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Wolfram Alpha Rekindles Campus Math Tool Debate

Soulskill posted more than 5 years ago | from the why-is-my-calculator-smarter-than-me dept.

Math 339

An anonymous reader sends in a story about how Wolfram Alpha is becoming the latest tool students are using to help with their schoolwork, and why some professors are worried it will interfere with the learning process. Quoting: "The goal of WolframAlpha is to bring high-level mathematics to the masses, by letting users type in problems in plain English and delivering instant results. As a result, some professors say the service poses tough questions for their classroom policies. 'I think this is going to reignite a math war,' said Maria H. Andersen, a mathematics instructor at Muskegon Community College, referring to past debates over the role of graphing calculators in math education. 'Given that there are still pockets of instructors and departments in the US where graphing calculators are still not allowed, some instructors will likely react with resistance (i.e. we still don't change anything) or possibly even with the charge that using WA is cheating.'"

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"Pockets of instructors"? (2, Funny)

Anonymous Coward | more than 5 years ago | (#28315015)

Are they protected?

Re:"Pockets of instructors"? (2, Funny)

Anonymous Coward | more than 5 years ago | (#28315029)

Only if they have tenure.

Re:"Pockets of instructors"? (2)

Profane MuthaFucka (574406) | more than 5 years ago | (#28315793)

I don't have tenure, but if I have two fives, does that count?

Seriously thats what they worry? (1, Informative)

konigstein (966024) | more than 5 years ago | (#28315025)

I'm worried about all these highfallutin complex math equations enabling this thing to evolve into skynet, and these guys are worried that it's going to help people with their homework!?! *adds another layer to tinfoil hat*

iirc (3, Interesting)

langelgjm (860756) | more than 5 years ago | (#28315027)

IIRC, in regular college level calculus I wasn't allowed to use a graphing calculator. This was at a large public research university. I also don't think it would have helped...

Oh the horror!! (2, Funny)

SBrach (1073190) | more than 5 years ago | (#28315059)

How did you play tetris during class?

Re:iirc (4, Interesting)

vux984 (928602) | more than 5 years ago | (#28315169)

IIRC, in regular college level calculus I wasn't allowed to use a graphing calculator. This was at a large public research university. I also don't think it would have helped...

I helped me. It would have caught the silly mistakes I made. Like confirming a function had no zeroes, rather than me wasting time thinking I'd screwed up. or catching that the function was discontinuous in the region I was supposed to take a derivative in, etc.

"Seeing the curve" in general will reveal things about it, like how its roots work, or help you estimate what an integral should work out to, explain why newtons method is flaking out and give you a better starting point, etc.

It makes checking that the limit you worked out is right trivial.

I got hooked on Maple, not for its ability to do my homework, which it could have done, but for its ability to graph and illustrate and help me understand the problems better. Unfortunately, a lot of my classmates used it to just do the homework. Their loss in the long term for the lack of the deeper understanding ... but they still got an A in the class. And sadly, that's actually worth more on a cynical level.

Re:iirc (1)

linzeal (197905) | more than 5 years ago | (#28315423)

Their A's in class will not help them in an actual research position. Research is increasingly becoming the bastion of actual knowledge whilst everyone who gets artificial A's just regurgitates by rote. Try talking to these people about something that requires a bit of mathematical knowledge and watch most of them conceptually fail.

Re:iirc (2, Interesting)

FishWithAHammer (957772) | more than 5 years ago | (#28315707)

Calculus classes aren't just for people going into research fields. In all likelihood they'll "lose" little to nothing.

I've never once used a single scrap from calculus (computer science major).

Re:iirc (3, Insightful)

T Murphy (1054674) | more than 5 years ago | (#28315455)

For the people not in engineering/math/science, I don't see why they need to be deprived a calculator or similar for a calculus class. Either write problems that require the student to understand the material, or consider whether they even need calculus. I enjoyed learning it, but only a math professor has to know how to perform integration by parts by hand. If an introductory calculus course is all that is needed, concepts are more important than being able to perform the operations by hand. Business majors and the like just have to be able to see d$/dx, not freak out, and understand how to maximize $.

Re:iirc (1, Insightful)

Anonymous Coward | more than 5 years ago | (#28315507)

I don't really see how it's possible to not know how to perform a simple integration by parts by hand and still understand the concept behind it, sorry.

I had to learn trig with tables in mid/late-80s (2, Insightful)

Anonymous Coward | more than 5 years ago | (#28315759)

My high school trig teacher made us learn to solve trig problem using just tables. She also made us memorize the easy ones.

In the same school we had to learn to multiply using logarithms from tables and interpolation. We didn't have slide rules.

Only after we learned the theory were we allowed to use calculators.

Teach the skill. Once the skill is mastered let the student use tools.

Re:iirc (1)

0100010001010011 (652467) | more than 5 years ago | (#28315823)

My ODE I & II courses let you use Maple & a Calculator. There were 2 parts to the test. A Maple part and a calculator part.

Every one I tell this to from a different school thinks that the tests must have been the easiest ones in the world, quite the opposite. You actually had to have a grasp of the point of ODEs.

Meaning instead of x''+2x'+x'=y'' x(0)=4, etc
It was "the rate of which the rabbit population changes is based on the rate of the population of wolves. Rabbits breed this fast, wolves breed this fast. Find equilibrium".

I wouldn't have been able to do as well in HS if I didn't have a calculator. I was a very solid B student all because of my dyslexia. All I needed was a basic solar one and I made it through even Calc 100x better. Something about punching numbers in instead of writing them down.

I don't see how this matters (5, Insightful)

InstinctVsLogic (920001) | more than 5 years ago | (#28315033)

Just do what my school does and make assignments worth 10 - 15% and expect some noise. For a lot of professors, assignments are really only meant to keep the student up to date on the material. The students that rely on WolframAlpha will only end up screwing themselves over.

Re:I don't see how this matters (5, Insightful)

The Snowman (116231) | more than 5 years ago | (#28315087)

Just do what my school does and make assignments worth 10 - 15% and expect some noise. For a lot of professors, assignments are really only meant to keep the student up to date on the material. The students that rely on WolframAlpha will only end up screwing themselves over.

I had math and computer science classes where homework was not graded. All course credit came from exams. If you "cheated" on your homework, you came up short on the exam where showing all work was required to receive any credit for a problem. Those are the best types of classes, because it truly tests your ability to solve problems.

