Ireland’s brightest maths students are thriving. So why are experts worried about the Leaving Cert?

Mathematicians fear proposed cuts to rigorous topics could affect students far beyond those pursuing maths degrees, including STEM and business

Junior students concentrate on maths challenegs set at maths enrichment classes at UCC. Picture: Larry Cummins

Irish students more than hold their own on the international stage when it comes to maths, placing highly in some of the world’s most prestigious and gruelling competitions despite relatively low investment in supporting top-performing students.

The past two years has seen Team Ireland put in their best performances to date at the International Mathematical Olympiad (IMO), the world championships in mathematics.

Bright young minds from 117 countries are given 4.5 hours each day of the competition to solve six highly complex mathematical problems.

In April, Team Ireland also had its best performance yet at the European Girls Mathematical Olympiad, created 15 years ago to encourage young women to pursue maths at the highest levels. The accolades of these students are no small feat, and they are thanks largely in part to a team of dedicated volunteers from the Irish Mathematical Trust (IMT).

The group runs maths enrichment courses across the country, free weekend classes that aim to challenge the next generation of Ireland’s young mathematicians.

“We ask the students when was the last time they encountered a difficult problem or a problem they didn’t know how to solve, in maths class [in school],” said Neil Dobbs, lecturer in mathematics at University College Dublin (UVD) and IMT chairman. “They don’t remember. Never is a frequent answer.”

The publication of the draft specification for the new Leaving Cert maths curriculum has sparked concerns amongst mathematicians, both at second level and in higher education. Their concerns are not just for the top students, or those considering a career in advanced mathematics, but for the impact downstream on the entire third level sector.

The documents, which are now out for public consultation, were cast into the spotlight this week as news broke of two high-profile resignations of experts in their field from the group tasked with the subject’s redesign.

Aoibhinn Ní Shúilleabháin, associate professor of mathematics education at DCU, resigned this summer from the National Council for Curriculum Assessment (NCCA) Mathematics Development Group. Pauline Mellon, emeritus professor of mathematics at the School of Mathematics and Statistics at UCD, resigned from the group in January.

Discussing her reasons for resigning this week, Ms Ní Shúilleabháin said the proposed draft specifications fail to adequately prepare students for their future lives in society.

“I’m very worried about the lack of rigour or the reduction in content and abstraction that we have for our high-achieving students,” she told RTÉ.

Neil Dobbs shares these concerns. “The current Leaving Cert curriculum is offering very little already to the top 5% of students. They spend most of their time bored in maths class, both at Junior Cert and Leaving Cert.

“These changes are going to harm the next 10 - 15% of students who will just end up with no idea what to expect from third-level mathematics that is required in any STEM degree. There’s international evidence from the Programme for International Student Assessment studies that we are already underperforming at the higher end. These changes will make things worse.”

Having reviewed the draft, he believes the current proposals remove the topics that challenge students intellectually and provide examples of rigorous structured arguments.

“The more rigorous structured arguments they see, the easier it will be for them to write their own and structure their own thoughts,” he said.

“They are at an age where being challenged intellectually will make them smarter, and this is being cut from the curriculum. The majority of the cuts are to the deeper topics.

UCD lecturer in mathematics and IMT chairman Neil Dobbs at the IMT Awards ceremony in UCC. He believes the current Leaving Cert maths curriculum offers little for the top 5% students. Picture: Chloe Lehane

“By cutting the more consequential topics like complex numbers or proof by induction, and we’re not replacing them with something as equally deep, that is doing them harm.”

In her resignation letter to the NCCA in January, Prof Mellon pointed out how material on the course had been “diluted”, while at the same time “essentially nothing new has been added”. “Both breadth and depth have gone,” she said,

It proposes cutting “more or less all of” geometry, including all geometric proofs, a lot of trigonometry, mathematical induction, financial mathematics, and complex numbers.

She said “the essence of mathematics is diminished, namely, the role of abstraction, the concept and role of proof, of definition and the clarity and precision of its language are no longer adequately represented”.

