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Comments: 339 + - Science: Wolfram Alpha Rekindles Campus Math Tool Debate on Friday June 12 2009, @06:25PM
Posted
by
Soulskill
on Friday June 12 2009, @06:25PM
from the why-is-my-calculator-smarter-than-me dept.
from the why-is-my-calculator-smarter-than-me dept.
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education
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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Submission: Wolfram | Alpha = "Math War"? by Anonymous Coward
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iirc (Score:4, Interesting)
Oh the horror!! (Score:3, Funny)
Re: (Score:3, Funny)
By hand, on graph paper with pen/pencil, with an egg timer, and a d20 (or dN) to pick the next tile.
Re:iirc (Score:5, Interesting)
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.
Parent
Re: (Score:3, Insightful)
Re: (Score:3, Interesting)
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: (Score:3, Insightful)
I've never once used a single scrap from calculus (computer science major).
Why does A=pi*r^2? Because integral from 0 to r of 2*pi*a*da=pi*r^2. See disk integration [wikipedia.org] for the sphere equations.
Re: (Score:3, Insightful)
Let me see now (Score:3, Funny)
If Computer Science were about computers they'd call it astronomy. No, that's not right. They'd call it Telescope Science. No, that's not right either. If Computer Science were about computers they'd call it Computer ..Hmm.
Re: (Score:3, Insightful)
There was no web when I graduated, had to learn it "on the job". I have never heard of anyone learning calculus "on the job" but it would explain why buildings and bridges sometimes fall down.
Calculator...or electronic book? (Score:3, Insightful)
Re: (Score:3, Funny)
You mean, your students are actually there to learn academic skills? Heretic! They should be learning practical things, like, um, leadership skills. Or networking.
Re:iirc (Score:4, Insightful)
Parent
Re: (Score:3, Interesting)
I don't see how this matters (Score:5, Insightful)
Re:I don't see how this matters (Score:5, Insightful)
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.
Parent
Re: (Score:3, Funny)
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 (Score:5, Funny)
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!
Parent
Re:I don't see how this matters (Score:4, Funny)
In Soviet Russia, tank exams you!
Parent
Re:I don't see how this matters (Score:4, Funny)
I assume they were rather dry?
Parent
Re:I don't see how this matters (Score:5, Insightful)
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.
Parent
Re: (Score:3, Informative)
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
Re:I don't see how this matters (Score:5, Insightful)
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".
Parent
Re:Stop ignoring what I say (Score:4, Informative)
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.
Yes, I already said that, which is why I said that I had no better alternative, and was simply pointing out that a typical exam isn't just testing your knowledge and understanding of the subject, it's also testing your exam-taking ability.
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.
Truthfully, I'm great at taking exams. I could even pass ones when I didn't really understand the material that well. That's not bragging, because that ability is basically useless in the real world.
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.
Be honest -- you're good at taking exams, but are too arrogant to admit that this doesn't necessarily mean you're the greatest at the subject matter, and too self-centered to consider how this affects anyone but yourself.
Besides, if you actually pay attention and read what I say I'm not damning exams. If this was a test in reading comprehension... So, go get a point then come back.
Parent
Re: (Score:3, Informative)
Not only this, it's also testing the ability of your professor or whoever to create a valid and reliable exam in this format. Not everyone can do it, and for a lot of people, the temptation to include trick questions is very high.
Re:I don't see how this matters (Score:5, Insightful)
I said this same thing in Algebra 1, and Geometry, and Algebra 2. Around precalc I started to get the picture. I can't imagine going to a reference book to see that the b in y=mx+b is the y-intercept.
Parent
Re:I don't see how this matters (Score:4, Insightful)
And yet another person interprets "in real life you can always use references" to mean "in real life you don't have to know anything without a reference."
Parent
Re: (Score:3, Funny)
Ability to solve problems in the limited-time test format.
Heh. Not really related, but I have fond memories of some "tests" from upper division real analysis and abstract algebra courses during my undergraduate degree. They were open-note, open-book, take-home, with only 6-8 problems and we were given a full week to finish them. Of course, all of the problems began "prove or disprove:" and each one took several hours of hard thinking/playing to grasp the core issues so that you could either write a proof or construct a counterexample.
I guess they were technic
Re: (Score:3, Informative)
I couldn't disagree more. I do this every day. Of course, I don't do 25 problems in one hour, but I do 25 problems/hour, i.e. solving a simple problem in a couple minutes many times per day.
Yes. Occasionally throughout your day you encounter a simple problem that can be solved in a few minutes. Of course you don't do them all back to back, of course they aren't all isolated and artificial, and of course if you go slightly slower on one such that it took you a cumulative hour and one minute to finish the 2
Re: (Score:3, Informative)
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
As long as engineers have to take literature... (Score:3)
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 (Score:5, Insightful)
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.
Parent
Re:I don't see how this matters (Score:4, Interesting)
Wolfram Alpha has a "Show steps" button.
Parent
Protestant Work Ethic (Score:5, Insightful)
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 (Score:5, Insightful)
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.
Parent
No kidding (Score:5, Interesting)
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.
Parent
Instant Results? (Score:5, Interesting)
The ability to check your work is crucial! (Score:3, Interesting)
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 s
Re: (Score:3, Insightful)
You've described a situation, but I don't see a reason there.
Oh man (Score:5, Funny)
Too general (Score:4, Insightful)
Re: (Score:3, Insightful)
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! (Score:5, Funny)
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"
Sweet, let's try it out! (Score:5, Funny)
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: (Score:3, Interesting)
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.
Re: (Score:3, Funny)
Is this really a problem? (Score:4, Insightful)
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".
Using the book is cheating! (Score:5, Funny)
a physics teacher's perspective (Score:5, Interesting)
I teach physics at a community college. Based on my own experiences, some of this speculation seems overblown to me.
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.
I'm a math professor, and I don't care about Alpha (Score:5, Insightful)
I teach plenty of calculus.
When I grade, I don't care about the answer. I look at the way the student solves the problem. If the setup is correct, the computations are reasonable, and the flow of the solution demonstrates that the student knows what she's doing, then I give it full credit even if the answer is wrong. I couldn't care less about careless errors (poor pun intended). I'm measuring the student's problem solving abilities, not her ability to do lots of tedious computations in a short amount of time (that's what computers are for). Likewise, if a student magically produces the correct answer without showing any work (or if the work is clearly B.S.) then I give them no credit. The answer is irrelevant, it's the process that matters.
I am completely unconcerned about Wolfram Alpha.
I also have a CS background, and I recognize that most CS related jobs don't require calculus. However, the whole point of taking calculus is to practice logical reasoning. A good calculus course will force you to solve lots of long complex problems, clearly express your reasoning, and maybe even do a bunch of delta-epsilon proofs. Unfortunately, many calculus courses end up being reduced to mundane computations of derivatives and integrals... those courses ARE a waste of time.
p.s. If you're a student who actually wants to learn a subject, then go to that "rate my professor" site and look for professors who are "clear" and "hard". Take those professors. You won't learn much from an easy professor, and three years after you graduate that easy "A" will be meaningless.