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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.'"
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.
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.
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.
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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.