“It seems to me that this has been a misguided principle of some of our NCCA colleagues, namely, we make mathematics friendlier by making it less mathematical.”

Speaking to the Irish Examiner this week, Prof Mellon raised concerns about the entire redevelopment process, which has been and is being replicated across all subjects as part of ongoing Leaving Cert reform.

Taking maths as an example, she points to international best practice.

“You’d have mathematicians who are thinking about the broad picture in mathematics, about how it’s changing, what’s moving in the background across the sciences, business and technology. 

"You’d have that represented by mathematicians, people with PhDs in mathematics in addition to experience at third level. Then you’d have people who deal with the whole pedagogy of the subject, and then you’d have second-level expertise.

“These all bring totally different expertise, and experience and viewpoints and perspectives. Each of those groups would be fully and properly represented. Each would bring their strengths at different stages of the process, and it would move flexibly. But that is not happening.”

NCCA response 

This week, when asked to comment on Prof Mellon’s concerns, the NCCA said it would “emphasise that the purpose of Leaving Certificate mathematics is broader than preparation for students who may wish to pursue mathematics or mathematics-related courses in higher education.”

The subject aims to “develop the mathematical knowledge, skills, values, and dispositions needed for continuing education, life, and work,” it said.

“It is designed to support the diverse needs and future pathways of students, including progression to higher and further education, apprenticeships, employment and informed participation in society.”

For Prof Mellon, her concerns are broader than the small cohort of students who will pursue a degree in maths.

“It’s easy to say ‘she’s a mathematician, she only cares about the people doing degrees in mathematics’. At no stage did I ever speak to that tiny cohort; that was never the case. I never related any of my concerns to people who are becoming mathematicians.

“I am speaking about people doing commerce, agriculture, engineering, all of the sciences. All require maths. I am talking about any student who goes on to do anything with any kind of quantitative basis whatsoever. Almost everyone has to take some form of maths. It’s not a small cohort; it’s replicated across higher education. We’re talking about the majority of students, not the elite who will go on to specialise in mathematics. That’s not who I am concerned about. I am worried about the majority.”

“The first thing you should do is do no harm. These syllabi will do harm. It will really harm mathematics education, and I don’t think these syllabi are serving students at any level. I don’t think they are serving higher level; I don’t think they are serving ordinary level or foundation.

If progressed, I genuinely believe it is going to pull back mathematics education, and I’m not talking about just a high level.

I’m talking about people who are going into all of our business courses, all of our engineering, all of our STEM, our computer science, our information technologies, all of the related courses in data science and data processing, across the board in all of our third level institutions. It will pull it all back.”

In a statement this week, the NCCA said all questions relating to the draft curriculum’s rationale, aims, structure, content and assessment are “all matters for public scrutiny and consideration during the open and transparent consultation over the next three months.”

“All feedback gathered during this time will be brought to the Development Group and carefully considered by them as they carry out further work to finalise the specification.”

A spokesperson for the Department of Education said: “These are only draft specifications; they have not been finalised.”

“Over the next three months, the NCCA is inviting feedback from teachers, school leaders, students, parents, people working in further and higher education, employers, mathematicians, and other stakeholders.

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“This feedback will help to identify areas requiring further work or refinement, and shape the next stage of work and ensure the final mathematics specifications are clear, rigorous, inclusive and practical to implement. Once complete, the NCCA will publish the findings from this consultation.”

As with all subjects, the Subject Development Group is chaired independently and “contains a range of expertise including the third level sector, school management and teacher representatives, with all members of the group bringing their experience and expertise to the group’s work”, she added.

For Prof Mellon, the impact of getting this aspect of the curriculum wrong will be stark.

“If this is progressed, it will step back mathematics education, and it will step it back for two decades. That’s going to have downstream effects across third level, in almost every subject that has any quantity values in it whatsoever. It’s going to have massive effects down the line for industries — the Googles, the Microsofts, AI. Mathematics underlies almost all of AI .”

• Jess Casey is Education Correspondent.