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That Scottish Higher Maths Paper 1…

Posted in Education, mathematics with tags , , , on May 15, 2026 by telescoper

Talking of Examinations, I saw an article on the BBC website about a recent Higher Maths paper in Scotland which has generated complaints and a petition because it was allegedly unfair. The introduction to the petition states:

This is not a complaint that the paper was too hard. Students expect to be challenged. The problem is that the 2026 Higher Maths Paper 1 used language and phrasing that was confusing, ambiguous, and inconsistent with every past paper students had revised from. Questions were not simply difficult — they were worded in ways that made it genuinely unclear what was being asked.

Past SQA Higher Maths papers have followed a recognisable style: clear command words, standard notation, and questions that test understanding rather than the ability to decode unusual phrasing. The 2026 Paper 1 departed from this in ways that penalised well-prepared students simply because the wording did not match the conventions they had been taught to expect.

Numerous other news outlets have covered the story too. It is frustrating that most of the pieces focus on what people said about the paper but don’t actually include a link to the paper itself, making it impossible to make your own mind up.

So you can make your own mind up here is a scan of the actual paper (obtained from here):

2026_Higher_Maths_Paper_1_ScanDownload

Bear in mind that the Scottish examination system is not the same as in England & Wales – the “Highers” are not as advanced as A-levels and are more similar to the Irish Leaving Certificate.

My opinion, for what it’s worth having neither taught nor studied in the Scottish system, is that there is nothing out of the ordinary with this paper. There is a lot to do in just 75 minutes – for 12 questions that’s just over 6 minutes a question. I don’t like examinations that are speed tests.

That said, the questions look well structured and the “command words” are without exception on the list here. Some questions are easy and others harder: I think Question 12 is the most difficult, but I think that’s intentional – to stretch the stronger students. The only thing I would quibble with is the wording of 11(a) (ii):

The second sentence is redundant. How can one possibly “explain why” without giving “a reason”? The reason is basically that the quadratic remaining after you have taken out the factor (x+2) does not factorize.

I looked at the 2025 Paper 1 and it seems a similar level, though the questions are phrased in a terser fashion. Here it is for reference:

NH_Mathematics_Paper1-Non-calculator_2025Download

There may well be context that I’m missing, however, so I’d welcome comments on the diffculty and/or fairness through the box below.

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After Lectures but before Examinations

Posted in Education, Maynooth, The Universe and Stuff with tags , , on May 14, 2026 by telescoper

This morning I did my last teaching session of the Academic Year 2025-6, an informal revision lecture/tutorial on Computational Physics. It was optional, for the students, as this is officially a study break, and was at 9am, and only a handful of students showed up, but I hope those that did found it useful. As is often the case with optional sessions, I think the students who came were the keenest and probably therefore those who least needed last-minute tips for the examination, but that’s always the way.

In the past such revision classes have been routine, at least for me, but for some reason the University has taken to locking most of the teaching rooms during the study break. This causes huge problems finding a space to do revision sessions. I really don’t understand this. There are constant complaints from students about the lack of study space, and the response from the University is that right before the examinations they lock dozens of empty rooms.

Anyway, the Examination Period starts tomorrow morning, Friday15th, but most of the students who turned up this morning have their first examination on Tuesday 19th May (which happens to be Computational Physics).

take the opportunity to wish all students the best for their examinations:

You shouldn’t really be relying on luck of course, so here are some tips (especially for physics students, but applicable elsewhere).

  1. Try to get a good night’s sleep before the examination and arrive in plenty of time before the start. Spending all night cramming is unlikely to help you do well.
  2. Prepare well in advance so you’re relaxed when the time comes.
  3. Read the entire paper before starting to answer any questions. In particular, make sure you are aware of any supplementary information, formulae, etc, given in the rubric or at the end. You can always ask for log tables if there’s something you can’t remember.
  4. Start off by tackling the question you are most confident about answering, even if it’s not Question 1. This will help settle any nerves. You’re under no obligation to answer the questions in the order they are asked.
  5. Don’t rush! Students often lose marks by making careless errors. In particular, check all your working out, including numerical results obtained your calculator, at least twice
  6. Please remember the UNITS!
  7. Don’t panic! You’re not expected to answer everything perfectly. A first-class mark is anything over 70%, so don’t worry if there are bits you can’t do. If you get stuck on a part of a question, don’t waste too much time on it (especially if it’s just a few marks). Just leave it and move on. You can always come back to it later.

