When maths teacher Horst Punzet sets assignments for his secondary school students, they sometimes resemble art classes.
Students are asked to make different types of origami, such as intricate petals or kusudama flowers, using precisely folded pieces of paper.
In the run-up to Christmas, some of his maths classes can be seen making decorative snowflake patterns using Sierpinski patterns – named after the Polish mathematician – made up of tiny equilateral triangles subdivided into smaller triangles.
“Some of the students probably go home and wonder why they’re doing so much art, but this kind of practice is all about helping with spatial awareness,” says Punzet, who taught at Rathdown College until this year, a formerly all-girls school in Dublin. “They learn how important precision is. It also helps [them] with geometry, visualisation and problem-solving.”
Spatial ability, or the ability to understand the meaning of space and use it as a vehicle for structuring problems, finding answers or expressing solutions, is a very strong predictor of success in maths.
It is also cited as a key factor in a new report that explores why there has been a sharp decline in girls’ performance in Leaving Cert higher level maths compared to boys since 2012.
For example, in the early 2000s girls accounted for about 44 per cent of top grades or H1s in higher level maths in the Leaving Cert. There was a gradual decline in relative female performance until 2012, when a sharp drop saw the proportion of females with H1s fall to about 25 per cent, even though the number of boys and girls sitting the exam was broadly equal.
The trend persisted until the Covid-19 pandemic, when teacher-estimated grades resulted in the gap disappearing. However, the return of normal exams has seen the gender gap re-emerge. In 2023, for example, girls accounted for about 37 per cent of top grades,.
There is a similar pattern at Junior Cycle level. In every year from 2001 to 2009, more female than male students achieved an A grade in the old Junior Cert higher level. However, in every year since 2011, more male than female students have achieved this grade. The trend has continued with the new Junior Cycle paper.
So, what’s going on, exactly?
Researchers say the widening gap coincides with the introduction of Project Maths reforms and changes in the exams which now require greater problem-solving proficiency.
A Society of Actuaries’ report published a fortnight ago references how “application style” questions introduced to the Leaving Cert exam as part of the Project Maths syllabus require not just mathematical skills, but the application of spatial reasoning.
There is a proven link between spatial ability and problem-solving ability. The research also points to an internationally recognised gender gap in spatial reasoning, which is known to widen through the secondary school years.
The paper’s authors believe these changes have disproportionately discriminated against female Leaving Cert students.
The authors also cite research in Ireland and abroad which has found that teenage girls are generally less confident than teenage boys when it comes to maths problem-solving.
The authors, for example, cite research at Harvard Kennedy Business School which found that in a competitive test-taking environment with penalties for wrong answers, women were less willing to guess, resulting in a loss of potential points and lower scores compared with male test-takers.
In addition, female second-level students are much less likely than males to choose subjects that hone spatial reasoning skills such as applied maths, design and communication graphics, and physics.
The Society of Actuaries’ report, in turn, references a report published by the Irish Mathematics Teachers’ Association in 2021 in which teacher Aidan Roche examined these trends. He also found that a widening gender gap appeared to be linked to a greater emphasis on problem-solving proficiency in the exam.
Another change is the introduction of bonus points in 2012. The measure, which awards 25 additional points to higher level Leaving Cert candidates who score a H6 or more, has prompted a doubling in the number of students sitting the higher level paper from about 16 per cent in 2011 to well over 30 per cent by the end of the decade. This, in turn, say many teachers, has changed the way maths is taught, with more students of mixed ability in the classroom.
However, most believe the impact of expanded numbers is likely to have been gender-neutral.
In terms of potential solutions to help level the playing field, teachers point to some key changes.
Eoghan O’Leary, deputy chair of the Irish Maths Teachers’ Association and a teacher at Hamilton High School in Bandon, Co Cork, says he sees first-hand how subject choice can have a crucial role in maths performance among girls and boys.
He says students who choose subjects that require numerical and problem-solving skills – such as physics, applied maths and accounting – have a much higher chance of securing a top grade.
“All those subjects really help in the background and can provide a massive advantage,” he says.
Traditionally, at least, subjects such as applied maths were much less common in all-girls schools, although that is changing.
“Increasing access to applied maths would be a very effective way of addressing the gender gap,” he says. “There is a new syllabus for applied maths which is wider and more accessible than the old one and has broader appeal A lot of schools still don’t offer it, but students would benefit by taking it.”
Jane Keenan, a maths teacher at Salerno Secondary School in Salthill, Galway, says the quality of tuition is also crucial.
“Passionate teachers do help, but they are so hard to find in today’s world,” she says. “Ideally, students need teachers who really put their heart and soul into it, as opposed it just being a job or second subject. A teacher who lights that fire and encourages them every step of the way makes such a difference.”
Ensuring there is enough time for maths on the timetable is also crucial, she says. While Keenan says her school has a very good time allocation, she says it can vary widely. Some, she says, struggle to complete the curriculum or have time left to revise in the lead-up to the exams.
The Society of Actuaries says the gender performance gap requires urgent attention, especially given the potential for females to be underrepresented in senior roles in financial services and elsewhere.
“While it is clearly an issue for the actuarial profession, we believe it is also likely to be an issue for Stem [science, technology, engineering and maths] careers more widely, both within financial services and beyond,” it adds.
As for Horst Punzet, he feels that creative approaches to boosting girls’ spatial reasoning and problem-solving skills have a crucial role to play in boosting girls’ performance.
It is, he feels, one factor behind why girls at the school he taught in have bucked national tends and secured high proportion of top grades.
“I see many girls are, by and large, very effective at rote learning, whereas boys can be better at problem-solving,” he says. “So, for girls, it’s about developing those skills. Addressing this doesn’t have to be a hard grind. It can be fun, for both boys and girls.”
Girls and maths: in numbers
44%: proportion of top grades in higher level maths secured by girls in 2001
24%: top grades in higher level maths secured by girls in 2012, when Project Maths was introduced
37%: proportion of top grades in higher level maths secured by girls in 2023
