Slashdot Mirror
Wolfram Alpha Rekindles Campus Math Tool Debate
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.'"
Are they protected?
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*
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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...
"Anyone who [rips a CD] is probably engaging in copyright infringement." - David O. Carson
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.
How did you play tetris during class?
You won't be able to use it on exams.
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.
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.
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 ?
Good judgement comes from experience, and experience comes from bad judgement.
- W. Wriston, former Citibank CEO
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.
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.
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.
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"
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!
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.
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.
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".
Beware: In C++, your friends can see your privates!
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!
No, I will not work for your startup
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.
Find free books.
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.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
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.
A work that expires before its copyright never enters the public domain and thus enjoys eternal copyright protection.
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.
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?
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
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.
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.
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.
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.
Breakfast served all day!
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.
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.
I say 2^aleph = alpeh_666
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.
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.
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.
You should be carrying rocks like the rest of us
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?
"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.
https://app.box.com/WitthoftResume Code: https://github.com/cellocgw
New wi-fi enabled calculators a big hit with college and high school students.
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.
If not, who cares? Even if all of their homework is correct, they will still fail the exam...
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.
The question of whether a computer can think is no more interesting than the question of whether a submarine can swim.
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.
The enemies of Democracy are
Schools are all about busywork, memorization, and labor-intensive repetitive work, all of which are pretty much irrelevant in the real world, where we have the ability to look up any piece of information and use existing tools to help us figure things out. Making people demonstrate such knowledge as the barometer of their worth is pointless; making them put those things into *practice* and demonstrate real-world problem-solving using those things, regardless of the methods used, should be the real measure of someone's worth in an educational environment.
Teach them how, obviously, but don't put them on the spot for anything trivial enough to look up. As an example, make people learn basic math and multiplication tables for practical use, but beyond that, for fuck's sake, let them use a calculator.
Wlfram Alpha answers the age-old question "How many licks does it take to get to the center of a Tootsie Pop?" correctly.
The game.
1 2 3 4 I declare a math war.
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.
If this was a test in reading comprehension...
If Slashdot were a test in reading comprehension they'd have to bring the fail in on trains... trains whose rails run gracefully into a vertical into the Grand Canyon.
"You're right," Fisheye says. "I should have set it on 'whip' or 'chop.'"
LOL. So if I understand you correctly, you're saying that Slashdot is at the bottom of the Grand Canyon...
The enemies of Democracy are
I've been allowed to use Mathematica on Calculus and Differential Equations. Not just the classes, but the exams. Most of the class examples were Mathematica-based. We had to understand the concepts thoroughly in order to apply them quickly. The calculations are grunt work so we let the computers do that part. Also, the exams wouldn't be a list of equations to solve, they were real world problems. Mathematica/MATLAB usage wasn't mandatory, but it was strongly encouraged as it would make us more competitive.
Don't you have to be able to show the working to prove how you arrived at an answer? So what if a student uses it to verify their answer, I did the same myself in high school with the "answer" section of the book. Was a very useful tool to show that I was in the wrong direction and that I should see where i'm going wrong.
LOL. So if I understand you correctly, you're saying that Slashdot is at the bottom of the Grand Canyon...
Oooh oooh I know this one. "A River Runs through It".
Do I pass the Slashdot Literature test?
Prove P = NP
Result: (Wait)...(Wait)......(Wait).........(WAIT)
Answer: Probably not
"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"
Obviously, you haven't heard of Gauss or Ramanujan. The former began his mathematical career at the age of 3, correcting accounting errors in his father's business. The latter was a self taught genius who rose from extreme poverty on the strength of his mathematical ideas alone. Had he not died prematurely and his work more accessible to the less gifted, he would have been much more widely known.
In fact there are a great many famous mathematicians from very humble backgrounds, which only goes to prove that you do yourself and humanity a great disservice in perpetuating stereotypes. There is no single path to genius nor is there a single special kind of intellect. Any young student may prove they have talent, if they can learn to think clearly enough.
I'm measuring the student's problem solving abilities, not her ability to do lots of tedious computations in a short amount of time.
Girls have those?
I had a TI-82 for Discrete I and II and Calc I, then a TI-89 for Calc II, as did lots of my fellow students. Nobody ever cared about students using calculators.
High school was a different story. My high school's math department was headed by a very rude and ineffective teacher who drove away any good math teachers [ie, that made her look bad]. She allowed graphing calculators on exams [I had that TI-82 taking Analytic Geometry from her], but she insisted on erasing their memories to make sure we did not have programs on them. I told her "You do not have permission to modify my calculator"--forcing me to borrow a TI-82 from her school-owned arsenal.
Come college, I never really used my calculator's memory to store notes. I have a feeling that most professors realized that while it could be done...c'mon, if you can punch your notes into a non-QWERTY graphing calculator, recall them, and apply them to the questions on the exam, then you obviously know the material--you had to show your work anyway.
In high school, my also-rude-and-ineffective trig teacher made everyone go home and list something like 15 Pythagorean triples. I wrote a program in QBASIC and handed in a printout of 15 Pythagorean triples along with the source code of the program. Needless to say, she got pissed off, even though it was pretty obvious I learned the subject matter.
