Wolfram Alpha Rekindles Campus Math Tool Debate 339
An anonymous reader sends in a story about how Wolfram Alpha is becoming the latest tool students are using to help with their schoolwork, and why some professors are worried it will interfere with the learning process. Quoting:
"The goal of WolframAlpha is to bring high-level mathematics to the masses, by letting users type in problems in plain English and delivering instant results. As a result, some professors say the service poses tough questions for their classroom policies. 'I think this is going to reignite a math war,' said Maria H. Andersen, a mathematics instructor at Muskegon Community College, referring to past debates over the role of graphing calculators in math education. 'Given that there are still pockets of instructors and departments in the US where graphing calculators are still not allowed, some instructors will likely react with resistance (i.e. we still don't change anything) or possibly even with the charge that using WA is cheating.'"
iirc (Score:4, Interesting)
Instant Results? (Score:5, Interesting)
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.
Re:Sweet, let's try it out! (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.
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.
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 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.
Misguided Universities (Score:2, Interesting)
The professors who are afraid of calculators and automatic problem solvers are the same as those who think class attendance matter. A university, if anything in the world, should be a place for learning, not a very expensive kindergarten. In that perspective the activities of the students are irrelevant: if they learn practical abilities through Wolfram Alpha, great. If they don't, that's their problem. Ultimately the student is the paying customer. Professors much too often slide into this illusion of grandeur where they think the student owes them anything or needs to satisfy the professors when it's in fact the other way around.
If you choose to go to and pay for a university education, do it your way. If Wolfram Alpha gives you the insights you need, then that's the right tool for you. If your style of learning is snoozing under a tree, occasionally watching an apple fall, then do that. If you never go to a class in your life but you come out as the next Einstein you have succeeded. If you waste all your time 'cheating' that's your problem. You're the boss, you're the one paying for it.
And before somebody brings it up, grades are arbitrary statistics based on a flawed system. If they are affected by something as simple as the use of Wolfram Alpha that's just another demonstration of how little real world value they have.
Re:I don't see how this matters (Score:1, Interesting)
This. A full 6 years after graduation and this is what I have realized.
Knowing *when* to integrate is far more important than knowing how. If you dont know when you have to, its fairly useless to know how.
Once you have been exposed to the underlying theory, unless you are going into more theoretical work, there is no reason to not use MATLAB to solve that system of Diffy Q's. In the real world, when your on somewhat of a schedule, and other peoples money is on the line who do you think is going to get the contract? The guy who just solved the circuit equations by hand, and now knows the values for R, C, L etc? Or the guy who used Spice and has a working prototype of the design to show?
For most of us we simply need to get work done. We learned the theoretical underpinnings once upon a time, and if need be we can spend a couple hours (or weekend) and brush up on a specific topic. But, even that weekend pales in comparison to the time spent solving *everything* by hand. So there is no good reason to make students believe that upon graduation and employment, they will be sitting in an office working everything out by hand.
Slightly off topic, but food for thought nonetheless: If you want to talk about reasons why engineering and science enrollment are down, or why many leave those fields of study, this may be a good place to start.
I belong to that pocket of math instructors... (Score:2, Interesting)
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.
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.
Re:iirc (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:I don't see how this matters (Score:4, Interesting)
Wolfram Alpha has a "Show steps" button.
Calculators in class? (Score:1, Interesting)
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.
Re:iirc (Score:3, Interesting)
If these students are required to work everything by hand, there is a chance they are being given the wrong approach. As an ME student, I value the ability to work everything by hand, but students requiring only a cursory overview of calculus will not remember or use many differentiation or integration methods. Teach them what they need to know - when you confuse people they give up and won't learn, and that is when they start using the calculator as a crutch.
Re:iirc (Score:2, Interesting)
Re:I don't see how this matters (Score:2, Interesting)