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I've been using ChatGPT (GPT-4) to help with creating quiz questions, solving math problems, and answering students' queries in my classes. Although it sometimes gets things wrong, with the right prompts, it usually provides remarkably helpful answers.

Our university provides students access to ChatGPT (GPT 4). However, not many are using it. They become frustrated if they don't understand the answers or find errors on their first try.

I'm thinking about a couple of things:

  1. Learning to Use AI: Should teaching students to use AI tools like ChatGPT be part of their education? It's not in our syllabus, but it might be a useful skill.

  2. Increasing Usage: Have any teachers successfully got their students to use AI tools regularly? What strategies worked?

I'd appreciate any advice or examples of what has worked in other math classes.


Just to give you an example, what follows is a actual conversion I had with ChatGPT (GPT 4.0). You can judge if it is good enough to be a tool for students. (It did get the 4th one wrong.)

Also note that if I add "Answer the question one by one, and only continue if I say so.", then ChatGPT would correct answer all five. It has problem with long reasoning, breaking the reasoning into small steps increases accuracy.

Me:

Which of the following five statement in linear algebra are true? Explain your answer to each one briefly.

  • If there exists a set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ that spans $V$, then $\dim V \leq p$.
  • If there exists a linearly independent set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ in $V$, then $\dim V \leq p$.
  • If there exists a linearly dependent set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ in $V$, then $\dim V \geq p$.
  • If $\dim V = p > 0$, there may not exist a set of $p+1$ vectors $\{\mathbf{v}_1, \ldots, \mathbf{v}_{p+1}\}$ such that $\mathrm{Span}\left\{\mathbf{v}_1, \ldots, \mathbf{v}_{p+1}\right\} = V$.
  • If for every set of $p$ vectors $\{\mathbf{v}_1, \ldots, \mathbf{v}_{p}\}$ in $V$, $\mathrm{Span}\left\{\mathbf{v}_1, \ldots, \mathbf{v}_{p}\right\} \ne V$, then $\dim V \ge p+2$.

ChatGPT:

Let's evaluate each statement one by one:

  1. If there exists a set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ that spans $V$, then $\dim V \leq p$.

    • True. If a set of vectors spans $V$, it means every vector in $V$ can be expressed as a linear combination of these vectors. If $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ spans $V$, the dimension of $V$ is the maximum number of linearly independent vectors in $V$, which cannot exceed $p$. If there are more than $p$ linearly independent vectors, the set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ would not be able to generate all vectors in $V$, contradicting the assumption that it spans $V$.
  2. If there exists a linearly independent set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ in $V$, then $\dim V \leq p$.

    • False. The dimension of $V$ is defined by the maximum size of a linearly independent set. A linearly independent set of $p$ vectors does not necessarily span $V$; it could be part of a larger linearly independent set. Thus, $\dim V$ can be greater than $p$ if additional vectors can extend the set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ while maintaining linear independence.
  3. If there exists a linearly dependent set $\{\mathbf{v}_1, \ldots, \mathbf{v}_p\}$ in $V$, then $\dim V \geq p$.

    • False. A linearly dependent set means at least one vector in the set can be written as a linear combination of the others. This does not provide information on the dimension of $V$ relative to $p$ because the redundancy (linear dependency) might imply that the effective number of independent vectors is less than $p$. Therefore, $\dim V$ could be less than $p$.
  4. If $\dim V = p > 0$, there may not exist a set of $p+1$ vectors $\{\mathbf{v}_1, \ldots, \mathbf{v}_{p+1}\}$ such that $\mathrm{Span}\left\{\mathbf{v}_1, \ldots, \mathbf{v}_{p+1}\right\} = V$.

