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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

#111

Post by JadeNB »

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…

I'm with my sibling commenter impendia (https://news.ycombinator.com/item?id=14719497), and am also a math professor.

My way of saying it is that it's great if you get help from any source you can, but it's way too easy to get something that seems helpful (because it makes short-term goals easier to achieve) while being damaging in the long run. It's fantastic if you had the personal discipline to use a solution manual to deepen your understanding, but there are lots of students who will use the solution manual as a copybook—the material in it going, as the saying goes, from page to pen without passing through brain on the way. Since I, as a teacher, don't have a ready way at the beginning of the semester to distinguish the students with your discipline from those without, I'm just going to discourage everyone from using solution manuals—but, as long as your homework solutions aren't copied from it, I don't care much if you go against that advice.

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

#112

Post by Robotbeat »

HillaryBriss wrote: post #90
SteveCoast wrote: post #27

When I was 18, back in 1999, I had an internship at WRI (Wolfram Research) in Illinois. I'd applied armed only with a library copy of the Mathematica book, so they sent me a CD with Mathematica on it. I made some demo things and got a slot, and flew to Champaign. I worked on polyhedra for a summer, writing code that could unroll a polyhedral model to its 2D net. Find the volume, the number of faces and all kinds of s…

> ... why don't you use spoons instead? reminds me of one of the arguments against minimum wage hike theory: if raising the minimum wage makes workers better off and has absolutely no drawbacks for anyone, why raise it to a mere $15/hour? why don't we do some real good and crank it all the way up to $100/hour?

And why not eliminate it, if it's bad? That way we can pay people to dig with spoons instead of expensive backhoes.

Seriously, though, to answer the question: there's a point where a raise in the minimum wage will stop being helpful, and everyone who supports the minimum wage understands this.

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

#113

Post by xiaoma »

adamnemecek wrote: post #93
btilly wrote: post #89

Earlier quoted context omitted.

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…

> 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.

> "I think that if you see a complex equation, you should be able to roughly imagine it in your head."

This breaks down in many cases. What if your equation involves complex numbers for each component? What if it's an eight dimensional space or perhaps a multi-hundred dimensional space for recommender system?

At some point, you have to be comfortable with more abstract representations.

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

#114

Post by JadeNB »

Rjevski wrote: post #105
vlasev wrote: post #73

Earlier quoted context omitted.

Plug and chug with Wolfram Alpha is very similar to plug and chug Stack Exchange answers in your code base.

Math and programming are a bit different though - to my knowledge in math you're not dealing with malicious users trying to give you incorrect input in hopes of exploiting bugs in your algorithm. Edit: but to be honest if you needed to give the result Z for a set of inputs X and Y without worrying about invalid/malicious input, then a Stack Exchange copy/paste is totally fine by me.

> Math and programming are a bit different though - to my knowledge in math you're not dealing with malicious users trying to give you incorrect input in hopes of exploiting bugs in your algorithm.

But in fact you are! Actually it's even worse; in programming, you are just up against the ingenuity of actual human (or at least humanly programmed) users, whereas, in mathematics, you are up against the whole of 'reality' (in a Platonic sense). A whole tower of consequences will be built upon one mathematician's work, and, even if no human can spot the flaw in that work, if it is there then 'reality' will find it, and somewhere in the chain of consequences there will be an error that will bring the whole thing crashing down.

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

#115

Post by adamnemecek »

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…

I mean this particular equation not really no but that might be because I haven't done much general relativity. But I can kinda visualize other somewhat complicated equations.

Sure but then you are giving an advantage to the more visual people no? Can't I just flip your argument?

Yes, symbols are useful but you should have an understand of what they are actually doing.

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

#116

Post by fnbr »

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…

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").

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

#117

Post by JoeAltmaier »

yequalsx wrote: post #74
JoeAltmaier wrote: post #61

Earlier quoted context omitted.

Sounds like Mathematica is the way to go then? Because it turned out students who could do the problems. The 'old paradigm' leaves most behind, which serves no one.

Students could not do the computer based problems. Save for a few. More students get through with the old paradigm. Old paradigm problem. Here is f, using the definition of derivative find f'. New paradigm problem. Here is f. Here is a Mathematica function defining f(x+h) - f(x) divided by h. Graph this function for appropriate values of x and h to show whether or not f is differentiable at 2. The old paradigm proble…

Thanks for the clarification

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

#118

Post by mikeash »

roumenguha wrote: post #55
SteveCoast wrote: post #27

When I was 18, back in 1999, I had an internship at WRI (Wolfram Research) in Illinois. I'd applied armed only with a library copy of the Mathematica book, so they sent me a CD with Mathematica on it. I made some demo things and got a slot, and flew to Champaign. I worked on polyhedra for a summer, writing code that could unroll a polyhedral model to its 2D net. Find the volume, the number of faces and all kinds of s…

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.

That's going to depend heavily on the problem in question. Multiplying large numbers? Probably. Computing the fifth root of pi to eight decimal places? Probably not so much. (Maybe there's some quick way to do that second one mentally, substitute something different if so.)

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

#119

Post by adamnemecek »

xiaoma wrote: post #113
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.

> "I think that if you see a complex equation, you should be able to roughly imagine it in your head." This breaks down in many cases. What if your equation involves complex numbers for each component? What if it's an eight dimensional space or perhaps a multi-hundred dimensional space for recommender system? At some point, you have to be comfortable with more abstract representations.

I think of complex numbers as just points/vectors.

As for multidimensional spaces, you might not be able to visualize all the dimensions at once but by doing them three dimensions at a time, you can go Pretty far.

You should check that the abstract representations still make sense intuitively.

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

#120

Post by limeblack »

opaque wrote: post #75
SteveCoast wrote: post #27

When I was 18, back in 1999, I had an internship at WRI (Wolfram Research) in Illinois. I'd applied armed only with a library copy of the Mathematica book, so they sent me a CD with Mathematica on it. I made some demo things and got a slot, and flew to Champaign. I worked on polyhedra for a summer, writing code that could unroll a polyhedral model to its 2D net. Find the volume, the number of faces and all kinds of s…

> working with what I still think is one of, if not the, best language ever. Really? Mathematica is amazing and uncontested for symbolic algebra, but writing anything more than a notebook/paper is a nightmare. In built stuff is good, but functions you have to define yourself instantly become an incomprehensible mess of parentheses. Leaving aside the fact that it's a propriety language and the many flaws of its eponym…

I would agree the language can be confusing but they language isn't exactly propriety. There are open source implementations of it like mathics.net
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