Wolfram Alpha Is Making It Extremely Easy for Students to Cheat • Hacker News Board

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

#121

Post by adamnemecek » Fri, Jul 07, 2017, 4:45 PM UTC

fnbr wrote: post #116

btilly wrote: post #110

Earlier quoted context omitted.

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").

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

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

#122

Post by Veratyr » Fri, Jul 07, 2017, 4:48 PM UTC

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…

> But, it would have been nice to use them in some contexts and not just deny their existence.

My high school classes in Victoria, Australia, had tests and exams both with and without TI CAS (graphic calculator that also does algebra and calculus with a pretty screen) and I agree that it's pretty nice. Interestingly, I think our curricula were based on the UK's originally.

I think it's similar to learning all the simpler math. You're taught to add large numbers on paper but in the end doing it with a calculator saves you a lot of time and effort. Learning to use a CAS or Mathematica or the like seems essential if you're going to be working in a field that uses calculus for practical things like engineering, medicine or finance.

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

#123

Post by aesthetics1 » Fri, Jul 07, 2017, 4:53 PM UTC

hguant wrote: post #34

I fail to see the problem here. In a curriculum that takes the joy out of math and attempts to reduce the student's mind to a calculation machines, students employed a calculation machine. I understand the arguement that math is important, but the way it's taught in America, even at the AP level, is criminal. It boils down to "if you see this pattern, apply these steps" without any effort at going beyond. We teach "h…

This drives me crazy in my mathematics courses. Sometimes I just do not recognize the pattern, and tools like Mathway or Wolfram Alpha can say "right here dummy" and give me the first step. It is not always about cheating, but seeing the steps for solving the problem logically outlined. I often back myself into a corner working out a difficult problem and need a lifeline.

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

#124

Post by gautamdivgi » Fri, Jul 07, 2017, 4:55 PM UTC

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…

I use alpha quite frequently. I have these big formulae that need differentiating/integrating (non-linear solvers, jacobian matrices, etc.) for a paper I'm looking to publish. Now, the algebra kind of gets seriously tedious and error prone. Here alpha comes to the rescue. I don't have the budget for a complete mathematica package. So, in the end I take the results and use scipy/numpy to write the code to use them in numerical computation.

So, to that end I agree here. They are absolutely wonderful tools if you know what you're applying them for. However, they can be pretty bad if you're trying to use them to cheat (just like everything else).

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

#125

Post by losteverything » Fri, Jul 07, 2017, 4:55 PM UTC

The big issue to me is things that matter take effort.

So many things (like math answers) are made so available with no effort.

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

#126

Post by vmilner » Fri, Jul 07, 2017, 5:05 PM UTC

"while a few were still using it at their jobs as engineers or quantitative analysts"

Er... which is a good thing, surely?

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

#127

Post by cgoughnour » Fri, Jul 07, 2017, 5:13 PM UTC

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.

Well, she certainly proved that there's at least one problem whose solution she can sometimes produce faster unaided than at least one high school student with a calculator.

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

#128

Post by btilly » Fri, Jul 07, 2017, 5:15 PM UTC

adamnemecek wrote: post #115

btilly wrote: post #110

Earlier quoted context omitted.

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.

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

Sure, you can flip the argument. You'll be wrong, but you just did it.

People naturally lean towards understanding using different methods. Each mode of thinking has strengths and weaknesses, and so do people. Some things are better understood visually. Other things not. Some things have the best way of understanding varying by person.

So yes, on some things you'll have an advantage over me because you're visual. On some things I'll have an advantage over you because I probably understand complex abstract relations more naturally than you do. And your insistence that everyone is best off trying to think like you do is completely misguided.

Anyways I've explained my position enough. If you don't wish to get it, you won't. I'll let other people take over the task.

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

#129

Post by btilly » Fri, Jul 07, 2017, 5:20 PM UTC

HillaryBriss wrote: post #98

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…

> we won't lose equations and symbols. Ever. They are essential, and there is no possibility of real understanding without them. i don't know. sometimes i think these symbols and equations are just machinery created by deeply talented, deeply insightful people to help the rest of us arrive at correct statements and give us a little glimpse of a vast panorama of truth which their minds see intuitively, unaided by all…

Yes, and no.

Good mathematicians and scientists that I have personally known have a wide variety of styles of understanding and thinking. The first and most basic divide in mathematics is between people whose natural inclination is algebra versus analysis. The best at analysis seem to have a deep intuition like what you project. The best at algebra operate pretty directly with symbol manipulation.

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

#130

Post by pletnes » Fri, Jul 07, 2017, 5:24 PM UTC

There's a significant point a lot of people are missing. In e.g. physics and chemistry, the math is not the point. Using e.g. Wolfram Alpha is great if it allows students to solve larger and more complex problems, without sitting there solving integrals over and over (for instance).