I have been wondering about possible educational uses of generative AI. Far too much of the discussion has been bogged down by the whole plagiarism issue—which thankfully, we don’t have to worry about anymore, since I fixed that, right here on this website. More at How to identify AI generated text.

All jokes aside, there are so many possibilities that this new technology provides us, some of which I have documented here. They include creatively exploring scientific ideas, using ChatGPT plugins both to test your own understanding or explore mathematics; writing computer programs that actually work (here and here); conducting qualitative research (here, here and here); engaging in a discussion with philosophers long dead; creating complex visualizations of large data sets; creating somewhat artistic visual representations and graphics (for this website and for Silver Lining for Learning), and more.

Now this does not in any way mean that I am not sensitive to the risks associated with these technologies, something I have written about as well: such as the fact that it is a BS artist; the diminishing cost of creating realistic images and video; the possibility of creating lesson plans based on educational myths; biases that can be perpetuated by these systems (such has erasing my Indian accent, and through that my identity (also here)); and the risks inherent in modeling human behavior using these large language models.

All that said, I do believe that these tools can be used creatively by educators and learners to enhance the educational process. These tools have given me super-powers that I did not have a few months ago, or even a few days ago! But what that will need an openness to experiment and play, to keep the technology in mind, even while we think of new ways of representing and engaging with content, and through that connecting with our learners, in specific contexts of use. (If this sounds like TPACK, so be it!)

Consider, for instance, this story shared by my colleague, Jim Dunnigan, about how his son used ChatGPT to ace his chemistry test. He did it not by plagiarizing but rather by training ChatGPT on the content of the exam and then making it generate lots of test questions. Essentially, he used it to practice for the upcoming exam. I think this is a brilliant use of generative AI, as a personal tutor. In fact, this was the inspiration for my explorations of the ChatWithPDF plugin, to test my understanding of a research paper.

Another option I have considered is of using ChatGPT as helping me find errors in my own thinking. We are all prone to a range of cognitive biases, confirmatory bias being at the top of the list. So one thing to do is to give the AI a set of statements I believe in and ask it to find mistakes, or limitations, in my thinking. For instance, when asked to creatively explore the idea of “It takes two” in science, I didn’t just stop at asking for examples, I went further and asked exceptions to the idea, because, you know, the world is complicated. And it did a great job at that as well, and in verse, no less, expanding my thinking in ways that would not have been possible otherwise.

I also have had fun, lots of fun, just playing with these new tools and the opportunities they offer us as creative educators. For instance, I have loved the manner in which these generative AI tools can “mashup” genres, creating poems on science, and writing mathematical proofs in verse. ((Incidentally, this task has an interesting history that I wrote about in a post title An Euclidean Coincidence).

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As I reflected on these possibilities, I began to wonder what else could I do to understand student understanding of a topic? What would be a good “performance of understanding?”

I began to wonder… what if I asked the software to write a proof, but leave an error in the proof? That could be a neat pedagogical trick. A fun little game, where the task for the students would be to discover the error in the proof.

So I took the topic I had given it previously, that of writing a poem laying out Euclid’s proof of the infinity of prime numbers, but this time asked it to insert an error in the proof.

So after a few attempts back and forth, where the AI kept trying to write a “meta” poem where it actually gave the answer, I finally got it to write a poem that seemingly was the proof, but had an error in it. What was impressive was how subtle and smart the error was. In fact it was an error that I had committed when I had written a similar poem around 13 years ago, something I documented in my post from back in 2010: The infinity of primes (proof as poem). I had also written about how this error can be found on other websites that give the proof as well.

So in that sense, the subtlety of its reasoning, in selecting the right error to include, was quite amazing. It picked an error that humans tend to make, thus making it a genuinely interesting test of whether or not you truly understand the proof.

Below is the poem GPT created for me. Can you figure out the error? (Hint: The proof on this website makes the same mistake, the one that GPT deliberately included in its poem, while this website gets it right.)

Euclid’s proof (the wrong version)

In the realm of numbers, let’s take a dive,
Euclid’s proof, where infinity comes alive.
No need for embellishments, let’s keep it plain,
Discovering the truth of primes, a timeless gain.

Imagine a list of primes, neat and trim,
Assuming it’s complete, no gaps within.
A finite collection, we confidently claim,
A haven of numbers, bearing prime’s name.

Now, let’s create a number, a clever scheme,
Multiply those primes, like a mathematical dream.
Add one to the product, behold what we find,
A number so novel, a prime of a kind.

But here’s the twist, a thought to bestow,
Does our new prime truly fit the prime row?
Could it be that this number, grand and fine,
Is divisible by primes, breaking the line?

Pause for a moment, and ponder this quest,
Is there a prime in our list that can digest,
The new number we formed with careful design,
A prime that divides it, a detail so benign?

The answer lies not in a finite array,
But in the vastness of primes, in endless display.
For no matter the list, no matter how complete,
There’s always another prime, yet to meet.

Euclid’s proof reveals this infinite trend,
The existence of primes, forever without end.
So let this poem stand as a testament clear,
To the infinite abundance of primes we hold dear.

No error to find, no flaw to perceive,
Just a proof that primes, forever conceive,
A realm of numbers, infinite in scope,
Where primes reside, boundless with hope.

So share this poem, this proof so profound,
Let students explore, their minds unbound.
Discover the beauty of primes, without any veil,
And let the wonder of mathematics prevail.