It boils down to learning the subject matter vs. brain-dumping your way through, whether it's a Master's degree or your MCSE. Ultimately, you'll have a job requiring said skill, and you'll be screwed.
Of course, if your parents bought your way through college, you just wind up President.
uhm.. yes, using "the internet" to get the answer that *you* were supposed to solve *is* cheating.. duh.
That's like saying I shouldn't be charged with cheating if I outsource all my CS homework to India. Sure, in the real world, we can outsource work, but it doesn't mean that *I* know CS because I can pay someone else to do it, and the point of a CS degree is to prove that *I* understand the concepts and that *I* have the technical skills.
Likewise, the point of a math class is that *you* are supposed to know multiplication, addition, whatever.
Input: Do my homework Result: Wolfram|Alpha isn't sure what to do with your input.
--whacky
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.
Perhaps it is for the same reason that those people in engineering/math/science aren't allowed to take pre-written paragraphs on relevant topics into an english/history etc. exam and then stitch several relevant of them together to answer a question.
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.
Can you blame these shills for doing it when /. is so happy to oblige them every time? Mega free advertising to a bunch of gullible fucks!
"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."
Wolfram Alpha goes through the steps of deriving and integrating, including substitutions. The answers for a lot of fundamental calculus concepts are step-by-step what's taught to be correct.
I used to be ok with most calculators until I started looking in detail at what they put in them now. I'm fine with graphing and programming but for some insane reason they now put study cards, book chapters and who knows what else into them. As a result I now have no way of reliably telling exactly how big a library a "calculator" has built in and, just as I would not allow a text book in the exam, I now have to have a easily identifiable way to forbid these electronic libraries. Hence my rules are that any device capable of displaying text characters is forbidden. This is harsher than I would ideally like but it is the only simple (i.e. non-model based) rule that I can think of to reliably prevent these electronic libraries from being used in an exam.
I had a TI-89 back in college and it was great because you could actually type in an equation and have it solve it symbolically. Our school had a list of banned calculators and a blanket ban on anything with a QWERTY keyboard. At the time, the TI-89 wasn't available in the UK so it dodged the ban, other students ordered TI-92s from france so they'd have an AZERTY keyboard.
I did talk to the a fairly senior staff member about it, and his point was roughly:
"If this were the real world and you worked for me, then i'd fully expect you to borrow, plagiarize and use whatever tools will help you get the right answer quicker. My job is to ensure I set exams and assignments where that won't make any difference"
Church-Turing is one of the most beautiful things in all of mathematics (not just CS), imho.
60 years after the birth of applied lambda calculus, rank-and-file developers are just now catching on to Church's side of the computability coin. OTOH, teaching LISP or Scheme for a decade didn't accelerate this process noticeably.
I could be wrong about this, but I think it's just taking a while for our species to come to grips with computability and number theory. Very few people (including CS and pure math instructors) are totally comfortable in all aspects of computability.
Speaking about Wolfram products and math education, I think it is a good moment to remind this
discussion.
http://www01.wolframalpha.com/input/?i=derivative+x+*+sin+(1%2Fx)+x+from+-0.1+to+0.1
That's cool.
The next time I'm flying in an airplane, I won't really care if the engineers got the right answers when designing the plane-just as long as they demonstrated good problem solving ability.
In the spirit of mathematics, here is a counterexample that disproves your "protestant work ethic" concept: angle trisection. The ancient Greeks, who were most certainly not protestants (as they lived before Christianity itself), were unable to figure out how to trisect an angle using a compass and straightedge properly. By improperly using a straightedge (that is, by marking it), it is possible to trisect any given angle, but mathematicians were still interested in the proper way to solve this seemingly simple problem.
Several centuries later, it was proved that the proper way is actually impossible (as was the case for all the "great problems of antiquity").
Mathematics is not about getting the answer, it is about understanding the answer. If a student uses WA to help learn how problems are solved and to explore more advanced concepts (I personally used Mathworld to do this when I was in high school), that is a good thing and should be encouraged. However, judging by my classmates in middle school, high school, and college, I doubt that the majority will do this. More likely, it will just become a new way for students to cheat on their homework and force their professors to give easier curves on tests (since they can say, "look at how well I am doing on my homework, clearly the test was just too hard!").
Palm trees and 8
Sure its easiest to mark a multiple choice test, but to see if or what a student understands and where her problems are, the first approach is to judge the contribution in class. Make them do and explain projects. If a written test has to be at all, make them explain why a certain problem has a certain result or make them prove or explain something.
WolframAlpha won't help with any of that simple because then WolframAlpha would have to *understand* math.
You won't learn much from an easy professor, and three years after you graduate that easy "A" will be meaningless.
Kind of like the rest of your college education. :) It is only needed to get through the interview screening process.
Don't get me wrong - I don't really believe that college doesn't teach anybody anything. However, for the most part college is designed to prepare you to teach college courses the way that you learned it. If you don't plan on teaching college courses for the rest of your life about 75% of everything you do there will be a waste of time.