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Jobs Under Threat at Nottingham University

Posted in Biographical, Education with tags , , on May 14, 2026 by telescoper

I saw this picture on a LinkedIn post from a former member of staff in Physics at Nottingham University:

It shows a notieboard in the foyer of the Physics Building, which houses the School of Physics & Astronomy. Earlier this week members of staff received letters informing them that their jobs are “at risk of redundancy”. As an act of solidarity the staff members concerned showed posted their letters publicly. I don’t know the names of the people who have received these letters – and if I did I wouldn’t share them here – but there are 17 letters.

UPDATE: I have since heard that 56 members of academic staff in the School – out of a total of 71 – have received these letters. The University wants to reduce the staff numbers in Physics & Astronomy by about a third.

I also know that the undergraduate course in Mathematical Physics, taught jointly with the School of Mathematics, has been suspended and will not admit any students. I taught on this course for many years when I was at Nottingham University (from 1999 to 2007).

The threat of redundancy is not specific to Physics. It seems almost 2,700 individuals across the University have received such notices and the University is attempting to cut 600 positions. Not all those in receipt of an “at risk” letter will actually be made redundant, but the intention is clearly to scare people into leaving in order to save on redundancy payments.

More details can be found here.

There is a petition against these job cuts here which I encourage you to sign.

The background to this disaster is explained here. In summary, the University’s current financial meltdown is caused by the actions of the former Vice-Chancellor of the University of Nottingham, Prof. Shearer West,, who presided over the hare-brained decision to purchase a large new campus. None of the “at risk” staff is at fault., but they will have to bear the burden of management ineptitude. You would think that the people responsible for this fiasco would be held to account and pay at least some of the price for their incompetence. But no. Prof. Shearer West left her post in 2024 to take up the position of Vice-Chancelor at the University of Leeds on a salary of more than £330K, leaving others to clean up the mess.

I fear more such news is coming. The UK Higher Education sector is shrinking rapidly. Nottingham University won’t be the last, and I doubt the contagion will be restricted to the UK either…

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Lectures’ End

Posted in Biographical, Education, Maynooth, The Universe and Stuff with tags , , on May 8, 2026 by telescoper

At last we’ve made it to the end of term. This morning I delivered my last particle physics lecture. Given that it is the last day of the semester I was half-expecting no students would turn up, but in the end I had about 60% attendance. At the end of my lecture there was even a smattering of applause, which I interpreted as meaning that the students were happy that I’d finished.

I thought I would end this module with some topics that I didn’t have time to cover in any detail, but thought the students should know at least something about. These loose ends included:

  • Renormalization
  • Grand Unified Theories (GUTS)
  • Supersymmetry (SUSY)
  • Particle candidates for Dark Matter
  • Baryogenesis

I only had time for a superficial treatment of these topics, but felt the class should at least hear the words. There are some very good unanswered research questions under those headings, which I think is an appropriate way to end a final-year module, given that at least some of the class are intending to carry on to further study in physics.

This afternoon we had a colloquium by our PhD student John Ibrahim on the subject of the “Quark‑Gluon Vertex and Confinement of Quarks”. It was a nice talk but it struck me how big the gap was between what I’d been teaching at undergraduate level and the standard that a PhD student has to reach.

Today was also the deadline for Computational Physics projects. I’ll be grading them next week. Even then the term won’t quite be over – there is the small matter of exam marking to be done – but at least I’ve got no more formal teaching to do until September.

Last night on the way home I decided to buy a nice bottle of white wine and put it in the fridge so I could drink it in celebration of the end of term when I get home, with a nice fish supper.

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Last Chance Lab

Posted in Biographical, Education, Maynooth with tags , , on May 7, 2026 by telescoper

Today is the penultimate day of teaching in the Spring Semester at Maynooth University and I’m here in the Computer Lab for the last time. This afternoon’s session is just a drop-in consultation session for Computational Physics students doing their projects and although it has been busier than previous weeks it has not exactly been a hive of activity. The deadline for project submissions is tomorrow afternoon, so I was expecting a bit of a rush at this session, which is the last of its type, and also at my office hour this morning. I did have one student attend this morning, and a couple of others this afternoon, but other than for them it has been quiet.

On the other hand, over a day before the deadline, three students have already submitted their project reports and code. I’m impressed with that, but also a little surprised. I’ve come to expect just-in-time delivery for such things.

Yesterday I did my last particle physics tutorial of the year and followed that immediately afterwards I attended a long session of final-year project talks, from 3pm to just after 6pm. It is obvious that some students find these presentations a bit of an ordeal but it is important to learn how to present your work so such things are part of the rite of passage. It is good for staff to get an overview of the all projects being done in the Department too.

