsehood:
"You need to understand Y to be good at using X"


Jaywalk3r wrote:I can't help but feel a perverse joy knowing that I am the one who let you in on the dirty little secret, that your teachers tricked you into learning algebra without you realizing it. Morever, you use algebra often!


Again you're merely expressing it as an algebraic system. that doesn't make it algebra nor require you to know algebra on any level, you can express many algebraic problems with calculus, that doesn't make it calculus. you can express most methods of calculation in others in the same way that you can express any programming language in any other, that makes them equivilent but that does not mean that you know haskell just because you know C and a haskell interpreter can be written in C or that you know C just because you know haskell and a haskell intepreter can be written in C (though the one you're actually using may instead be written in, lets say,assembly).

If someone says, "I can't program computers" I don't feel the urge to force them, nor do I feel the urge to turn around and say "well, every time you click a button on a web page you're issuing instructions to a computer so you're really just using a subset of programming" because that would be nothing but inventively thick. true yet not usefuly so in any way shape or form and completly unhelpful.

It would make me into this guy:

http://data.whicdn.com/images/27221588/ ... _thumb.jpg

Everything you do on a computer, from editing a word document to playing pong may be a subset of the tasks possible on a universal turing machine but forcing kids to program universal turning machines will improve neither their word documents nor their ability to play pong and they don't need to know a damned thing about universal turing machines in order to do either well. they're not programming a universal turing machine on an instinctive level or anything else silly like that because they've never heard of one nor learned anything about one. the mere fact that what they're doing can be expressed as opperations on a universal turing machine doesn't change that.

Might people be better off if they learned a little basic scripting? maybe.
Might they be better off if they learned "from the ground up", starting with programming for a turing machine completely disconnected from real world problems?

I don't hate my field enough to force kids to do that.

Adam H wrote:And every time I throw something into the wind I think "roughly 35 degrees for maximum distance!"


You're a remarkable human being. how's your aim? I expect you can throw a football further and more accuratly than the kids who wasted their time merely practicing to throw a football far and on target.

Adam H wrote:Every time I accelerate or brake in a car, I think "heh, the derivative of acceleration is jerk."


And sometimes when I flex my arm I think "heh, ATP transports chemical energy within cells for metabolism"
But that doesn't help with the act in any way. I may be using ATP but I'm not using the knowledge.
you "use" math when you drive the same way you use chemistry to live. (unless you crash a lot)
Last edited by HungryHobo on Wed May 09, 2012 12:20 pm UTC, edited 1 time in total.
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Re: 1050: "Forgot Algebra"

Postby mric » Wed May 09, 2012 10:18 am UTC

Jaywalk3r wrote:You've missed the point. Simple addition and subtraction is algebra. What is colloquially referred to as arithmetic is, in fact, algebra. Therefore, if one does "arithmetic" after high school, that person does algebra after high school.

If that is the substance of your assertion, then it is trivial, and has no impact on the point.

Try this conversation out. "I really love nuts, and eat them every day - pistachios, brazils, cashews and almonds are among my favourites". "No, you don't eat nuts every day, those aren't nuts, they are other fruits.". Has the pedant, correctly pointing out that those 'nuts' don't meet the formal botanical definition, successfully made his point? Or has he shown a willful disregard for ordinary linguistic usage? In particular, has he shown that the first speaker doesn't eat brazils, cashews and almonds?

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Re: 1050: "Forgot Algebra"

Postby eran_rathan » Wed May 09, 2012 12:04 pm UTC

goomba25 wrote:Hmm. That's not a way I would have thought of. I pictured scenarios more along the lines of "I see this curvy object and I can integrate that using calculus." To each their own.


One of my favourite uses involves figuring pressure at the base of dams.
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Re: 1050: "Forgot Algebra"

Postby queueingtheory » Wed May 09, 2012 1:33 pm UTC

Alex-J wrote:Course, many of the kids who whine about learning math are also the ones who do whine about foreign language and fine arts (and school in general).


I loved math. I liked foreign languages (although I didn't work them as much as I should have). I like science. But I whine about arty stuff.

I don't mind the subjects being available to students or everybody having to try them but I think people need to consider that life is finite and you shouldn't make people do things they hate for multiple years unless you can give a damn good reason.


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