Re:I don't see how this matters (2, Funny)

sexconker (1179573) | more than 5 years ago | (#28315117)

No, those are the best types of classes, because no one does any work and everyone tanks the exam, making the curve oh so easy.

Re:I don't see how this matters (0)

Anonymous Coward | more than 5 years ago | (#28315277)

You CS whinies had it easy. For us EEs, the exams came pre-tanked.

Re:I don't see how this matters (4, Funny)

Chris Burke (6130) | more than 5 years ago | (#28315305)

You CS whinies had it easy. For us EEs, the exams came pre-tanked.

Well in my CE department, we came to the exam pre-tanked!

Re:I don't see how this matters (4, Funny)

Anonymous Coward | more than 5 years ago | (#28315685)

In Soviet Russia, tank exams you!

Re:I don't see how this matters (4, Insightful)

Chris Burke (6130) | more than 5 years ago | (#28315289)

Those are the best types of classes, because it truly tests your ability to solve problems.

Ability to solve problems in the limited-time test format.

And I say this as someone who excels at 50 min or 80 min exams, yet would at times feel that one of my peers clearly understood the material as well or better than I did, but did not excel at the exam format and thus received worse course grades.

Since graduating, never in my career have I encountered a situation where I had to solve 25 simple yet unrelated problems in under an hour without the use of references or collaboration. I'm sure it's possible someone has, or could construct a scenario in which they would, but in general I just don't think the ability to do this is necessary to demonstrate competence in your field.

I do agree that exams are important for making sure a student really knows the material themselves, and there's only so much you can do with the format. I don't have a better way of doing things to suggest. I'm just pointing out that exams throw another arbitrary dimension on top of the course material that some people may or may not excel at regardless of how well they know the material and how well they can solve the problems.

Re:I don't see how this matters (2, Informative)

Stiletto (12066) | more than 5 years ago | (#28315367)

Since graduating, never in my career have I encountered a situation where I had to solve 25 simple yet unrelated problems in under an hour without the use of references or collaboration.

So you shouldn't have to know how to solve a given problem yourself, in a vacuum, because in the "real world" we have reference books and other people to collaborate with.

Now, apply that logic to the whole population of potential collaborators / reference book writers.

Everyone now assumes there's someone else to collaborate with. But who? Since anyone you might collaborate with also believes the above, they won't know how to solve the problem either. Who would write the reference books? Same problem.

At some point the buck stops at the individual. You need to know how to solve the given problems, by yourself. That's why we do tests, and that's why you (generally) can't collaborate or consult references.

Re:I don't see how this matters (5, Insightful)

Chris Burke (6130) | more than 5 years ago | (#28315651)

So you shouldn't have to know how to solve a given problem yourself, in a vacuum, because in the "real world" we have reference books and other people to collaborate with.

By yourself, in a vacuum, with no reference books or people to collaborate with, and an arbitrary one-hour time limit, and arbitrarily simplified problems that don't actually represent what you have to solve "in the real world"? Yeah, you shouldn't (hypothetically, like I said I have no better alternative to exams) have to do that because most people -- certainly myself -- don't have to do that in "the real world"! Ever! I've been out of college twice as long as I was in it, and I've never had any challenge at work that was anything like test format.

Now, apply that logic to the whole population of potential collaborators / reference book writers.

Who is it that you think is writing reference books solely from their own memory, without referencing any other books or sources? That's not how it works. And even more outrageously, who is tasked by their publisher to write 10 paragraph-long essays on 10 unrelated subjects with a 1 hour deadline for a technical reference?

Since anyone you might collaborate with also believes the above, they won't know how to solve the problem either.

See, the problem with "apply that logic" type arguments is when you completely fail to properly represent the logic, in this case by excluding most of it. I never said "won't know how to solve the problem", in fact I said the opposite. It is a simple fact that you can know to solve problems, yet not do well on exams.

And since real life isn't your ludicrous strawman of "nobody knows how to solve anything, so who can you collaborate with", collaboration has a wonderful knowledge-multiplying effect. Because if there's something I don't know in order to solve something, but a coworker does, then I can use their knowledge to enhance my own and solve the problem instead of failing.

At some point the buck stops at the individual. You need to know how to solve the given problems, by yourself.

I clearly said "they understood the material as well or better than I did". Like, by themselves. Just they did worse on the test format. I was very specific about what I was talking about. "Knowing how to solve problems by yourself" is not equivalent to "doing well on exams".

Stop being dim Chris (-1, Troll)

Anonymous Coward | more than 5 years ago | (#28315749)

It is difficult to determine who is cheating in course work and who is supplying the most input with team work. At least with an exam there is a test of knowledge and understanding. Little chance to cheat, and no leaning on your fellow team members.

Come on Chris tell the truth. It's your friend who's good at exams and you who understand everything but can't, no matter how much you try, pass the damn things.

It is no wonder the middle of the road conscientious but not too bright are always in support of course work and ever ready to damn exams.

Re:I don't see how this matters (1)

node 3 (115640) | more than 5 years ago | (#28315697)

Why would you apply that to the entire population? Some people are going to be good at taking tests without reference under time constraints and some won't (notice you entirely ignored the time constraint aspect of it). Those that don't need references will write the reference books. Those that do need them will work on projects where they use them.

By your argument, the only people who need to take tests would be the reference book writers and no one else, but it gets worse. One needn't take a test to be capable of writing a reference book without the help of a reference book, one only needs to know things about a subject that aren't currently in a reference book. Taking a test isn't going to help you know things that aren't yet in the books.

Re:I don't see how this matters (1)

Dr Tall (685787) | more than 5 years ago | (#28315757)

Yes, there are so many textbooks out there with only one author and no sources cited. And find me a Nobel laureate who never collaborated with anyone.

Re:I don't see how this matters (0, Flamebait)

linzeal (197905) | more than 5 years ago | (#28315381)

Anyone else hate exams that require you to "show all work" when advanced students (perhaps yourselves) are then burdened with consciously writing down each step instead of utilizing the methodology that solves the problem in fewer steps? Teachers that scream at you to show your 'work' typically only know how to solve a problem one way and often by rote. IF you come at them with something they have not seen like when in high school I solved a double integral for a classical hydrodynamics problem involving two pitchers of water they freak out at you. The teacher accused me of plagiarizing the answer from the internet, which admittedly I had learned the concept from but this was before wireless internet and for this over-demonstration of knowledge I had to plead my case in front of her superiors. I won after 2 weeks of wrangling but it damaged my reputation amongst the other teachers until I finished high school. That is why the first thing any sane student does is check the exams from last semester to see if they jive with how they work. Rote learning can't teach you how to think it can only force feed you the answer and make you throw up answers on cue.

