Back to Teaching and Coping with GenAI
Summer is well and truly over: it’s a chilly day in Maynooth; the Autumnal Equinox takes place tomorrow; and tomorrow I return to teaching at Maynooth University. So begins my antepenultimate academic year as a university teacher.
I’ve often remarked how the academic year at Maynooth is largely defined by the astronomical phenomena of the equinoxes and solstices. This year demonstrates this perfectly: Semester 1 lectures for undergraduates begin tomorrow (22nd September), the day of the Autumnal equinox; they end on Friday 19th December with the Winter Solstice on 21st. The half-term study break coincides with Samhain, a cross-quarter day. It’s all refreshingly pagan.
This time last year, having been away on sabbatical the year before, I was preparing to teach two new modules. I have those two again this year so this year should be a bit easiest than last year. I still have to get everything sorted out, though, including setting up my Moodle pages and preparing the materials, which is what I’ve been doing today.
The timetable for my Engineering Mathematics (EE206 Differential Equations and Transform Methods) module has not changed, so my first lectures on that (a double session) are not until Tuesday. I’m also doing MP469 Differential Equations and Complex Analysis for 4th Year Mathematical Physics students again, but the lecture times for that have changed. That is because, as a consequence of the merger of the Departments of Theoretical Physics and Experimental Physics to form a single Department of Physics, times have been coordinated as far as possible to ensure that Physics students can have flexibility in their choice of theoretical or experimental-based modules. The Engineering Mathematics module has not changed because the times for those lectures are such as to fit with the needs of the Department of Engineering, rather than Physics.
The upshot of all this is that my first lecture of the new term is for MP469, tomorrow afternoon at 2pm and my second is also MP469, at 11am on Tuesday. This means that I have three hours of lectures on Tuesdays this term, but at least that makes it possible to have a day without teaching (Wednesday).
You will notice that both the modules I am teaching this term are mathematical in nature. I have been concerned about the integrity of the coursework element of these modules in the light of improvements in Generative AI. Only a couple of years ago GenAI could not solve the sort of problems I set for homework, but now it generally can – especially for EE206. I don’t altogether object to people applying artificial intelligence to solve mathematical problems, but the issue is that it does make mistakes. Moreover, instead of saying “sorry I can’t solve that problem” it will generally present a superficially plausible but incorrect solution. Although students will probably use GenAI for problem-solving, I think it is important that they learn to do such problems themselves, otherwise they won’t know whether the solution coughed up by the algorithm is correct or not. That way lies disaster.
The only way to learn mathematics is by doing it. If students get GenAI to do the mathematics for them, then they won’t learn it. In the past we have given marks for coursework (usually 20% of the module mark) mainly to encourage students to do them. Students who don’t bother to do these exercises generally do badly in the final exam (80%).
For these reasons I am moving the assessment from weekly homework sheets – which could be tackled with AI – to supervised in-class tests for which students can use notes on paper, but not laptops or phones, just like they would in the final examination. I will of course give examples for the students to have a go at themselves, and I will give feedback on their attempts, but they will not contribute to the module score. Another advantage of this approach is that students won’t have to do so much work against deadlines outside of class.
Anyway, that’s the approach I am going to try. I’d be interested to hear what others are doing to deal with GenAI. The Comments Box is at your disposal.
P.S. There is a rumour circulating that The Rapture will occur on Tuesday 23rd September, but it is as yet unclear whether this will happen before, during, or after the lectures I am due to give on that day.
September 21, 2025 at 4:55 pm
Software that can solve symbolic mathematical problems, including differential equations, is nothing new. It’s been around since the early 1960s, pre-dating GenAI by half a century or more.
By the late 1980s, computer algebra systems such as Maple, Macsyma and Mathematica could solve a wide range of ODEs of the kind that are common in engineering maths courses. Even Derive, a computer algebra system designed to run on an IBM PC with just 640k of RAM, was able to solve many classes of ODE including non-linear 2nd-order.
Inevitably, there was concern among university maths teachers that students might use such systems to do their classwork.
September 22, 2025 at 9:32 am
Yes, years ago I failed after considerable effort to crack the first-order ODE for the temperature T of a radiating wire having a fixed heat capacity and resistivity and passing an alternating current,
dT/dt +aT^4 = b sin^2 (2pi ft)
Maple gave me the solution albeit in implicit form. But it never told me how it got it, and a later version of Maple failed to crack it! If not for the printout I’d wonder if it was a dream.
In how few years will AI give a correct and comprehensible answer to an unsolved problem in mathematics, such as proving (or disproving) the Riemann hypothesis, the non-existence of odd perfect numbers, or Goldbach’s conjecture?
September 22, 2025 at 9:39 am
The timing of the Rapture according to the bible is contended among Christians. The ‘pre-tribulation’ version that novelists and Hollywood are fond of is far from universally accepted. Many Christians think it takes place moments before the Second Coming of Christ. That event is clearly associated with the Festival of Tabernacles in the autumn in Jerusalem, so whoever is saying these things has at least got the time of year correct.
September 22, 2025 at 5:14 pm
I also think the prevalence of GenAI use during the school year is a good opportunity to improve class assignments by removing busywork and moving more tasks and assignments to pen and paper
September 28, 2025 at 12:59 pm
[…] done quite a few posts recently about the ending of summer – the Autumnal Equinox, the resumption of teaching, the start of a new season at the National Concert Hall are three indicators – but now we […]
October 13, 2025 at 3:44 pm
[…] As I mentioned a while ago, I am concerned about the integrity of the coursework element of these modules in the light of improvements in Generative AI. Only a couple of years ago GenAI could not solve the sort of problems I set for homework, but now it generally can. I don’t altogether object to people applying artificial intelligence to solve mathematical problems, but the main issue is that it does make mistakes. Moreover, instead of saying “sorry I can’t solve that problem” it will generally present a superficially plausible but incorrect solution. Although students will probably use GenAI for problem-solving, I think it is important that they learn to do such problems themselves, otherwise they won’t know whether the solution coughed up by the algorithm is correct or not. […]
October 17, 2025 at 11:46 am
[…] it was foretold, I conducted my first set of my new-style in-class tests this week. These tests, as I mentioned a while ago, were introduced because of concerns about the integrity of the coursework element of my modules […]
November 25, 2025 at 5:51 pm
[…] the introduction of in-class tests to replace take-home assignments (for reasons I outlined here). I’ve also been handing out voluntary exercises for practice, not counting towards the […]
December 1, 2025 at 9:02 am
[…] doing the same modules this academic year as last. The big change in that regard has been the adoption of different assessment methods to deal with the possibility of students using AI to do their coursework. That seems to be going […]