In previous years the final project presentations for students in the Departments of Theoretical Physics and Experimental Physics were done separately, the former having a somewhat smaller audience than the latter. The two previous Departments having merged into a single Department of Physics, this time round we had all the talks together (though spread over two days, yesterday and the Wednesday before). I think the combined sessions worked quite well and we will probably do it this way next year.

After the session of talks there was a small drinks party in the foyer of the Science Building. That was a nice occasion, and it struck me that it would have been the last time this group of students would all meet together until their graduation. Tomorrow I do my last particle physics lecture and it will be the last time I see quite a few of the students in that class until graduation too. They’ve been a nice group to work with, very engaged and easy to interact with. It is a great pleasure to be teaching students who are eager to learn . That’s the aspect of academic life I’ll miss the most when I retire.

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Ten Signs of a Toxic University

Posted in Education, Maynooth with tags , on May 3, 2026 by telescoper

I saw this on LinkedIn the other day, and thought I should share it here:

If you work in a University, what’s its score? I was thinking we could make a League Table, but so many institutions would get 10/10 that would be pointless.

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Thoughts on 1st May

Posted in Biographical, Education, Maynooth with tags , , , on May 1, 2026 by telescoper

Today, 1st May, Beltane (Bealtaine in Irish), is an old Celtic festival that marks the mid-point between the Spring Equinox and the Summer Solstice. It’s one of the so-called Cross-Quarter Days that lie exactly halfway between the equinoxes and solstices. These ancient festivals have been moved so that they take place earlier in the modern calendar than the astronomical events that represent their origin: the halfway point between the Spring Equinox and Summer Solstice is actually next week. Anyway, “May Day”, Lá Bealtaine in Irish, is today – the name Bealtaine applies to the whole month of May.

In Ireland the Bank Holiday associated with Bealtaine is on Monday 4th May, so another long weekend beckons.

Workwise, after today we will have completed the penultimate teaching week of Semester 2 so after Monday’s Bank Holiday we will have just four official days of teaching left, before a Study Week and the start of examinations. Yesterday I correctedthe last of my Computational Physics class tests so I am up to date with the continuous assessment and feedback of both my modules. I now have a week before the Computational Physics projects are submitted, and another week before the exam period starts.On Wednesday last we had project presentations for about half of the final year class; the other half do their things next Wednesday.

Now, I have a particle physics lecture to give – the antepenultimate one of the semester – after which I’ll be launching myself into the long weekend.

Lá Bealtaine shona daoibh go leir!

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A Chatbot Masters?

Posted in Artificial Intelligence, Education with tags , , , on April 30, 2026 by telescoper

I laughed out loud when I saw an item in the Times Higher about new Masters courses at the London School of Innovation (which I had never heard of before) that will be taught and assessed by AI. I see that for the new courses – apparently in subjects such as machine learning, digital innovation, entrepreneurship and business transformation

Content will be delivered through an online learning system that the university built from scratch. Students can choose to have content delivered in a written format or presented to them by an AI avatar.

Moreover,

…assignments will be assessed and given feedback by AI…

and

At the end of each module, students will engage in a “Socratic dialogue” with their AI tutor about the content to answer questions and reflect on their learning.

Whether the AI bot will end up corrupting young people and being compelled to drink hemlock is not specified…

I laughed when I read all this because it doesn’t seem to have occurred to anyone that if you have a qualification that can be delivered and assessed by chatbots then the job that you think it will qualify you for can also be done by chatbots…

Still, the London School of Innovation has been granted degree-awarding powers by the “Regulator” so it must be kosher.

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Two Weeks To Go…

Posted in Biographical, Education, Maynooth with tags , , , on April 27, 2026 by telescoper

There are just two weeks of teaching left in the Spring Semester at Maynooth University. Actually slightly less than that because next Monday (May 4th) is another bank holiday. That day doesn’t make any difference to my own teaching, however, as I have no teaching sessions on Mondays anyway.

As I mentioned last week, the formal teaching part of one of my modules (Computational Physics) is already over and the students are now – or should be – busy doing mini-projects.

My other module, Particle Physics, has four remaining lectures. That means that I’m on schedule, despite missing one lecture on Good Friday. The very last lecture for this module is on the last day of term, May 8th, so I don’t know how many students will be there. Come to think of it, because this is a final-year module, it may actually be the last lecture of all at Maynooth for some students…

The end of teaching does not mean the end of the term, however. We have a short “break” and then, on May 15th, the examinations start. In the break I’ll have to mark a stack of Computational Physics projects. That’s always quite hard work as I have to run the codes and check the results as well as read and grade the written reports.

