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.'"

Comments

"Pockets of instructors"?

[Anonymous Coward]

Are they protected?

Re:"Pockets of instructors"?

[Anonymous Coward]

Only if they have tenure.

Re:"Pockets of instructors"?

[Profane MuthaFucka]

I don't have tenure, but if I have two fives, does that count?

iirc

[langelgjm]

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...

Re:iirc

[vux984]

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:iirc

[T Murphy]

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 $.

Re:iirc

[FishWithAHammer]

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:iirc

[p!ngu]

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.

Re:iirc

[Thinboy00]

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.

Re:iirc

[TapeCutter]

"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.

Re:iirc

[TapeCutter]

Yep, the vast majority of people who have been taught calculus are unable to recognise it's fruit.

Re:iirc

[T Murphy]

My point is unless you are in engineering/math/science you typically just need to understand the concepts behind calculus so you can understand functional analysis, finding maxima and minima, and simple differential equations. At least that is my impression of business/econ types. Should they need integration by parts, they simply have to get a computer do it for them. Maple is powerful, but it won't tell you WHY a firm maximizes profit when marginal cost equals marginal revenue - the student has to know the concepts in order to write a few sentences reasoning that conclusion.

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

[Phoghat]

When my kids were in grade school, they were sort of introduced to calculus in the second grade (in the 70's) by a very progressive teacher (a nun no less). She also taught other things like using an abacus. When they were in college they didn't breeze through it, but had a much easier time because they knew the basic concepts. Sort of like a child learning languages at a very early age. Sigh, Sr. Marianne, I wish you taught me in 2nd grade.

Re:iirc

[biryokumaru]

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.

I don't see how this matters

[InstinctVsLogic]

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.

Re:I don't see how this matters

[The Snowman]

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:I don't see how this matters

[sexconker]

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.

Re:I don't see how this matters

[Chris Burke]

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:I don't see how this matters

[Chris Burke]

You CS whinies had it easy. For us EEs, the exams came pre-tanked.

Well in my CE department, we came to the exam pre-tanked!

Re:I don't see how this matters

[Stiletto]

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 with. But who? Since anyone you might collaborate with also believes the above, they won't know how to solve the problem either. Who would write the reference books? Same problem.

At some point the buck stops at the individual. You need to know how to solve the given problems, by yourself. That's why we do tests, and that's why you (generally) can't collaborate or consult references.

Re:I don't see how this matters

[Chris Burke]

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".

Re:I don't see how this matters

[Anonymous Coward]

In Soviet Russia, tank exams you!

Re:I don't see how this matters

[node 3]

Wolfram Alpha has a "Show steps" button.

Re:I don't see how this matters

[node 3]

Furthermore if, in reality, I find a faster and more efficient way of completing my work I don't get fired for "cheating". I get a raise and possibly a promotion if I keep improving things.

Actually, in the real world, you just get more work.

Re:I don't see how this matters

[Pseudonym]

In the real world you can use any software you wish.

Oh, you poor, naive person.

Let me introduce myself. I'm from the real world. Let me explain how things happen here.

We have to deal with tricky problems. Sometimes, a function has more than one formal integral, and some forms are more appropriate than others in different situations. Good luck coaxing your CAS into giving you exactly what you want.

We have to deal with deadlines. If you can solve a problem in two minutes on paper, that's usually quicker than loading up most software packages and trying to get your equation into the syntax of the system. (Naturally, no two systems use the same syntax.)

Even worse, we have to deal with software licensing. Mathematica and Matlab ain't cheap. Software vendors try to argue that you're a commercial institution, not a research institution, so they can gouge you for licence fees. Cross your fingers and hope that there is a small enough number of people using the software concurrently so that you can get in. Otherwise, you're screwed.

Re:I don't see how this matters

[Brian Gordon]

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:I don't see how this matters

[Chris Burke]

And yet another person interprets "in real life you can always use references" to mean "in real life you don't have to know anything without a reference."

Re:I don't see how this matters

[Chris Burke]

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 25 problems, nobody shouts "time!" and forces you to stop such that the problem remains unsolved. Not on a one-hour timescale, anyway.

In other words, what you do is nothing like taking an exam.

If you need to take ten minutes, possibly digging through reference materials, to solve a simple problem

Having artificially simple problems (such that 25 can be completed in an hour long exam) is exactly one of the things I was saying was unrealistic about exams. In real life, problems are complex, sometimes but not always decomposable into simple problems suitable for an exam, but in any case more like a class project than an exam.

And if you never encounter a simple problem that requires a reference, as in you can contain all the knowledge ever required for your field in your head at one time (example of simple reference-requiring problem: What's the opcode for a MOVDQA), then the job itself is pretty simple.

Re:I don't see how this matters

[swillden]

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 technically more like assignments which constituted a major part of your grade, but they sure felt like exams, even when I was working on them at home in the bathtub (my favorite place for the part of the thinking process where no paper or pencil is required; after the nature of the problem is thoroughly internalized, but the key structure not yet apparent). My wife remembers those tests, too, mostly me staring blankly into space for hours on end until I finally shouted "Gotcha!" as the last pieces fell into place.

Wolfram Alpha would not have been the slightest assistance with those tests :-)

Re:I don't see how this matters

[Hognoxious]

and had just drunk about 4-6 ounces of desert wines

I assume they were rather dry?

Re:I don't see how this matters

[vectorious]

This is basically the entire teaching method of Oxford University science and maths undergraduate degrees, and even to some extent the arts courses. You have a week for 6-8 questions, have to go away find out what on earth they are talking about, have your "gotcha" moment, and then report back at the end of the week in a 2 student to one teacher tutorial. You are not even expected to be able to do it all - you are expected to do what you can and learn from the tutorial the tricks and tweaks from what you could not.

Oh the horror!!

[SBrach]

How did you play tetris during class?

Re:Oh the horror!!

[Thinboy00]

By hand, on graph paper with pen/pencil, with an egg timer, and a d20 (or dN) to pick the next tile.

Protestant Work Ethic

[unlametheweak]

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.

Re:Protestant Work Ethic

[Chris Burke]

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.

Instant Results?

[Kyune]

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.

Re:Instant Results?

[XanC]

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

Oh man

[Caboosian]

I just don't know if I can deal with all this math-debating.

Too general

[dexmachina]

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:Too general

[honkycat]

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.

Damn you Wolfram!

[Anonymous Coward]

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"

Sweet, let's try it out!

[l00sr]

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!

Re:Sweet, let's try it out!

[Keith_Beef]

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.

Re:Sweet, let's try it out!

[selven]

Well, at least it knows what the world's population per capita is!

Is this really a problem?

[Jugalator]

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 the book is cheating!

[GWBasic]

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!

a physics teacher's perspective

[bcrowell]

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.

The ability to check your work is crucial!

[maillemaker]

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.

Re:The ability to check your work is crucial!

[jhp64]

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."

Misguided Universities

[Siker]

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.

I belong to that pocket of math instructors...

[Mao]

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

[Sycraft-fu]

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.

As long as engineers have to take literature...

[Fred Ferrigno]

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.

I had to learn trig with tables in mid/late-80s

[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.

Re:Stop ignoring what I say

[Chris Burke]

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.

I'm a math professor, and I don't care about Alpha

[onionman]

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.

Let me see now

[ClosedSource]

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.

Calculator...or electronic book?

[Roger W Moore]

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.

Re:Calculator...or electronic book?

[wisty]

You mean, your students are actually there to learn academic skills? Heretic! They should be learning practical things, like, um, leadership skills. Or networking.

Re:Stop ignoring what I say

[rpillala]

it's also testing your exam-taking ability.

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.