Re:I don't see how this matters (1)

Pseudonym (62607) | more than 5 years ago | (#28315807)

Rote learning can't teach you how to think it can only force feed you the answer and make you throw up answers on cue.

This isn't "rote learning", it's drilling you on the method. The reason why you're required to "show all working" is to show that you've learned that method, even if there are simpler methods which work on that problem. That way, when you come across a real problem in the wild for which that method is most appropriate, you'll be ready for it.

The purpose of an exam is not to show how clever you are at solving problems, it's to show how much of the material you've learned.

Re:I don't see how this matters (1)

forkazoo (138186) | more than 5 years ago | (#28315525)

I had math and computer science classes where homework was not graded. All course credit came from exams. If you "cheated" on your homework, you came up short on the exam where showing all work was required to receive any credit for a problem. Those are the best types of classes, because it truly tests your ability to solve problems.

For something like a Math class, I agree. I think making large amounts of homework contribute significantly to your grade is just silly. OTOH, for something like a film class, it would be hard to grade a student director on films that he can make completely in a 50 minute class period.

Re:I don't see how this matters (1)

xaxa (988988) | more than 5 years ago | (#28315837)

OTOH, for something like a film class, it would be hard to grade a student director on films that he can make completely in a 50 minute class period.

Friends of mine had 10-hour (IIRC) Art exams, spread over two school days. This was age 16, in England, in 2002.

Re:I don't see how this matters (1)

QuoteMstr (55051) | more than 5 years ago | (#28315597)

I prefer this grading style too; not only does it have the advantages you mention, but it also allows students who are overqualified for a class to get through it without wasting too much time on tedious assignments.

Re:I don't see how this matters (1, Informative)

Anonymous Coward | more than 5 years ago | (#28315111)

Exactly. This thing isn't going to help you pass an exam. As it is, you can use an engineering calculator to solve equations the same as using WolframAlpha. Neither are going to be allowed on exams and I never had any homework in my engineering courses where it was okay to omit each step used to reach the solution.

Re:I don't see how this matters (3, Interesting)

node 3 (115640) | more than 5 years ago | (#28315715)

Wolfram Alpha has a "Show steps" button.

Re:I don't see how this matters (0, Flamebait)

Karganeth (1017580) | more than 5 years ago | (#28315223)

Screwing themselves over? How? In the real world you can use any software you wish. The only people screwing themselves over are those who waste their time learning how to do the things that wolfram alpha can do instantly for you. Knowing how to do very large sums is just as useless as knowing how to integrate.

Re:I don't see how this matters (1)

Shadow of Eternity (795165) | more than 5 years ago | (#28315331)

This. I'm studying law, not fucking engineering. I don't need or want to know calculus, and the USA will not fall if the millions of people NOT going into a math-centric field don't know anything above highschool algebra and geometry. If anything we'd be in the far better position of having people studying much harder in the fields they're interested in and not having the budget drain of all the people taking these classes just to fill some random requirement.

Furthermore if, in reality, I find a faster and more efficient way of completing my work I don't get fired for "cheating". I get a raise and possibly a promotion if I keep improving things.

Re:I don't see how this matters (1)

Kotoku (1531373) | more than 5 years ago | (#28315575)

Calculus, Linear Algebra, and other items getting thrown into ACCOUNTING curriculum are stunning. All they serve to do is frustrate (though the college claims it as strengthening your "high level reasoning"), as witnessed by everyone I've taken them with.

I enjoy the theory behind math, but being able to spit out answers without referencing the method to do it just to prove I can is not enjoyable.

As long as engineers have to take literature... (2)

Fred Ferrigno (122319) | more than 5 years ago | (#28315675)

If the idea of general education classes is that every student should have some familiarity with a breadth of fields before they graduate, I think understanding basic calculus is a reasonable minimum expectation at the university level.

Re:I don't see how this matters (5, Insightful)

node 3 (115640) | more than 5 years ago | (#28315725)

Furthermore if, in reality, I find a faster and more efficient way of completing my work I don't get fired for "cheating". I get a raise and possibly a promotion if I keep improving things.

Actually, in the real world, you just get more work.

Using a wheel is cheating too (1)

sissyneck67 (1567253) | more than 5 years ago | (#28315799)

You should be carrying rocks like the rest of us

Re:I don't see how this matters (1)

xaxa (988988) | more than 5 years ago | (#28315871)

This. I'm studying law, not fucking engineering. I don't need or want to know calculus, and the USA will not fall if the millions of people NOT going into a math-centric field don't know anything above highschool algebra and geometry.

For your next life, try and be born in a different country. I know that in the UK you can stop studying maths at age 16. At university almost everyone studies only one subject, there's no such thing as majors/minors.

Personally, I'd have liked to study a bit more non-CS when I was doing my CS degree in the UK, just for a bit of variety and a break.

Re:I don't see how this matters (1, Interesting)

Anonymous Coward | more than 5 years ago | (#28315491)

This. A full 6 years after graduation and this is what I have realized.

Knowing *when* to integrate is far more important than knowing how. If you dont know when you have to, its fairly useless to know how.

Once you have been exposed to the underlying theory, unless you are going into more theoretical work, there is no reason to not use MATLAB to solve that system of Diffy Q's. In the real world, when your on somewhat of a schedule, and other peoples money is on the line who do you think is going to get the contract? The guy who just solved the circuit equations by hand, and now knows the values for R, C, L etc? Or the guy who used Spice and has a working prototype of the design to show?

For most of us we simply need to get work done. We learned the theoretical underpinnings once upon a time, and if need be we can spend a couple hours (or weekend) and brush up on a specific topic. But, even that weekend pales in comparison to the time spent solving *everything* by hand. So there is no good reason to make students believe that upon graduation and employment, they will be sitting in an office working everything out by hand.

Slightly off topic, but food for thought nonetheless: If you want to talk about reasons why engineering and science enrollment are down, or why many leave those fields of study, this may be a good place to start.

Re:I don't see how this matters (0)

Anonymous Coward | more than 5 years ago | (#28315599)

In the real world you can use any software you wish.

