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Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

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Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#131

Post by posterboy »

btilly wrote: post #110
adamnemecek wrote: post #93

Earlier quoted context omitted.

> So no, we won't lose equations and symbols. Ever. They are essential, and there is no possibility of real understanding without them. I didn't say get rid of them. But I think that if you see a complex equation, you should be able to roughly imagine it in your head. Working only with symbols won't get you there.

But I think that if you see a complex equation, you should be able to roughly imagine it in your head. Working only with symbols won't get you there. You're wrong. To take a real example, visualize G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }. I dare you. That's Einstein's field equations for General Relativity. I don't visualize a system of 2nd order partial differential equations involving man…

You might be thinking visually without even recognizing, because to call that kind of imagination visual (as in optical) is misleading. A Hydrogen 2 molecule has 6 degrees of freedom already, give that color and you have 8.

There was a story on HN about activity in the "visual" system of blind people. Here is a similar story google spit out: https://news.ycombinator.com/item?id=14720225

Commutative diagrams are a development that has applications in algebra, too. I'm currently reading Physics, Topology, Logic and Computation: A Rosetta Stone (J. C. Baez, M. Stay) https://news.ycombinator.com/item?id=12317525

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#132

Post by posterboy »

adamnemecek wrote: post #121
fnbr wrote: post #116

Earlier quoted context omitted.

Hmmm. I would disagree with you. It is impossible to visualize the equations as that isn't possible to do in 3 dimensions, but it is possible to develop an intuition. After taking functional analysis, for instance, I began to develop an intuition for how function spaces work, and was able to visualize that to a certain extent (for a given definition of "visualize").

You get it. Few people understand what's happening in every dimension at every point, but getting a feel is doable.

The whole argument is that its not doable without the right tools and that visualizations are a very good tool for this.

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#133

Post by posterboy »

btilly wrote: post #89
adamnemecek wrote: post #33

Earlier quoted context omitted.

> we need to learn 'the basics' and survive without tools to some degree This is the wrong approach. There's no way you wouldn't understand math much better with these tools. I'm hoping that in the future, math will be less about equations and symbols and more about graphing and being able to move around in the spaces described by the equations. I would draw an analogy with a compiler. After using it for some time, y…

Both are true. Clearly we are more productive with the tools. However it is very, very easy for people to see the tools as magic. At some point we need to actually understand what it is that we are doing. For which those equations and symbols are essential. Yes, the computer can draw a pretty picture. Pretty pictures are helpful in conveying information. But they are a horrible way to understand inherently complex to…

> Clearly we are more productive with the tools. However it is very, very easy for people to see the tools as magic. At some point we need to actually understand what it is that we are doing

And that's why computer science needs to be part of the math curriculum in schools asap.

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#134

Post by posterboy »

scarmig wrote: post #94
roumenguha wrote: post #55

Earlier quoted context omitted.

To add another point, my A-Level teacher always said anything the calculator can do, you can do, and just as fast. And then she chose a question from the book, had one of us start typing, and she started at the board solving the same thing. She finished first. Not by much, and obviously the calculator is the faster choice more often, but she finished first.

Reminds me of the story of Feynman vs the Abacus. [1] Though, as a story, the conclusion he draws is pretty self-congratulatory and bothers me a bit. The substrate on which you implement an algorithm like arithmetic doesn't really speak to whether you "know numbers." It's like the high schooler thinking being very good at computing integrals makes you good at math. [1] http://www.ee.ryerson.ca/~elf/abacus/feynman.htm…

Being powerful, ie good in something, is a function of Work over Time, so if you are good without much effort, that implies some sort of talent I think.

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#135

Post by posterboy »

makmanalp wrote: post #13
res0nat0r wrote: post #2

You may cheat all you want on your homework, but if calculus tests are like they were when I was in college, taking your exam with no notes or calculator, if you've only cut and pasted from Wolfram Alpha all semester is going to lead you to getting an F in the course.

