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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.'"
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.
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.
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.
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".
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You've described a situation, but I don't see a reason there.
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 $.
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I don't really see how it's possible to not know how to perform a simple integration by parts by hand and still understand the concept behind it, sorry.
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 the same thing.
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.
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'm not sure what you're talking about -- mathematics is taught lots of different ways: there is no single, monolithic, method for "how math is taught."
This is the way Bi-Coloured Python-Rock-Snakes always talk.
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.
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.
That's what stupid people say. And if you don't think going to class is important, then you will never be successful. You will learn sooner or later that in order to get real things done you need to participate with others on a consistent basis. At this point I don't think you will care, but the challenge of any program is to be successful within the program. It's not about making up arbitrary rules for yourself for your own convenience. This is not to say independence is not important. You don't need to sign up for classes if what you want is independence.
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.
We try to teach the engineers, physicists, etc. about where the methods that they are using are actually coming from. Admittedly, this is sometimes a forlorn task, but the same is true of what these demographics try to teach to students not of their field. Mathematicians are aware that other fields exist, and that approximations are the name of the game in the real world. This is nothing new. Please try to get up to date about how mathematicians think about the world. It's (clearly) not useless if you think about it for a modicum of time, and these notions of "purity" are (usually) in jest to a certain degree. Of course, there are minorities who are obsessed with this notion, but such is true of any field.
I've never once used a single scrap from calculus (computer science major).
Why does A=pi*r^2? Because integral from 0 to r of 2*pi*a*da=pi*r^2. See disk integration for the sphere equations.
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The student is not a paying customer in the same was as they are in starbucks. Student satisfaction is obviously important, but that shouldn't come at the expense of academic rigour: the student has just as much of an obligation in the opposite direction to learn the material and demonstrate that they have learnt the material to an acceptable standard - at least if they want a qualification at the end. It undermines the whole enterprise and renders the qualification worthless otherwise - what use is a degree if students have no obligation to actually demonstrate they have learned anything or participated. If you don't think you owe the institution anything, then the institution doesn't owe you a degree - it's supreme arrogance to think otherwise even if you smart.
Class attendance does matter... there are outliers but there's a pretty strong correlation between learning the material and (shock, horror) attending the class. It can be one way for students to satisfy professors that they are participating and learning the material, and it can often be an effective way to stop a downward spiral of worsening attendance, lowering standards, and poorer educational outcomes.
Grades are somewhat arbitrary statistics based on a flawed system, yes, but it's an enormous logical leap to say that they have no value. I wonder how you would have people demonstrate their knowledge. When the assessment is half-decent and the expectations are clear, they are still very indicative of how well a student understands and has mastered a body of material.
In short, if you don't want to actually participate in classes, or you think that actually being required to do the work is somehow an abrogration of your freedom, don't go to university, simple as that, the whole enterprise will be better off without you.
"Teach it [calculus] at that level and leave us web developers alone."
There was no web when I graduated, had to learn it "on the job". I have never heard of anyone learning calculus "on the job" but it would explain why buildings and bridges sometimes fall down.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
Yep, the vast majority of people who have been taught calculus are unable to recognise it's fruit.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
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.
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.
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