Analysis: an archive of Leaving Cert maths' papers tells a fascinating story of how the exam has changed since 1925

By David Malone and Hazel Murray, Maynooth University

We often hear people telling us that the Leaving Cert was much harder in the past, but what were the exams actually like?  Over the last few years we have collected Leaving Cert and Junior/Inter Cert exams, so people can find out. We were sparked into action by a Twitter-based claim by a friend who claimed to have had studied differentiation and complex numbers for Inter Cert mathematics in the 1980s (spoiler: they hadn't). We have collected many of the STEM exam papers from 1925 to present day. Why 1925? Well, that's the first year the Leaving Cert and Inter Cert were examined by the newly-minted Department of Education.

Building an archive is trickier than it sounds. While the National Library of Ireland and Trinity College library have officially issued collections of exams, there are some systematic gaps. For example, there was a large revision of the syllabus at the end of the 1960s, which seems to have resulted in the past papers not being issued, presumably because they were no longer directly relevant to students and teachers.

We have been lucky to have some help building the archive. The State Examinations Commission have been able to provide us with access to some of the more elusive exam papers. Many gaps have been filled with help of teachers and students around the country who have sent us papers from their own collections.

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From RTÉ Six One News in 2019, a pilot programme offering free maths grinds has proven to be a hit with Tallaght students

At Leaving Cert Level, the archive includes papers from Maths, Applied Maths, Physics, Chemistry, Biology, Design & Communication Graphics and the newly-added Computer Science. This cross section represents traditional science subjects and also some technology. At Junior/Inter Cert level we have collected Maths, Science and Technical Graphics papers.

Tales from the archive

We've learned many things from the archive already. For example, did you know that there was no Biology course before 1971?  Instead, there were two courses "Botany" and "Physiology & Hygiene".  We've also spotted some interesting trends - papers seem to be growing longer (in terms of pages) and have more pictures and figures than they used to. Also, the pattern of pink for higher level Leaving Cert papers and blue for ordinary level goes back to 1930!

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From RTÉ Radio 1's Liveline, listeners discuss issues with the 2015 Leaving Cert maths papers

Maths for girls

Another discovery is that there were girls and boys-specific exams and questions at various points in the history of the examinations. One particularly interesting example of this is "Elementary Mathematics for Girls Only" that runs from 1930 to 1968.  While this might seem like a straight forward example of sexism, it is a fascinating story that is more nuanced than you might expect...

In 1920s Ireland, girls were (largely) taught in girls schools by women. Maths was not even compulsory for girls at the Inter Cert: you could take "arithmetic with another subject", such as science, to avoid taking mathematics. The department identified that girls were capable of maths and that "a knowledge of the subject is of considerable importance to girls as well as boys".

However, they also identified what we would now call a pipeline problem. Girls often did not take maths to higher Leaving Cert level at school. As a result, there are not enough women studying maths at college, so there would continue to be a dearth of strong mathematics teachers for girls.

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From RTÉ Radio 1's Today with Claire Byrne, Dr Aoibhinn Ni Shuilleabhain on maths and gender stereotyping

In 1930, the Department introduced Elementary Mathematics for Girls to encourage the study of maths in girls schools. Since boys don't have the pipeline problem problem, they weren't permitted to take the paper. It is not so much "Elementary Maths for Girls", as "not for boys".

Once this subject had been introduced, it became somewhat entrenched in the system, and it was not until the large syllabus reform in 1968 (the same reform that made some exam papers hard to find!) that maths for girls was finally killed off.

Have the exams got easier?

A question from the 1986 Leaving Cert Ordinary Level Maths' paper

Deciding if exams have got harder or easier is difficult, because it depends on what you mean by harder.  Let's restrict our attention to a single subject like mathematics. In 1926, students were expected to use a result that you might teach to undergraduates today, so on the face of it, the exam was harder. On the other hand, the unusual wording of the question suggests that this might actually have been bookwork that many students would learn by rote, which is something today's maths exams have moved away from.

You could also ask how students performed in the exams, but a meaningful comparison is difficult. In 1926, just 427 boys and 128 girls took Leaving Cert maths. Now, almost one hundred times as many students take the Leaving Cert.

A question from the 1996 Leaving Cert Ordinary Level Maths' paper

A few things are clear from the exams. The increased length of the papers allows more explicit instructions on what is required of students. Students now also have less choice: students are usually expected to answer all the questions on the maths paper, though some exceptions are being made for Covid-19 in 2021.

The exams also show syllabus changes. For example, vectors and matrices were introduced in the 1960s and retired in the 2000s to give more scope for the study of subjects like statistics. Who knows if vectors or statistics is harder?

A question from the 2006 Leaving Cert Higher Level Maths' paper

So, rather than giving our answer, we will leave answering this question as an exercise to you. You can find all the exam papers here and make that decision for yourself

Prof David Malone is a senior lecturer at the Hamilton Institute and Department of Mathematics & Statistics at Maynooth University. Hazel Murray is a PhD student at the Department of Department of Mathematics & Statistics at Maynooth University and a visiting lecturer at the University of Chicago. She is an Irish Research Council awardee. 


The views expressed here are those of the author and do not represent or reflect the views of RTÉ