    • True. If $\dim V = p$, any set of $p+1$ vectors in $V$ must be linearly dependent, since the maximum number of linearly independent vectors in $V$ is $p$. Thus, while a set of $p+1$ vectors can still span $V$, they cannot all be linearly independent, and thus some of the vectors in this set are not necessary to span $V$.
  5. If for every set of $p$ vectors $\{\mathbf{v}_1, \ldots, \mathbf{v}_{p}\}$ in $V$, $\mathrm{Span}\left\{\mathbf{v}_1, \ldots, \mathbf{v}_{p}\right\} \ne V$, then $\dim V \ge p+2$.

    • False. If no set of $p$ vectors spans $V$, it implies that $\dim V > p$. However, $\dim V$ could be exactly $p+1$, where just one more vector is needed to span $V$. Claiming that $\dim V \geq p+2$ assumes that at least two additional vectors are needed, which is not necessarily the case.
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  • $\begingroup$ Needless to say that I have asked ChatGPT to polish the language of the question a little bit. 😜 $\endgroup$ Commented May 6 at 2:49
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    $\begingroup$ Is this a first? The teacher wants the students to have someone (thing) do their work for them and they're resisting? You'll probably say that's not what you meant, but I can't think of another interpretation. $\endgroup$
    – Thierry
    Commented May 6 at 18:32
  • $\begingroup$ Teachers cannot be able to answer questions 24 hours a day, but bot can. In fact, if this is out of self-interests for teachers, the question should be how to ask universities to ban chatbots so the jobs of teachers and tutors. $\endgroup$ Commented May 6 at 18:37
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    $\begingroup$ I just saw the edit. So it got one wrong, and for the ones that are false, not once does it give an actual simple counterexample using a familiar vector space: for example, for question 3, "False. $\{e_1,2e_1,3e_1\}$ in $\mathbb{R}^2$" could be the entire answer (I'd go even simpler with $\mathbb{R}$, personally). I have to agree with most other posters here and maybe I should even make this an answer. It's just not good. $\endgroup$
    – Thierry
    Commented May 7 at 3:45
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    $\begingroup$ Just to clarify: ChatGPT absolutely can give counter examples if I had asked, and it will have no problem doing these five problems had I give them one by one instead of five together. This is also way beyond what can be expected from an average college student. $\endgroup$ Commented May 9 at 0:47

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Your question is too broad, covering two separate topics (should and how).

But answering the first one, I say "no".

First, it's not like kids are (in general) crushing the basics, withe time for off topic work. This is especially the case with mass college education and with social promotion (at all levels).

Second, this is just the latest fad. Having a good solid education will allow kids to function with whatever buzzword or tech is in fashion.

Third, it's not especially crucial to "know how to use ChatGPT". And if it ever becomes so, we'll have dedicated content and exercises for it. Not your ad hoc stuff.

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Let's take your use cases as an example:

help with creating quiz questions, solving math problems, and answering students' queries in my classes

ChatGPT can indeed save time on things like this, but it only works because you could do these things without ChatGPT if you had to, and you know how to check and correct the output.

You're seeing what happens when ChatGPT is used in the middle of learning a new concept: students can't check ChatGPT's output for correctness, because they don't understand enough yet. It's like encouraging students to use calculators before they know how to add.

If you think chatbots are a useful tool for your students to learn, I'd do things differently. Confine the use of ChatGPT to a dedicated section of your syllabus, perhaps involving applied problems where the necessary calculations are in principle doable using techniques your students have mastered, but would take a ton of time to do by hand.

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    $\begingroup$ It's worse than students using calculators before they know how to add. It's like students using calculators that give the wrong answer 20% of the time before they can add $\endgroup$ Commented May 13 at 23:35
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The best use of ChatGPT I've found so far is for norming. Norming is the process where you show students how things will be graded so you and the students have a common understanding of expectations (the "norms" for an assignment).

When I assigned a project to my Differential Equations students, I gave them a list of tasks and my rubric for grading the tasks. I was hoping to also give the students some kind of example submission to the project that appeared reasonable but was actually very bad, so I could show them how the rubric would be used to grade bad submissions (This is the norming part).

It sounded like I had a difficult task ahead -- how long was it going to take me to create an artificially bad submission for a project that still sounded reasonable at surface level?