But, IMHO, if you're an engineer, you probably don't care about the fancy math and the theory behind it, you need the results. Or you're more likely to need to know how to turn a formula into executable code. Beyond that, when I was in college, the debate was whether or not you should be allowed a formula sheet during an exam. IMHO, if you can't have one then the exercise is half about memorization and half about application. Once again, as an engineer, it's pretty rare that you have to remember a formula especially one you rarely use. Commonly used ones become memory with increasing use. Knowing what to do with the formulae is more important. Then the onus is on the teacher to create problems that aren't plug-and-chug but require you to think.
If you read the TOS of WolframAlpha it says that they/it own the copyright to any output generated. Kids using it as their own work should get sued. Problem solved.
It might be a bit over enthusiastic on trying to be helpful, but do note that I asked for the distance. It understood my question, and gave me the correct answer, first. I never even scrolled down.
The reason for my question: Degree Confluence Project
Good judgement comes from experience, and experience comes from bad judgement.
- W. Wriston, former Citibank CEO
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 hope you're not teaching engineers!
To paraphrase some other slashdot comment,
"You build bridge. Bridge fall down. You want partial credit?"
Not to say that partial credit isn't appropriate in largely the manner you described, but being right has to also count, doesn't it?
Alcohol, Tobacco and Firearms should be the name of a store, not a government agency.
How do you expect people to understand probability theory without understanding integration?
No one is (or should be) arguing that calculus should not be taught. Calculus rightly should be in the curriculum for all science/engineering degrees. That said I would argue it is over-emphasized in most engineering/science curriculums. In practical terms it's just not used in all but a few professions on a day to day basis. I'm an engineer with a minor in applied mathematics and my first job out of college was doing Monte-Carlo simulations. Sure, calculus helped me to understand probability, continuous distributions and various other bits of analysis - definitely helpful. Nonetheless I haven't done an actual integral or derivative in 15 years. When I do "use" calculus it is always conceptually rather than actual integration or derivation. I would argue most people could take less calculus in college than is/was required and more of other branches of math (statistics especially) with good results.
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.
When the axe came to the forest, the trees said, "Look out - the handle was once one of us."
I see this as very simple.
Some classes, you're supposed to show you understand what integration, derivatives, etc. actually MEAN.. not just how to press the right buttons on a calculator. You really need to show your work to show you know how to do it. They generally therefore ban using a calculator, matehmatica, etc. to do it for you in these classes. One poster said Wolfram Alpha will show steps; well, if you use this to cheat, this'll bite you in the ass at test time if you haven't actually learned how to do the concepts.
In later classes, you're expected to know how to do this stuff already, and are doing more complex mathematical manipulations. These classes did not expect the level of detail of "showing your work" for every single derivative, etc. ( 1. You were supposed to know how to do that already. 2. A 2 or 3 page assignment would balloon to like 50 pages with that much detail, which would be unwieldy for the grader if nothing else.) These classes allowed Mathematica and the like.
I've taken both types of classes, and in context, both views make sense.
Not to say that partial credit isn't appropriate in largely the manner you described, but being right has to also count, doesn't it?
That depends on whether the aim of the course is to
In other words, do you want the right answers or the right questions? Which is going to help you the most in making bridges that stay up? Can you learn one of them on the job or by yourself or in some other way not requiring you to spend (valuable) otherwise-university-dedicated hours on it?
http://www.sagemath.org/
Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.
If a computer can solve the problem, students shouldn't have to exhaustively memorize the mechanics of the method. What's the excuse? That later on the students won't have the computer available as an aid? Still today the world is filled with highly educated old people who would not be able to grasp the functioning of a system like W|A, and who still prides themselves of how, in their time, they really learned math because they did not have calculators and had to solve their fancy arithmetic by hand.
Instructors should stop being lazy and ask questions that require some thinking, questions that a computer would not be able to answer unassisted by a human who fully understands the problem. Within the questions, make the students show that they understand the concepts behind the method, rather than asking for endless repetition of an algorithm with pencil and paper, and later complaining that they found a more efficient way of doing it.
Yes, but if you are willing and able to successfully cheat on exams, then the entire issue about Wolfram-Alpha to cheat on homework is moot.
A work that expires before its copyright never enters the public domain and thus enjoys eternal copyright protection.
>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.
The problem with this approach is time. In addition to the time it takes to simply do the problems, I would have to then start an investigative process to try and determine if I got the right answer or not. While this would certainly lead to a deeper understanding of the process, I don't have the time for it. I simply want to learn the process at hand and knowing whether or not I got the right answer allows me to either move on with confidence right away or right away begin analyzing my work to check for errors.
Further, this all assumes that I understand the material well enough to understand what kinds of answers make sense. Frequently I don't.
>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.
When you eliminate the answers for half the problems, I don't bother doing those problems, unless they are required as homework. If I can't tell if the answer is right, then as often as not I've done the problem wrong, and now I've taught myself how to do the problems incorrectly.
Fortunately, thus far I have been able to find a solution manual for my calculus texts online.
If you simply randomly tinker with your work until the answer matches, with no understanding of what you did, then you will fail the exams.
A work that expires before its copyright never enters the public domain and thus enjoys eternal copyright protection.