You obviously haven't spent any time in the corporate world and dealt with a typical IT department.

Re:I don't see how this matters (2, Informative)

Pseudonym (62607) | more than 5 years ago | (#28315857)

In the real world you can use any software you wish.

Oh, you poor, naive person.

Let me introduce myself. I'm from the real world. Let me explain how things happen here.

We have to deal with tricky problems. Sometimes, a function has more than one formal integral, and some forms are more appropriate than others in different situations. Good luck coaxing your CAS into giving you exactly what you want.

We have to deal with deadlines. If you can solve a problem in two minutes on paper, that's usually quicker than loading up most software packages and trying to get your equation into the syntax of the system. (Naturally, no two systems use the same syntax.)

Even worse, we have to deal with software licensing. Mathematica and Matlab ain't cheap. Software vendors try to argue that you're a commercial institution, not a research institution, so they can gouge you for licence fees. Cross your fingers and hope that there is a small enough number of people using the software concurrently so that you can get in. Otherwise, you're screwed.

It won't matter (0)

Anonymous Coward | more than 5 years ago | (#28315061)

You won't be able to use it on exams.

Protestant Work Ethic (5, Insightful)

unlametheweak (1102159) | more than 5 years ago | (#28315113)

It's the Protestant Work Ethic that if it is easy (or easier to do) then it is somehow bad. Like all learning tools, this may be used for cheating, just like a butcher knife can be used to murder somebody. If I could have had feedback that was quick and easy when I was in school then I probably would have excelled at Mathematics instead of dropping it as soon as possible. Tools like this are great for people who can't afford tutors and who don't have family members who are educated enough to help them with their homework.

Math, I have heard it said, is the great (social/economic) equalizer, but experience has demonstrated that only people who are lucky enough to have exceptional teachers or middle class families will have the environment to excel. A well written software program cannot ignore you, no matter how poorly you are dressed or who your friends and enemies are.

Teachers who worry about cheating obviously don't have the skills to assess their students abilities.

Re:Protestant Work Ethic (4, Insightful)

Chris Burke (6130) | more than 5 years ago | (#28315415)

It's the Protestant Work Ethic that if it is easy (or easier to do) then it is somehow bad. Like all learning tools, this may be used for cheating, just like a butcher knife can be used to murder somebody.

In college I took "Calc II with Maple". Maple, fyi, is a program for doing symbolic mathematics (as opposed to say matlab which is analytic), and it knows more calculus than I ever would or could. We not only got to use Maple on our homeworks, we took our exams in a computer lab.

Easy, right? Ha! That class was pure evil. Since they knew that we were freed from the tedium of the raw mechanics of integrating/deriving, that meant they were free to make the problems as complex as they wanted. Yeah Maple could tell you the answer, but only after you'd figured out how to frame the question, and if you knew how to use the result to reach the next step of the problem. You had to know how to apply the calculus. Very educational, very rigorous, very hard. Compared notes with students in the non-Maple version... yeah, ours was way harder. But also we covered how to use the calculus in ways they'd never heard of, simply because they had to spend so much course time covering the mechanics.

My point here would be that I think the existence of WolframAlpha could open up opportunities for an even better, and yes for you Professor Protestants harder, curriculum.

On the other hand, this was Calc II. At some point, you would have to take Calc I and should learn the boring stuff like the integral of 1/x, and for that class Maple (or WA)would be detrimental.

No kidding (4, Interesting)

Sycraft-fu (314770) | more than 5 years ago | (#28315565)

The math class I learned the most in was a community college precalc class. I had to take it my senior year in high school because I had a schedule conflict with the high school precalc class. In the end, that was a really good thing.

As background, I am "good" at math, but not nearly to the extent of many geeks. I don't struggle with it to a great degree, but nor do I find it trivial. In university integration gave me a huge problem and I had to drop calc 2 to an audit after the first test because I couldn't learn it fast enough. I also am not a math head, I don't love it and desire to know tons about it. So I'm not bad at it, but not great at it.

Now then the class. Homework was given, and graded, but not counted. So you did as much or as little homework as you felt necessary. If you turned it in, the teacher would grade it thoroughly and give it back to you to let you know how you did, and where you made mistakes. No scores were recorded, it was for your learning. This let people like me, who find that listening in particular (I'm an auditory learner) and reading are more valuable than doing (I'm not much of a kinesthetic learner) spend time on that, rather than problems. Also if there was only a few areas you had trouble with, you did those problems, or more of those problems, rather than a bunch you already knew.

As for tests? All tests were graphing calculator allowed, open note, open book, open teacher. Yes, you could go up and ask him questions. He wouldn't give you the answer, but he'd help you figure out where and why you were stuck.

The way I know I learned so much in that class? Well one I did very well on the SATs which I took right near the end but more over was when I got in to university. One of the first things we did in calc 1 was take a precalc test. Teacher wanted to see where we stood. I aced that, beat everyone out, even those who had taken calculus in high school. Because of that precalc class, my precalc knowledge as solid.

Real, valuable, learning isn't about memorization. It isn't about how many facts and formulas you can store in your brain. That isn't useful anymore since a computer is way better at that than you will ever be. It isn't really even about analyzation, as in crunching numbers through formulas. Again, computers and crunch the numbers better than you. What it is about is synthesis, meaning integrating the knowledge in to your other knowledge, and about application, applying it to novel problems.

The reason is that's what you do in real life. When there's a network problem, my boss doesn't say "Fix that and you can't use any resources, you need to have everything in your head you need to know." I'm perfectly welcome to look in a reference book, check a website, use a calculator to do subnetting. The important ability is to solve the problem.

Those sorts of things should be perfectly testable, even when people have access to calculators, and books and the web and so on, just like in the real world.

So even with a highly analytical subject like math, you can teach like that. I know it can be done as I've experienced it. However it takes a good teacher, one who really understands the math, and not some guy who thinks math is just crunching a bunch of formulas from a book.

Re:No kidding (1)

sexconker (1179573) | more than 5 years ago | (#28315861)

That's a nice little story, but if you can't do your shit with a pencil and a sheet of paper, then you don't actually understand it.

A understanding of the fundamentals of the math you're doing is the most important thing.
I rarely found the need to memorize formulas for math and physics. I often found myself proving or reasoning out various formulas in the margins of my paper as I solved problems. I was able to do that because I understood the fundamentals of what I was doing.