Enter ChatGPT, which is excellent at generating reasonable-sounding but absolutely terrible answers to questions. I simply gave ChatGPT the prompt, then it gave me absolute garbage like it always does, then I graded it according to the rubric and gave it to my students. It scored an F, of course.

The students loved it.

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  • $\begingroup$ I did find GPT3.5 is very bad at math. But GPT 4 is quite an improvement. Have you tried it? Is it still F? $\endgroup$ Commented May 7 at 2:12
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    $\begingroup$ I don't know what version I used. It was very good at this task. It even generated a fake desmos link which it claimed was a visualization all sorts of neat things. $\endgroup$ Commented May 7 at 2:22
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ChatGPT (or other language learning models for that matter) swallow information and when asked, it will show what it has swallowed without any verification, but one thing is crucial: Whatever shown, it will never be new!!!
It is basically an advanced Google, but there is a catch: it looks like it presents new information, and as such it is welcomed by many lazy students:

  • Write me a paper on the role of the Irish king during the Second World War.
  • Write me a paper on the underground of Central Europe, as a direct reaction of the asteroid, which killed the dinosaurs.
  • ...

You can immediately see that lazy students don't need to perform any work anymore, even a Google search has become obsolete.

Therefore, the less students use such medium, the better.

In top of that: as stated in another answer, sometimes ChatGPT is flat wrong!

So instead of asking yourself how to teach your students how to use A.I., you need to wonder what kind of questions you can ask them for which they have no use of A.I..

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  • $\begingroup$ Firstly, nothing in an undergraduate linear algebra course is new. Two, ChatGPT on average gives muc better answers than an average undergraduate student. Third, I don’t give homework and only do weekly quizzes. So there isn’t really the problem of cheating with ChatGPT. $\endgroup$ Commented May 6 at 9:29
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    $\begingroup$ Your first argument is bogus: for students, everything they learn is new to them and sometimes they might invent something new too (at the age of $16$, I invented a way to divide by $5.8$ by dividing by $6$, again by $30$, and adding the results (it was a currency thing)). When you let students rely on a tool which is impossible to create something new (although it looks like new), you will chase their desire to make new things, and let that be the engine our society drives on. $\endgroup$
    – Dominique
    Commented May 6 at 9:35
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Teach proper use of Chat-GPT.

First, a warning: As per the pre-print «unreflected acceptance», AI plus university student does much worse than search engine plus university student, when solving hard problems. They believe too much in what the AI tells without thinking themselves.

But you can still teach to use Chat-GPT for its strengths, such as:

  • asking for a definition or a term or its meaning (though maybe ask Wikipedia first)
  • translating stuff and using foreign sources (but keep the original on the side and check any strangeness)
  • asking what methods one usually uses to solve this type of problem (to then check them out oneself)
  • asking for simple and well-known bits of programming code (to then test and correct them oneself), maybe to numerically test the feasibility of a solution

But you absolutely need to teach them to not trust Chat-GPT. Maybe have an exercise where students have to make Chat-GPT solve a mathematics problem wrong; it is a nice, open activity for the students and they become familiar with strengths and weakness of Chat-GPT and also have to use their mathematical abilities in a non-standard manner.

Big numbers or many calculations, as well as not asking Chat-GPT to write out the steps of a solution, increase the chance of failure.

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It does take some practice to learn how to prompt an LLM like ChatGPT to approach some problems. I highly recommend that you have your students watch this video by Jeremy Howard starting at the 17:13 mark, up to about the 31:00 mark

Hacker's Guide to Large Language Models

He explains some issues about LLMs and how to prompt in the context of the classic cabbage, goat, wolf river crossing problem.

I have made several assignments where I expect students to use an LLM, and require them to share their session with me by a link. By looking at how students approach problem solving with GPT, I learn a lot about their misconceptions!

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I think one needs to try to do it by hand first to see what is going with computer/software/ai

there needs to be understanding first, especially with the parameters, before we can use tools

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