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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

#91

Post by NamTaf »

Teach and test for understanding why and how the answer comes to be, not what the answer is. Maths education, in my experience, relies too much on testing of the arithmetic rather than the logic. This just results in plug and chug because it's lazy testing and students apply lazy solutions.

Good examiners will ask students questions that make them think about why and how, not what the answer is. These often don't even need algebra or arithmetic because it assumes students know the equations and instead goes a level deeper to test understanding of why those equations are the way they are.

I had the gamut in uni. I found that engineering more often successfully tested understanding as I describe above. Some didn't; my thermo was a case of 'learn how the equations work, then read the right graphs and go' but particularly some of my fluid and aerospace courses were great at asking questions that really tested deep understanding of the theories.

One good example of this that I came across more recently is some of the edX courses that used to exist featuring Walter Lewin (before his sexual harassment came to light). He was very successfully able to question his students on the why and how, not just the what. This actually proved even more important in the MOOC environment, where you can't as tightly control the environment in which students undertake examination.

It's hard, it requires good lecturers really spending a bit of time devising questions as well as supporting their tutors as they teach the students, but it's possible.

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

#92

Post by HillaryBriss »

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.

sounds like she proved that she could do it just as fast as a calculator. good thing i wasn't in that class. i would have proved her wrong: i couldn't out compute the calculator.

then again, they wouldn't have let me in that class in the first place.

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

#93

Post by adamnemecek »

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…

> 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.

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

#94

Post by scarmig »

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.

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.html

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

#96

Post by impendia »

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 it."

But we don't care per se if you can solve problems of the shape X, Y, or Z. We want you to develop your skills to the point that all of these lie naturally within your skill set, that you could do them even if you've never seen one exactly like that before. As such, some kinds of tutoring can be counterproductive.

But most aren't. In my opinion your professors' attitude was quite foolish. Kudos to you for seizing the initiative and figuring out for yourself how to best learn the material.

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

#97

Post by tree_of_item »

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.

> my A-Level teacher always said anything the calculator can do, you can do, and just as fast.

This is obviously false, and I don't really understand the point of saying this.

Plus, the benefit of using a computer is that computation is effortless, letting you use more of your brainpower on actually interesting problems rather than something that is easily automated.

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

#98

Post by HillaryBriss »

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…

> 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 the symbolic clutter.

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

#99

Post by Chris2048 »

adamnemecek wrote: post #33
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…

> 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…

Many vocations use computers, but should they all require learning about software, electronics etc?

If you don't need to "understand" the math, why risk opportunity cost learning it?

> I would draw an analogy with a compiler

staying "high level" is a good thing for some programmers. If every web dev had to dig into the low-level working of the browser, a lot less would get done.

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

#100

Post by throwawayjava »

err4nt wrote: post #57
mxschumacher wrote: post #21

If a computer can easily answer the question, it is not worth asking it to a human (this also applies in the real sense that it won't be valued by the marketplace and translate to higher wages). How about challenging students with problems that are difficult even when modern technology is used to its fullest extend? Or teaching students how to build tools that solve their homework?

> teaching students how to build tools that solve their homework? This would give them not only a thorough understanding of the problem they are solving, but teach them a very valuable life skill of finding ways to automate your work, and finding ways to package your expertise into software that can be run by a person without your expertise. This would amazing!

Basically, in most college courses the problems are either 1) easy enough that implementing a program to solve them isn't super insightful, or 2) difficult enough that complete automation would mean "do research".

I'll limit myself to Math since that's the topic of this article:

Calculus sequence: CS 1 is not a pre-req. And there's not enough time to teach both CS 1 and Calc 1/2/3 in a single course. "Implement it" works well for derivatives but not integrals. You're not gonna teach Risch, and implementing integration tricks isn't particularly insightful IMO. The cost/benefit ratio explodes in Calc 3, and the physical intuitions become as important as than the calculations.

Everything past that is proof-based and now you're kind of in "your homework is an open research problem in combining NLP with theorem proving" territory. Maybe with the exception of particularly bad Linear Algebra courses and a bit of the early stuff in Algebra.

From a "pragmatic skills" perspective, this approach is still highly suspect. E.g. no one's going to invent their way to Risch by implementing integration tricks.

Point is, every field teaches useful life skills / knowledge, and programming gets in the way as often or more often than it helps.

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