Archive for Higher Mathematics

The 2025 Leaving Certificate Mathematics Papers

Posted in Education, mathematics with tags , , on June 7, 2025 by telescoper

As I mentioned a few days ago, examinations for the 2025 school Leaving Certificate are under way. One of the interesting things about the Irish system is that the examination papers are put up online immediately after the examinations. Students took their first paper in Mathematics (either Ordinary or Higher level) on Friday (yesterday), and there has been some reaction.

Anyway, I thought I’d share the papers here so you can see what you think. Paper 2 is on Monday 9th June, so I’ll add those papers then.

They look reasonable to me. The thing that strikes me about them is that they are much more structured than the A-level mathematics examinations I took way back in 1981.

Comments are welcome through the box below.

Update: As promised here are the Papers 2:

Reaction to Paper 2 of Higher Mathematics is that it was more challenging than Paper 1.

The Returning and The Leaving

Posted in Biographical, Education, mathematics, Maynooth, Politics with tags , , on August 26, 2023 by telescoper

I got back to Maynooth last night after a pleasantly uneventful train journey. Just for the record both outward and return trips were perfectly on schedule. In fact it has been a very pleasant couple of days. Congratulations to the organizers for running the meeting so well and to all the speakers for delivering such an interesting programme. Next year’s INAM will be in Galway. I’m looking forward to it already!

Anyway, now I’m back I should mentioned that the 2023 Leaving Certificate results were released to students yesterday; the first round of CAO offers will go out on Wednesday 30th. Soon after that we will find out how many students we’ll have next year. Student enrolment begins on 11th September; Orientation Week for new students starts on Monday 18th September; and lectures start the following Monday (25th). I am on sabbatical for a year from next Friday (1st September) so I won’t be teaching the new students, but I know they’ll be in capable hands.

There’s a lot of discussion – much of it poorly informed – in the media about grade inflation in the Leaving Certificate (e.g. here). This happens every year (as it does with A-levels in the UK), and its very sad that people use this occasion to publicly disparage the accomplishments of students. The students can only take the examinations that are put in front of them. Any problems with the system are not their fault at all.

This year the problem stems from a decision by Minister for Education Norma Foley to impose a condition that overall grades this year would not be lower than last year. This has led to the deployment of scaling which has resulted in an uplift of around 8%. The Higher Mathematics Leaving Certificate results also benefitted from an alteration of the marking scheme because one of the papers was deemed to be too hard. Despite this, the number of students receiving the top grade of H1 fell this year from 18% to under 11%. One might argue that this disadvantages students applying to courses that actually require mathematics compared to those that don’t.

There seems to be a widespread misunderstanding that the CAO points required for a course is somehow a measure of the level of difficulty of that course. In most cases this is not the case: having a high points threshold is basically just a way of controlling the number of students allowed in. I find the connection that has been made between grade inflation and drop-out rates extremely unconvincing. High drop-out rates in recent years are probably dominated by the pandemic, housing crisis and cost of living increases, leading to many students struggling to study effectively.

During the pandemic years, grades were inflated by including coursework rather than examinations, a change enforced because of public health restrictions. The main argument for deliberate grade inflation this year was to prevent this year’s LC students being disadvantaged with respect to last year’s. It doesn’t seem to have occurred to the Government that the same argument could be used next year, and indeed forever. Fairly typically for a politician, kicking the can down the road for the next government to deal with seems to be strategy.

As a final thought, I find myself wondering what will happen to admissions at Maynooth this year. Will the decision by The Management to scrap the promised Student Centre have a big effect? And what about the further reputational harm caused by the recent furore over the Governing Authority? I suppose we’ll find out next week!

Talking about the Leaving Certificate

Posted in Literature, mathematics, Maynooth, Poetry with tags , , , , , , on June 10, 2023 by telescoper

One thing that I forgot to mention in my post about examinations a few days ago is that students at Irish schools all sit exactly the same examination papers at the same time. This is very different from the UK where there are several different Exam Boards that have different syllabuses and set different papers. One consequence of the Irish system is immediately an exam is over, there is a national discussion of the students’ and teachers’ reaction to it. The examination papers are posted online after the examination too – you can find them here – so that everyone can join in the discussion.

I have to admit that when I was a student I was never one for talking about examinations after I had taken them. While most of my peers stood around outside the Exam Hall conducting a post mortem on the paper, I usually just went home. I always figured that there was nothing I could do about the results then so it was best to put it behind me and focus on the next thing. That’s what I’ve recommended to students throughout my career too: don’t look back, look forward.

Anyway, the first Leaving Certificate examination this year (on Wednesday) was English Paper 1, followed by Paper 2 on Thursday. Both seem to have been received relatively favourably by students; see some discussion here and here. Paper 1 is really an English Language Examination, with exercises on comprehension and composition while Paper 2 focuses on literature. Every year summer I look at the set books and poems for the English Leaving Certificate Paper 2 and they’re usually an interesting mix. This year the novels included Mary Shelley’s Frankenstein, Raymond Chandler’s The Big Sleep, Oscar Wilde’s The Picture of Dorian Gray, and Margaret Atwood’s The Handmaid’s Tale. The list of poets for the Higher examination was Elizabeth Bishop, Emily Dickinson, John Donne, Patrick Kavanagh, Derek Mahon, Paula Meehan, Adrienne Rich, and W.B. Yeats. Not all the texts come up in the examination. In the case of the poets, for example, Mahon, Kavanagh, Meehan, Donne and Rich appeared on Paper 2 but there was no Dickinson, Donne or Bishop.

While I have a personal interest in English literature, the English examinations are not relevant to me in a professional capacity. On the other hand, the Leaving Certificate papers in Mathematics are of direct relevance to me as a Professor in the Department of Theoretical Physics because they indicate the level of mathematical preparation of students likely to come in next academic year.

General reaction to Higher Mathematics Paper 1 seems to have been much more mixed than for the English papers, with many students taking to social media to express shock that it was so difficult: the hashtag #MathsPaper1 is still trending on Irish Twitter; you can also find some reaction here.

I have looked at the paper but can’t really comment on the level of difficulty because I haven’s studied previous years examinations in detail but I will say that (a) there’s quite a lot to do in the 150 minutes allowed and (b) there’s nowhere near as much calculus as in my A-level Mathematics over 40 years ago (though remember that Irish students do more subjects in the LC than UK students who do A-levels). Note also that because of the pandemic, this would have been the first state examination taken in Mathematics by many students.

The Leaving Certificate Higher Mathematics examination is split into two sections of equal weight. Section A (‘Concepts and Skills’) requires students to answer 5 questions from 6 (each split into parts); Section B (‘Contexts and Applications’) gives a choice of 3 out of 4 longer questions. That’s less choice than I expected; students have to answer 8 out of 10 questions. The Ordinary Level Examination has the same structure, but the questions are much more straightforward.

Mathematics Paper 2 is on Monday, so I’ll update this post then.

Update: Mathematics Paper 2 seems to have gone down much better than Paper 1. You can find it, along with some reaction, here.