This week and next we also have the final presentations for project students. That will take up two whole full afternoons (this Wednesday and next Wednesday). There’s usually a bit of a do after these to give the students a send-off, as these are projects done by the graduating class. I have been supervising two students this year, plus an MSc student (though the latter will not finish until August).

People sometimes ask me why we have such heavy teaching loads at Maynooth University. Four modules a year – other staff do five (as I did a few years ago when was also Head of Department) – plus projects is far more than one would expect of a “research-led” University outside Ireland. Part of the reason is what I mentioned yesterday – that the University (along with most others) spends far too much of its income on Management salaries and projects that have nothing to do with research or teaching. Other than that I can’t comment. According to this document, Maynooth University has committed to

Introduce a University Workload Allocation Model (WAM) enhancing transparent processes and procedures in the allocation of work.

If there is such a model, it is news to me…

P.S. There’s an even older document here (dated 2014) that says:

The University is committed to ensuring that the allocation of work is reasonable and fair across and within academic units. It is also required to exercise oversight of the implementation of academic workload management. In support of this, the Head of Department / School / Institute will monitor and record workload allocations and will provide to the university, via the Faculty Dean, an annual report on the procedure and model used to allocate workloads, and also an anonymised summary of the average and range of workload distributions between teaching, research and service among all academic staff in the Department/School/Institute.

The design and implementation of workload allocation models will be undertaken by Departments/Schools/Institutes in accordance with the general principles outlined above.

Will it? When?

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The University Malaise

Posted in Biographical, Education with tags , , , , on April 26, 2026 by telescoper

The UK University sector is currently struggling very badly. The latest piece of news I have seen is from the University of Nottingham, where it seems the Management is planning to cut over 600 jobs. New appointments are being frozen and a voluntary severance scheme launched, but it may well come to compulsory redundancies given the scale of the proposal. I feel sorry for anyone there caught up in this because the mood must be very gloomy right now. None of this is the fault of the academics or support staff on whose positions the axe will fall.

The financial predicament of the University of Nottingham is largely the result of a reckless management decision to acquire a new campus called the Castle Meadow complex.

I worked in Nottingham from 1999 to 2007. At that time the Castle Meadow campus (left) was owned by HM Revenue & Customs. It’s next to the canal and not far from the Railway Station, but not very close to the main campus. I remember passing it many times on the train going in and out of Nottingham.

The University of Nottingham bought the campus from HMRC in 2021 for £37.5 million and spend over £45 million redeveloping it, with the idea of siting the Business School there (among other things), but there was no demand for it and in 2025, the university announced plans to sell the campus at a considerable loss.

Now you would think that the people responsible for this fiasco would be held to account and pay at least some of the price for their incompetence. But no. The former Vice-Chancellor of the University of Nottingham, Prof. Shearer West, with whom the responsbility for the Castle Meadow campus disaster, left her post in 2024 to take up the position of Vice-Chancelor at the University of Leeds on a salary of more than £330K, leaving others to clean up the mess. I’m sure the staff and students at Leeds are waiting nervously to see what plans she has in store for their ruination. No doubt she received a glowing reference from Nottingham.

Anyone who thinks that positions with high salaries are always held by highly skilled people need only look at the Higher Education sector for definitive counter-examples.

The pattern of incompetent “leaders” switching jobs before the impact of their incompetence is revealed is a well-established one, but it’s not only the fault of the people at the very top. The entire system of governance is rotten, and not only in the UK. universities and other higher-education institutions have forgotten that the exist above all for education and research. Nowadays they have been captured by a self-serving management class that has lost sight of this and instead acts as if the only purpose is the generation of revenue, not to be spent on teaching and research but on vanity projects (like the Castle Meadow campus) and employing even more managers. Even if they were not being steered unerringly onto the rocks, universities would in any case be in danger of sinking because they are unable to support the weight of their bloated management superstructure.

I saw a post on Bluesky recently that included the following:


I asked a senior administrator what’s causing the University budget deficit.

‘Research & teaching,’ he said, ‘both lose money, not financially viable’

I said, ‘Funny, then, we weren’t losing money in the past when central administration was half the size’

That’s it in a nutshell.

I only wish this were an isolated example. It’s a systemic problem. Management bloat, expensive vanity projects requiring the diversion of funds from teaching and research, and deeply flawed strategic decisions, are symptoms of a widespread malaise. Unless there are drastic changes, the HE sector is going to shrivel and die.

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