This - I think part of the issue is to stop homework from becoming busywork for grades. If everyone has the understanding that this is supposed to nail down and self-test understanding of material taught in class, then there's no reason students should "cheat". To this end, I like the approach of mentioning repeatedly that homeworks are for the students' own good, then give a test early on to make students quickly un…

Don't announce it, or it will work only for one or two years.

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#136

Post by jandrese »

_jal wrote: post #26
jandrese wrote: post #10

Earlier quoted context omitted.

My impression is that the article is about highschool students, where homework tends to be on the order of 75% of your grade simply because you get so much of it. If someone were really serious about abusing the service they could pull out a C in the class even with hard failures of the tests.

> where homework tends to be on the order of 75% of your grade I think I found the problem.

It's hard to balance when you have an hour of homework assigned every day, but only get tested about once a month. So you have 20 hours of homework vs. a 30 minute test.

The difference in magnitude ends up being too much. Either each homework assignment is worth almost nothing or they outweigh tests.

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#137

Post by ntsplnkv2 »

watbe wrote: post #4
res0nat0r wrote: post #2

You may cheat all you want on your homework, but if calculus tests are like they were when I was in college, taking your exam with no notes or calculator, if you've only cut and pasted from Wolfram Alpha all semester is going to lead you to getting an F in the course.

Agreed. This headline makes it sound like they're cheating in exams, but this is take-home assignments we're talking about. If wolfram alpha wasn't available, they'd be asking friends or posting in maths forums. Wolfram alpha is simply more efficient at this job but all take-home assignments have this problem inherently. Students just need to be aware that they should learn from solutions provided by wolfram alpha (t…

Exactly: Why is homework considered something that can be "cheated" on anyway? The whole purpose is to get practice and learn the material.

Just make the tests challenging-the ones who actually did their homework will pass. The ones who didn't won't.

Wolfram Alpha helped me many times-sometimes you're simply stuck on a problem and no one is there to help. But like anything, you can use it to cheat and not do work, or you can use it to help you learn more.

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#138

Post by defective »

williamstein wrote: post #106
Rjevski wrote: post #56

Earlier quoted context omitted.

Even if this was true, what's the problem? He built a successful business that many people find useful, and that's good enough for me.

I respect the abilities and accomplishments of Wolfram. My problem with the statement I quoted from the article is that I suspect it is bullshit; I think Stephen can do long division, and much much more...

"I never learned long division, and look at me." -- Stephen Wolfram

http://www.stephenwolfram.com/media/meet-inventor-who-makes-...

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#139

Post by aphextron »

throwawayjava wrote: post #78
deft wrote: post #65

Today I learned you can cheat on homework. So apparently giving up and having the wrong answers (or no answers at all) is what professors would prefer. Cool :)

> So apparently giving up and having the wrong answers (or no answers at all) is what professors would prefer. Cool :) It's much easier to correct known unknowns than unknown unknowns. The best advice I was ever given as a student was "Pretend like you'll get an automatic A on your report card and treat your grades as a feedback mechanism for figuring out what you do and do not understand. Just focus on learning." As…

>It's much easier to correct known unknowns than unknown unknowns.

This assumes you'll get any kind of personalized feedback and instruction in a lower division maths course. Good luck with that at a public university.

Re: Wolfram Alpha Is Making It Extremely Easy for Students to Cheat

#140

Post by gregmac »

impendia wrote: post #96
captain_clam wrote: post #76

In my two semesters of college math, I've gathered that the faculty has something of a phobia to, if not wolfram in particular, students' access to help outside of the department. Homework problems were oftentimes deliberately difficult, and attending tutoring/office hours was almost certainly necessary for most students to master the material. I got my hands on an instructor's manual of the textbook, and it was a tr…

> the faculty has something of a phobia to ... students' access to help outside of the department. Math professor here. I am most certainly happy if my students get help outside the department, and I think my attitude is quite typical. We can be a little bit wary of some kinds of help. Too much math teaching consists of "If you see a problem that looks exactly like X, here are the steps you should memorize to solve i…

> Too much math teaching consists of "If you see a problem that looks exactly like X, here are the steps you should memorize to solve it."

A significant amount of math testing is basically checking if you've memorized some theorem (and then can solve it), so is that surprising?

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