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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

#141

Post by posterboy »

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…

To find out whether f is differentiable at some point, I'd naively draw f around 2 and look for obvious discontinuities. Why encrypt the problem in such a way? Alternatively, finding f' and explaining if it is undefined at the point in question would work even more reliable - for corner cases the visualization of a graph might hide the fact, i.e. if the resolution is too poor.

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

#142

Post by Rjevski »

JadeNB wrote: post #114
Rjevski wrote: post #105

Earlier quoted context omitted.

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 'realit…

The thing is, if no humans can spot the flaw, then what difference does it make if they cheated in school? Either way they'll do flawed calculations if we assume your logic.

However, I wasn't really talking about people wanting to become actual mathematicians - those probably wouldn't use Wolfram just because they actually love crunching those numbers manually. The people who we're talking about here just see math as a roadblock they need to get through to do whatever they really want to do (programming, etc), and in this case this "cheating" is totally fine by me.

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

#143

Post by yequalsx »

posterboy wrote: post #141
yequalsx wrote: post #74

Earlier quoted context omitted.

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…

To find out whether f is differentiable at some point, I'd naively draw f around 2 and look for obvious discontinuities. Why encrypt the problem in such a way? Alternatively, finding f' and explaining if it is undefined at the point in question would work even more reliable - for corner cases the visualization of a graph might hide the fact, i.e. if the resolution is too poor.

Regarding the first sentence your wrote. That's how you solve the problem. Graph the difference quotient for x=2 and h in [-0.1, 0.1] or some such suitably small region. It's quite easy to do in the computer. One just needs to know that this is what you need to do. I did not encrypt the problem. It's quite straightforward provided one knows the concepts.

If students are allowed to use Mathematica during a test then asking them to find f' using the definition of f is not helpful in determining if they understand the concepts. They, for all reasonable problems, just need to execute a single command:

Limit[ (f[x+h]-f[x])/h, h->0]

This doesn't really test their understanding. If one is going to allow students to use Mathematica on a test then the problems need to be adjusted.

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

#144

Post by impendia »

gregmac wrote: post #140
impendia wrote: post #96

Earlier quoted context omitted.

> 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?

> is that surprising?

No. It's a difficult problem to mitigate.

There are always going to be some students who want to learn the minimum possible to pass the exam, and who will never work with the material again. Although I do my best to be respectful of such students (indeed, in some circumstances this can be a perfectly rational point of view), my pedagogy is aimed at the student who sees my class as something more than a meaningless hoop.

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

#145

Post by posterboy »

set92 wrote: post #48

Since when has wolfram alpha an AI? I always thought it was simply calls to Mathematica. Maybe when you ask general questions it uses an AI, but with functions and maths I think it only uses Mathematica.

Well, maybe it can even understand mathy questions given in natural language.

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

#146

Post by posterboy »

yequalsx wrote: post #143
posterboy wrote: post #141

Earlier quoted context omitted.

To find out whether f is differentiable at some point, I'd naively draw f around 2 and look for obvious discontinuities. Why encrypt the problem in such a way? Alternatively, finding f' and explaining if it is undefined at the point in question would work even more reliable - for corner cases the visualization of a graph might hide the fact, i.e. if the resolution is too poor.

Regarding the first sentence your wrote. That's how you solve the problem. Graph the difference quotient for x=2 and h in [-0.1, 0.1] or some such suitably small region. It's quite easy to do in the computer. One just needs to know that this is what you need to do. I did not encrypt the problem. It's quite straightforward provided one knows the concepts. If students are allowed to use Mathematica during a test then a…

In the first sentence, I didn't talk about the difference quotient, just plain f.

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

#147

Post by btilly »

posterboy wrote: post #133
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…

> 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.

Please, no.

Or at least not unless it is done well.

The problem is that we start with a reasonable idea like, "People should understand how the tools work." We make an obvious observation like, "Understanding computer science helps people understand how the tools work." Come to a conclusion like, "Computer science needs to be part of the math curriculum in schools asap." This turns into a mandate for educators who themselves have no understanding of computer science. Who then ask the question, "What does everyone need to know about computers?" Who then consult with what seem to them like appropriate experts. Soon you're hearing about how we'll have interactive computer science courses to guarantee that children have familiarity with how computers work. And to fanfare these are rolled out in schools.