A fundamental understanding will improve your performance (in testing and real-world usage) regardless of what tools you use. Open book? Open notes? Calculator? Why? A decently-written test will avoid things you need to memorize (such as transformations, physical constants, etc.) or provide them for you. A decent professor will follow your work through even if you get that formula or constant wrong.

Of course, it's hard to find a good professor or a good test these days.

(Obviously only using paper and a pencil isn't feasible for a lot of things, but I think you all get the point.)

Instant Results? (5, Interesting)

Kyune (948300) | more than 5 years ago | (#28315119)

Seeing as I'm about to graduate from CS with a minor in Math, the thing that I find funny is that there is so much focus on "results" and so little attention to process, particularly when it comes to learning. That being said, the biggest gripe I have with math in the classroom is the reliance by instructors and authors on readers to just "get" what is being taught; textbooks that provide one or two examples and assignments far beyond what the text really offers, or make the assumption that every reader is going to reflexively make all the intuitive leaps needed to get to the solution, and a correct one at that. Hey, I understand wanting to pass only the people who are willing to work hard to succeed, but right now the "system" makes people work hard for the wrong reasons. I can't say that I see Wolfram Alpha help the problem I outlined--it's a step sideward, really. At least now we can check our work? haha.

Re:Instant Results? (1)

SomeJoel (1061138) | more than 5 years ago | (#28315173)

Seeing as I'm about to graduate from CS with a minor in Math

My university did not allow this. The reason was simple, all of the requirements for a Math minor were already among the requirements for a C.S. major. Also, because there was only about a 2 or 3 course deficit, you weren't allowed to get a double major C.S./Math either.

Re:Instant Results? (2, Insightful)

XanC (644172) | more than 5 years ago | (#28315295)

You've described a situation, but I don't see a reason there.

Re:Instant Results? (0)

Anonymous Coward | more than 5 years ago | (#28315335)

That's bullshit money grubbing by your school.

Re:Instant Results? (0)

Anonymous Coward | more than 5 years ago | (#28315693)

That's a stupid policy, and fortunately my college did the sensible thing. The courses required to declare a minor could not have satisfied a degree requirement. So although you might have had to take a lot of math classes as a CS major, it would simply take more hours to declare a minor in math.

The ability to check your work is crucial! (2, Interesting)

maillemaker (924053) | more than 5 years ago | (#28315309)

I believe the ability to check your work is crucial.

This is why I am a firm believer that all math texts should offer the solutions to ALL the problems in the back of the book.

The way I learn to do math problems is by doing LOTS of math problems. Finally, after I have done enough of them, I see the pattern, and I have learned the mathematic principles behind the problems.

This, of course, is precisely backwards of how math is taught. They try to teach the mathematic principles, and then from that you are supposed to deduce how to do the problems. This has never worked for me.

I have to lots of problems, and finally I see the pattern.

In order for the lots of problems to be useful, however, I have to have the answers to the problems so that I can tell whether I did the problem right or not. There are not enough problems in textbooks now as it is. If I can only do the even ones (because that is all answers are available for) then that has cut my available problems to do in half. To me, there is no point in doing the problems that have no answers because I have no way to know if I did it right or not.

And the real problem is, if you spend your time "learning" how to do a bunch of math problems incorrectly (though you didn't know it), you have to "deprogram" yourself once you are shown how to do it correctly. I would rather know right away (by having the solution available) whether I made a mistake or not, so I can figure out what I did wrong and move forward.

Of course teachers don't want to give all the answers to the texts because they want easy homework assignments to hand out and grade.

I think this is crap for two reasons:

First, and most importantly, if you cheat on your homework, YOU ARE FUCKED ON EXAMS. Period.

Secondly, for many texts nowadays you can find a torrent for the teachers solution manual. I've done this for texts when I can, but not all are available.

Wolfram Alpha has the ability for me to possibly plug in difficult math problems and find the answer, and then I can figure out how to get that answer myself, WHICH IS WHAT LEARNING MATHEMATICS IS ALL ABOUT.

This whole cheating thing in Mathematics is just way overblown. Let students cheat on their homework. They will, absolutely and without question, fail their exams, and thus, the course. End of story.

Mod Parent Up! (1)

justinlindh (1016121) | more than 5 years ago | (#28315541)

Everything you say is spot on, in my opinion, and I think most professors would agree.

Most of my math/physics profs in college would ONLY assign the even numbers because the answer was in the book. They weren't lazy, and actually checked whether you were arriving at the answer in the correct fashion. We'd get dinged if we omitted steps which weren't obvious, but likewise, we'd get partial credit if parts of our work was correct. This also gave the profs some gauge on which parts of the processes needed to be elaborated on in class, and if not frequently messed up enough, at least mentioned on the assignment so the student could get some insight as to where they went wrong.

The actual answer was usually worth very little compared to the process. If it were the opposite, I barely would have learned anything in those classes.

Re:The ability to check your work is crucial! (2, Insightful)

jhp64 (813449) | more than 5 years ago | (#28315617)

I believe the ability to check your work is crucial.

So learn how to check your work. First, look at your answer and try to determine whether it makes sense, and then see if you made any silly algebra mistakes. Then if you're learning integration, for example, take the derivative and see if you get the original function back again. If you're learning differential equations, plug your purported solution in and see if it is actually a solution. In many situations, you have more than one method available to solve a problem, so try both and see if they produce the same thing.

In the real world you don't have a solution manual, so it's a valuable skill to be able to check your work without one. Furthermore, some students use solution manuals badly: if they don't get the right answer, they tinker with their work until their answer matches the right one, with no understanding of what they did wrong or what they did to correct it. It's a good idea to not have all of the answers available; for calculus, half seems about the right proportion.

This, of course, is precisely backwards of how math is taught. They try to teach the mathematic principles, and then from that you are supposed to deduce how to do the problems. This has never worked for me.

I'm not sure what you're talking about -- mathematics is taught lots of different ways: there is no single, monolithic, method for "how math is taught."

Re:The ability to check your work is crucial! (1)

geekoid (135745) | more than 5 years ago | (#28315653)

Yes, becasue it is impossible to cheat on an exam~

Community College (-1, Flamebait)

halcyonandon1 (1568125) | more than 5 years ago | (#28315123)

I find it funny that their article quotes a number of community college professors. So, their big concern is that the pregnant Denny's waitress and the 18 year old who graduated bottom 10% of his high school class are going to cheat at college algebra 101 in the pursuit of their respective associate degree in something trivial? A degree that probably won't even help them land anything above an entry level position anyways? Either way, I'll stick to cheating with my abacus.

