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Math Education

Wolfram Alpha Rekindles Campus Math Tool Debate 339

Posted by Soulskill
from the why-is-my-calculator-smarter-than-me dept.
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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Wolfram Alpha Rekindles Campus Math Tool Debate

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  • by Anonymous Coward

    Are they protected?

  • iirc (Score:4, Interesting)

    by langelgjm (860756) on Friday June 12, 2009 @06:29PM (#28315027) Journal
    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...
    • by SBrach (1073190)
      How did you play tetris during class?
      • Re: (Score:3, Funny)

        by Thinboy00 (1190815)

        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)

      by vux984 (928602) on Friday June 12, 2009 @06:43PM (#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: (Score:3, Insightful)

        by biryokumaru (822262) *
        Maybe you should have spent more time learning how to do math. Those "silly mistakes" are exactly the kind of thing you're supposed to be able to find on your own.
    • Re:iirc (Score:4, Insightful)

      by T Murphy (1054674) on Friday June 12, 2009 @07:17PM (#28315455) Journal
      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 $.
    • by Anonymous Coward

      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.

    • 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 t

  • by InstinctVsLogic (920001) <harmonyofchaos.gmail@com> on Friday June 12, 2009 @06:30PM (#28315033) Homepage
    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.
    • by The Snowman (116231) on Friday June 12, 2009 @06:35PM (#28315087) Homepage

      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: (Score:3, Funny)

        by sexconker (1179573)

        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.

      • by Chris Burke (6130) on Friday June 12, 2009 @06:56PM (#28315289) Homepage

        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: (Score:3, Informative)

          by Stiletto (12066)

          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

          • by Chris Burke (6130) on Friday June 12, 2009 @07:39PM (#28315651) Homepage

            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".

            • by springbox (853816)

              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"?

              I have been in this situation more than once outside of school.. In interviews (for some stupid reason..) They say it's to "test your though process," but it reflects poorly on people who feel rushed in an environment with artificially restricted resources.

          • by node 3 (115640)

            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 ca

          • by Dr Tall (685787)
            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.
        • by artor3 (1344997)

          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 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.

          If you need to take ten minutes, possibly digging through reference materials, to solve a simple problem then you simply won't get as much done as someone who can answer questions quickly. You can still be a valuable team player, but you won't be as productive, and it is entirely reasonable to grade you lower for that

          • Re: (Score:3, Informative)

            by Chris Burke (6130)

            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

        • by Brian Gordon (987471) on Friday June 12, 2009 @08:48PM (#28316153)

          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 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.

        • Re: (Score:3, Funny)

          by swillden (191260)

          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

      • by forkazoo (138186)

        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,

        • by xaxa (988988)

          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.

      • by QuoteMstr (55051)

        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.

  • by unlametheweak (1102159) on Friday June 12, 2009 @06:38PM (#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.

    • by Chris Burke (6130) on Friday June 12, 2009 @07:13PM (#28315415) Homepage

      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.

      • by artor3 (1344997)

        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.

        No. Maple is a program for fucking with students, and while it may know more calculus than I ever will, it'll be damned if it's gonna share.

        I have screen shots of that program giving entirely different answers for the exact same input after hitting the "reset and run this sheet from the beginning" button.

        I had nearly blocked that God-forsaken program from my memory....

    • No kidding (Score:5, Interesting)

      by Sycraft-fu (314770) on Friday June 12, 2009 @07:28PM (#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.

      • 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 wi

  • Instant Results? (Score:5, Interesting)

    by Kyune (948300) on Friday June 12, 2009 @06:38PM (#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.
    • by SomeJoel (1061138)

      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: (Score:3, Insightful)

        by XanC (644172)

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

    • 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

      • 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 b

      • Re: (Score:2, Insightful)

        by jhp64 (813449)

        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

      • by geekoid (135745)

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

  • Oh man (Score:5, Funny)

    by Caboosian (1096069) on Friday June 12, 2009 @06:39PM (#28315131)
    I just don't know if I can deal with all this math-debating.
  • How about an esoteric question?

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

    • 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.

  • Too general (Score:4, Insightful)

    by dexmachina (1341273) on Friday June 12, 2009 @06:44PM (#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: (Score:3, Insightful)

      by honkycat (249849)

      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.

  • by Anonymous Coward on Friday June 12, 2009 @06:45PM (#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"

  • by l00sr (266426) on Friday June 12, 2009 @06:46PM (#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!

  • 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.

    • by honkycat (249849)

      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.

  • by Jugalator (259273) on Friday June 12, 2009 @06:48PM (#28315225) Journal

    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 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!
  • by bcrowell (177657) on Friday June 12, 2009 @06:58PM (#28315297) Homepage

    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.

    • by Dice (109560)

      My experience as a physics student was that professors really only expected us to work things out by hand during the first two years, e.g. while we were still learning the mathematics. After we'd slogged through three quarters of Calculus and a quarter each for Linear and DE we were considered "good enough". After that it was pretty much expected that we would be using Mathematica or equivalent software to do the heavy crunching, many of my submitted homework assignments were in fact printouts of a Mathem

  • 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 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.

  • by Siker (851331)

    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 gran

  • 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 s

    • by geekoid (135745)

      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.

  • 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.

  • "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.

  • 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 kn

  • If not, who cares? Even if all of their homework is correct, they will still fail the exam...

  • by vikstar (615372)

    Back in the day in Poland (I don't know if it still happens) you were graded through a conversation with the teacher/professor. It would reveal whether you really understood the topic. Only problem is this requires a high level of quality teachers.

  • Wlfram Alpha answers the age-old question "How many licks does it take to get to the center of a Tootsie Pop?" correctly [wolframalpha.com].
  • by onionman (975962) on Friday June 12, 2009 @08:59PM (#28316229)
    I'm a math prof. at a reasonably large school.

    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.

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