Then you go and look at what is being done. A teacher who clearly doesn't actually understand how computers work has kids using a variety of interactive programs, ranging from Microsoft Word to animated presentations. They are calling that "computer science". No actual understanding is imparted. And the exercise reduces time available in the core curriculum that could have spent on things like quantitative reasoning. You know, stuff which ACTUALLY can lay the foundation for understanding how the tools work.

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

#148

Post by yequalsx »

posterboy wrote: post #146
yequalsx wrote: post #143

Earlier quoted context omitted.

Regarding the first sentence your wrote. That's how you solve the problem. Graph the difference quotient for x=2 and h in [-0.1, 0.1] or some such suitably small region. It's quite easy to do in the computer. One just needs to know that this is what you need to do. I did not encrypt the problem. It's quite straightforward provided one knows the concepts. If students are allowed to use Mathematica during a test then a…

In the first sentence, I didn't talk about the difference quotient, just plain f.

I see. Then I don't understand what point you were trying to make. There are lots of different ways of testing understanding of a concept. I presented one way of doing so with students having access to a computer.

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

#149

Post by JadeNB »

Rjevski wrote: post #142
JadeNB wrote: post #114

Earlier quoted context omitted.

> 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 'realit…

The thing is, if no humans can spot the flaw, then what difference does it make if they cheated in school? Either way they'll do flawed calculations if we assume your logic. However, I wasn't really talking about people wanting to become actual mathematicians - those probably wouldn't use Wolfram just because they actually love crunching those numbers manually. The people who we're talking about here just see math as…

> The thing is, if no humans can spot the flaw, then what difference does it make if they cheated in school? Either way they'll do flawed calculations if we assume your logic.

I don't think that my logic allows us to conclude that. The idea of mathematics is that it is possible for humans to create and apply a system whose correct application makes the genesis of errors, howsoever subtle or undetectable, impossible.

Given this, and the likelihood that a mathematical error (of the conceptual type "any convergent sequences of continuous functions converges to a continuous function", rather than of the computational type "1 + 1 = 1") will not be found, it is especially important that practitioners of mathematics know how to apply their tools correctly, which they probably will not have learned by cheating in school; and, if they are able to apply those tools correctly, then they will not create errors.

(I grant that the weasel word 'correct' and its derivatives risks making this argument circular. I grant that human mathematicians collectively make an awful lot of errors, although I hope that we make fewer professional errors than many other professionals.)

> However, I wasn't really talking about people wanting to become actual mathematicians - those probably wouldn't use Wolfram just because they actually love crunching those numbers manually.

This comment seems to suggest to me the source of our disagreement in the first paragraph. As a mathematician, I don't crunch numbers professionally, and, when I have to do so outside of my profession, don't love crunching them manually. I suspect most mathematicians are in the same boat.

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

#150

Post by Rjevski »

JadeNB wrote: post #149
Rjevski wrote: post #142

Earlier quoted context omitted.

The thing is, if no humans can spot the flaw, then what difference does it make if they cheated in school? Either way they'll do flawed calculations if we assume your logic. However, I wasn't really talking about people wanting to become actual mathematicians - those probably wouldn't use Wolfram just because they actually love crunching those numbers manually. The people who we're talking about here just see math as…

> The thing is, if no humans can spot the flaw, then what difference does it make if they cheated in school? Either way they'll do flawed calculations if we assume your logic. I don't think that my logic allows us to conclude that. The idea of mathematics is that it is possible for humans to create and apply a system whose correct application makes the genesis of errors, howsoever subtle or undetectable, impossible.…

I definitely agree that someone using tools should know how to use them right - however in this case maybe the curriculum should be tweaked to point out mistakes when using a tool? Ie, instead of assuming that someone would do it by hand, assume they'd do everything they can to cheat their way out of doing the work and trick them as much as possible so the tools would only work if you use them right. Instead of focusing on teaching them how to do it by hand (which they would never do in the real-world given the time constraints), teach them which tools to use and how to use them properly.

My point about crunching numbers manually or not was more about the fact that a lot of people taking those math tests do so because it's required by X policy and not because they are genuinely interested in math, and IMO that's fine - not everyone aims for a job that involves mission-critical math. Some for example might just want to develop games, where a screw-up could at worst result in a graphical glitch.

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