Oh man (5, Funny)

Caboosian (1096069) | more than 5 years ago | (#28315131)

I just don't know if I can deal with all this math-debating.

The thing works (1)

marcus (1916) | more than 5 years ago | (#28315141)

How about an esoteric question?

what is the distance between 89N 1W and 89N 2W ? [wolframalpha.com]

The thing ALMOST works (1)

PCM2 (4486) | more than 5 years ago | (#28315557)

On your search result, Wolfram|Alpha helpfully gives additional information, including "direct travel times." Unfortunately, the travel time for a car moving at 55 mph is given as "0 years." Not too helpful, that.

Re:The thing ALMOST works (1)

Captain Cabron (1135811) | more than 5 years ago | (#28315805)

Looks like someone at Wolfram reads Slashdot - I'm no longer seeing "car" under direct travel times.
FWIW, the results are better than Google's [goofram.com] .

What's new? (0)

Anonymous Coward | more than 5 years ago | (#28315157)

Math tools like Maple have existed for years. WA hardly added anything besides its ability understand English. If using WA is a problem, such problem should have surfaced years ago.

And a simple solution: just make students show their steps.

Re:What's new? (1, Informative)

Anonymous Coward | more than 5 years ago | (#28315215)

Wolfram Alpha also allows you to see all the steps that lead to a result, so your solution is not going to work.

Re:What's new? (1)

Captain Cabron (1135811) | more than 5 years ago | (#28315853)

In Maple, Tools -> Tutors will show you the steps to solving loads of the most common math problems.

f you don't know it, you don't know it. (0)

Anonymous Coward | more than 5 years ago | (#28315179)

It might mess around with the process of homework, but if a student has been using WA all semester to solve his work, he's still screwed when it comes to the in-class exam. Not to mention following class discussions.

Too general (3, Insightful)

dexmachina (1341273) | more than 5 years ago | (#28315191)

It depends a lot on the nature of the class, so there's no one-size-fits-all answer for when tools like graphing calculators or WA should be allowed. In first year calculus, when you're learning how to integrate, a program that can do symbolic integration isn't an appropriate tool. On the other hand, for a first class in ODEs, the integration is the least essential part of the process and so the right tools make it easier to focus on whats really important. Yes, I know WA can solve diff eq's too, but that's just an example. Just requiring that work be shown isn't always sufficient, since it's an important skill in mathematics to understand how to get a solution, even when you can't immediately see what the solution is. So I don't think it's unreasonable for graphing calculators or things like Wolfram Alpha to be disallowed for certain classes. That being said, labelling it academic misconduct is pretty unreasonable. I look at it in the same as recommended homework problems: it's just a suggestion, but come exam time it's your funeral. Back to the first year calculus example, I remember the syllabus explicitly saying that all problem sets were to be completed independently and without computer aids. No one really did that, and the TAs didn't even try to enforce it. In university, formal evaluation carries most of the weight in grading. The people who just copied off of other people or the internet had a smooth ride until the first test.

Re:Too general (2, Insightful)

honkycat (249849) | more than 5 years ago | (#28315261)

So I don't think it's unreasonable for graphing calculators or things like Wolfram Alpha to be disallowed for certain classes. That being said, labelling it academic misconduct is pretty unreasonable.

I agree that it's appropriate for some classes, inappropriate for others. However, if the instructor for the class declares that it's off limits, then it is certainly misconduct to disregard that direct instruction. Much the same way as instructors can set the collaboration policy (at least at some schools), they should be allowed to make the decision about what tools to permit.

Damn you Wolfram! (5, Funny)

Anonymous Coward | more than 5 years ago | (#28315201)

Well Wolfram Alpha has been a big buzz kill for me.... My query was "average penis length?".... WA answered: 5.94 inches.

Now I understand the meaning of "ignorance is a bliss"

Re:Damn you Wolfram! (1)

Anonymous Coward | more than 5 years ago | (#28315235)

flaccid or erect?

Re:Damn you Wolfram! (1)

PCM2 (4486) | more than 5 years ago | (#28315577)

You're being funny, but Wolfram|Alpha (correctly) interprets the question as "the average length of an erect human penis (age > 17 years)".

Sweet, let's try it out! (5, Funny)

l00sr (266426) | more than 5 years ago | (#28315209)

Let X_n and Y_n be positive integrable and adapted to F_n. Suppose E(X_{n+1}|F_n) \leq X_n + Y_n, with \sum Y_n \lt \infty a.s. Prove that X_n converges a.s. to a finite limit.


Wolfram|Alpha isn't sure what to do with your input.
.

Useless!

Re:Sweet, let's try it out! (2, Interesting)

Keith_Beef (166050) | more than 5 years ago | (#28315269)

http://www24.wolframalpha.com/input/?i=what+was+the+electricity+production+of+the+USA+from+1985+to+2005%3F

I've been trying to get some useful answers from Wolfram Alpha for a couple of weeks... I still don't have the hang of it.

K.

It even shows the steps (1)

IronicToo (514475) | more than 5 years ago | (#28315211)

Many professors got around the graphing calculator problem by requiring students to show their work. WA can even do this for you, if you click on show steps it will walk you though how to solve the problem. This could be a very helpful tool to learn math, but more probably it will be used as a short cut on homework allowing the lazy to learn even less.

Students will adapt. (1)

Dragonshed (206590) | more than 5 years ago | (#28315217)

Yet another rule for the higher-ed equivalent of the rat maze. If they already have understanding, will students still be forbidden from using the tool to make life easier?

I wrote for the TI-82 that would show various equation solutions as well as their stages of reduction. Not surprisingly I had alot more fun writing the program than copying the complete answers of ~60 problems to paper.

Re:Students will adapt. (1)

honkycat (249849) | more than 5 years ago | (#28315285)

If you already have the understanding, why are you taking the class? If you need the particular class for a requirement, and you already have the understanding, it shouldn't be hard to do the work the old fashioned way. In my experience a lot of the people who claim to have such a deep understanding that they shouldn't be bothered to go through the motions are seriously overestimating their own abilities.

Is this really a problem? (3, Insightful)

Jugalator (259273) | more than 5 years ago | (#28315225)

Surely there must be ways to write a test for their students where they are not Internet enabled?

Let them mess up their learning process all they want if that's what they wish. :p It's a bit of a cliche, but it's really true -- "they're only fooling themselves".

Re:Is this really a problem? (1)

geekoid (135745) | more than 5 years ago | (#28315631)

Also they are fooling everyone who sees they have a degree.

Using the book is cheating! (5, Funny)

GWBasic (900357) | more than 5 years ago | (#28315263)

Using math books is cheating. The only REAL way to learn algebra or calculus is to re-invent it like people did hundreds of years ago!

Re:Using the book is cheating! (0)

Anonymous Coward | more than 5 years ago | (#28315467)

Welcome to MAT521-MAT522 Advanced Calculus... Its an undergrad course required for math honors majors where you do just that. Start with set theory and build everything you've every theorem you've ever used in a math class. http://www.math.wisc.edu/522-advanced-calculus

a physics teacher's perspective (5, Interesting)

bcrowell (177657) | more than 5 years ago | (#28315297)

I teach physics at a community college. Based on my own experiences, some of this speculation seems overblown to me.

His concern is that professors may need to adapt their assignments or test questions.

I don't understand the part about test questions. Students aren't normally allowed at access the internet during an exam, and WA is a web-based service, so this seems like a total non-issue.

When it comes to homework, I can see slightly more reason for concern, but only slightly. Any math or science teacher who's collected homework papers knows that some students will always try to copy the answers from each other. Whatever way you have of handling that, I would think it would still work if they were getting their answers from WA. (Possible ways of handling it include not allowing students to turn in identical papers, or not counting homework for very much compared to exams.)

I don't see why it's a big deal that WA can show the steps it took to get the answer. That just makes it easier to tell whether the student is using WA. If 5 students in a class of 20 are using WA on their homework, it'll be pretty obvious that they all wrote down exactly the same steps in exactly the same order. This is very much like the situation where you hand out homework solutions every semester, and a student starts turning in homework papers that are verbatim copies of the homework solutions.

One thing that I really haven't liked in the past was that for a lot of the math classes at my school, they required students to buy a specific brand of graphing calculator, for about $300. That's a heck of a lot of money for a lot of broke community college students, and I don't see why a student who wants to learn calculus without a graphing calculator should have to buy one. There's actually quite a bit of FOSS symbolic math out there, e.g., sage, maxima, wxmaxima, yacas, and axiom. If the student has access to a computer, they can use one of those. If the student doesn't have access to a computer, then a web-based service like WA isn't going to make any difference. When it comes to web-based apps, integrals.com has been around for years now, so this isn't a new issue.

Re:a physics teacher's perspective (1)

gilleain (1310105) | more than 5 years ago | (#28315695)

Will the solution to a problem often have only one series of steps, in one order? As in - is it possible to tell that the (correct) answer a student gives is his own, or from a third party?

I guess the only experience I have of this is implementations of algorithms in code. It is usually possible to tell who wrote a piece of code by the style (whitespace, variable naming, etc) but for mathematical proofs, I'm not so sure. I guess the names of the mathematical objects used could be a giveaway, like if half the students start the answer with "let Zeta0 = {z0, z1, ..., zr}" and everyone else used different letters. Hmm...

Re:a physics teacher's perspective (1)

bcrowell (177657) | more than 5 years ago | (#28315751)

Will the solution to a problem often have only one series of steps, in one order? As in - is it possible to tell that the (correct) answer a student gives is his own, or from a third party?

I think your comparison with computer code is a good one. In both cases, there's typically a huge amount of variation between one person's work and another's, if they really worked independently. (Students are often very naive about this, which can make it easy to tell what they're doing. They think it's just "the answer" to the problem.)

Re:a physics teacher's perspective (1)

gilleain (1310105) | more than 5 years ago | (#28315813)

That makes sense. I guess I know that there are long-winded proofs, and shorter more elegant ones. It must also depend on how difficult the problem is, and how many pieces of the puzzle (intermediate results, notations) have been provided.

I know a guy who taught computational complexity, and had to mark students code written in a lisp-like language. He was half-seriously thinking about writing an automated prover to test their code for correctness. It might be a hard problem, but testing proofs/code for isomorphic solutions seems possible :)

Can't force a student to leanr (1)

fermion (181285) | more than 5 years ago | (#28315307)

And at the college level, I would rather see professors teaching and measuring learning than trying to force a person not to cheat. Not cheating should be learned in high school. In college a student is paying to learn, and any not learning should be asked to leave.

So to me the issue is original work. This is not a new problem. In Engligh one might copy a term paper, but not be able to write in class. That should be a big indication that a student should fail, if they are never able to write a paper in class. The same goes for other classes. Outside work is practice, the grade that counts is supervised class work. A student might cheat on all outside classwork, and it won't matter. A good test will show that nothing was learned.

On the issue on calculators, that needs to be a decision that is made on a individual basis. Some students are being trained at a level where calculators will not help them. Others are being trained at a level where calculators will help them. One really cannot make a broad statement that calculators are bad. What one can say is that calculators often require different assignments. For instance, I can write an assignment that a student who knows the math can finish quickly. A student with a calculator who can use the machine can finish, but it will take much longer. A student who does not know the calculator will invariably not be able to complete the assignment successfully. Such things can often be done to encourage proper behaviour.

Re:Can't force a student to leanr (1)

CorporateSuit (1319461) | more than 5 years ago | (#28315485)

In college a student is paying to learn.

That's how it used to be. Now, they're just paying for a degree. Learning is done on your own time.

How about proofs? (0)

Anonymous Coward | more than 5 years ago | (#28315341)

If they'd start moving the focus onto proofs in math classes instead of just memorizing algorithms for solving certain problems, students wouldn't be able to use Wolfram Alpha.

Um, Muskegon who? (1, Funny)

Anonymous Coward | more than 5 years ago | (#28315397)

No offense, but is there any particular reason we had to cite such a leading authority as Muskegon Community College? My raccoons say that Google Maps is the instantiation of the all-seeing eye of god and the definitive sign of the judgement day - can we get some front page coverage of that too?

really guys (0)

Anonymous Coward | more than 5 years ago | (#28315405)

I don't really think it will be an issue because its functionality is web based and if you can acess the internet on a test you could cheat off of the internet anyway

Misguided Universities (2, Interesting)

Siker (851331) | more than 5 years ago | (#28315477)

The professors who are afraid of calculators and automatic problem solvers are the same as those who think class attendance matter. A university, if anything in the world, should be a place for learning, not a very expensive kindergarten. In that perspective the activities of the students are irrelevant: if they learn practical abilities through Wolfram Alpha, great. If they don't, that's their problem. Ultimately the student is the paying customer. Professors much too often slide into this illusion of grandeur where they think the student owes them anything or needs to satisfy the professors when it's in fact the other way around.

If you choose to go to and pay for a university education, do it your way. If Wolfram Alpha gives you the insights you need, then that's the right tool for you. If your style of learning is snoozing under a tree, occasionally watching an apple fall, then do that. If you never go to a class in your life but you come out as the next Einstein you have succeeded. If you waste all your time 'cheating' that's your problem. You're the boss, you're the one paying for it.

And before somebody brings it up, grades are arbitrary statistics based on a flawed system. If they are affected by something as simple as the use of Wolfram Alpha that's just another demonstration of how little real world value they have.

Re:Misguided Universities (1, Insightful)

Anonymous Coward | more than 5 years ago | (#28315815)

And before somebody brings it up, grades are arbitrary statistics based on a flawed system. If they are affected by something as simple as the use of Wolfram Alpha that's just another demonstration of how little real world value they have.

That's what stupid people say. And if you don't think going to class is important, then you will never be successful. You will learn sooner or later that in order to get real things done you need to participate with others on a consistent basis. At this point I don't think you will care, but the challenge of any program is to be successful within the program. It's not about making up arbitrary rules for yourself for your own convenience. This is not to say independence is not important. You don't need to sign up for classes if what you want is independence.

I belong to that pocket of math instructors... (2, Interesting)

Mao (12237) | more than 5 years ago | (#28315493)

who do not allow calculators. Part of my rationale is that if I allow calculators, then those who have the fanciest equipment would have an unfair advantage over those who don't. And I hate to have students feel that they must buy expensive equipment in order to stay competitive in the class.

So, this WolframAlpha might actually be a good thing, for it could level the playing field (The majority of my students do have internet access). I am sure one could design math problems in a way that still tests a student's mathematical aptitude and knowledge, while taking into account the availability of WA.

Think about this the other way round: If WA doesn't exist, and some $1000 calculator can do what WA does, then the rich students who could afford to buy the calculator would have an unfair advantage over those who couldn't.

Re:I belong to that pocket of math instructors... (1)

geekoid (135745) | more than 5 years ago | (#28315609)

I am curious what level maths you teach?

If it's high level mathematics in college, wouldn't they use software tools?

You seem to be penalizing the rich and underestimating the not so rich.

OTOH, I only know what is in thst single post, so I would wager there is a fact or 10 I am missing.

Re:I belong to that pocket of math instructors... (1)

Mao (12237) | more than 5 years ago | (#28315769)

I am curious what level maths you teach?

If it's high level mathematics in college, wouldn't they use software tools?

Differential / integral / multivariable Calculus, ordinary differential equations.

You seem to be penalizing the rich and underestimating the not so rich.

No, and I don't know why someone would think that.

When I was a college student... (1)

danwesnor (896499) | more than 5 years ago | (#28315607)

Solving an equation is work for math geeks and computers. Writing the equation is work for engineers. I solved damn near every equation in calculus class by hand, but I'll be damned if I understood where they came from, so I learned nothing. Luckily, I was a computer engineer, so only I really only had to understand and, or, and not.

We rarely got graded on take-home work in engineering or math classes. Too many grad students who'd work for beer - or just so someone would pretend to be their friend.

Math war (0)

Anonymous Coward | more than 5 years ago | (#28315645)

I say 2^aleph = alpeh_666

Good (1)

djurban (124948) | more than 5 years ago | (#28315791)

Maybe finally people will have to pass exams testing *understanding* of the subject in contrast to knowing how to apply patterns and rewriting systems to solve simple taks that are computer solvable now. It's always good to see the bar going higher.

Just another Slashvert for Wolfram. (0)

Anonymous Coward | more than 5 years ago | (#28315809)

Why is it that Slashdot's ever so devoutly 'anti-proprietary anything' stance totally dissolves the moment somebody like Stephen Wolfram - oh, I'm sorry, that should be "an anonymous reader" - submits their lastest batch of advertising drivel to Slashdot?

Let me be the first to say.... (1)

cellocgw (617879) | more than 5 years ago | (#28315825)

"Feeling of Power" by Isaac Asimov.

FWIW, I'm opposed to *requiring* graphing calculators, not to *allowing* them. Calculators, graphics tools, etc. are not math; they're engineering tools. Mathematics is (with a few rare exceptions) purely symbolic. If you don't understand that, you don't understand math. And, yeah, YACAS and Mathematica do solve symbolic problems. I wouldn't allow them during tests, but if students want to use the tools instead of learning math, that's their own funeral.

In other news... (0)

Anonymous Coward | more than 5 years ago | (#28315833)

New wi-fi enabled calculators a big hit with college and high school students.

How to solve a problem. (1)

PeanutButterBreath (1224570) | more than 5 years ago | (#28315855)

If you can solve the problem, you can solve the problem. Who cares what tools you use? Whether you do the work with a pencil and paper, use the internet or read the answer off the next student over's test is your own prerogative. What, exactly, are Profs concerned about? That someone is going to cheat their way into some position of authority (or wealth -- hah!) without actually understanding the material? Doesn't seem likely. There are people who want to know a given subject and people who need to know a few things to achieve some other goal. The people who want to know will do it the hard way because they care. The people who just need to know should be allowed to use whatever tools are available. What matters is that they can understand a problem and select the correct tools to solve it.

I have no problem with people self-selecting the degree of intimacy they have with math (or any other subject) and using the most appropriate methods to achieve it. I have every faith that they are also self-selecting how far they can get in that particular field, and am not particularly concerned that people will cheat their way through and expect to be rewarded.

Education should be about learning how to think your own way through problems. It may tweak specialists when you gloss of their field on your way to some other objective. Too bad. I had to take calculus in the dark ages before Wolfram Alpha (before the mainstream internet!) because it was a requirement for all liberal arts degrees. I hate math. I barely passed. It was something to get out of the way. Perhaps with better tools I might have been able to develop some appreciation for it (long shot). But the point is, I passed it and now I couldn't tell you a single thing I learned doing things the "right" way. I could have used that time studying something I cared enough about to actually learn.

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