Top mathematician leaves Leaving Cert maths reform group

This opinion piece by Dr Aoibhinn Ní Shúilleabháin is well worth a read. It appears in this weekend's edition of The Irish Times.

Reading it I found myself asking what would the late Dominican priests Canice Murphy and John O'Gorman, both mathematics teachers, have to say about it; I imagine they would be in agreement. As a non-mathematician, I thought her comment that 'handpicked opinions appeared in drafts and input from some members was consistently ignore'.  Ní Shúilleabháin has to be complimented for her observation and courage in saying it.

Such practice is not exclusive to the NCCA.

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As a child in Mayo, I found it fascinating to look at the dark night sky and see light travelling through time from far-flung stars to our tiny planet. I chose to study theoretical physics at university, not because I was the best in class at maths, but because I wanted to learn more about how mathematics explains the world around us. It was a challenging but rewarding degree, which instilled in me a love of the rigour, abstraction and creativity associated with the subject of mathematics.

Game theory, quantum mechanics and modelling traffic flow were all interesting parts of our studies that we grappled with, collaborated on and, eventually, mastered. Most of my classmates are now leaders in global finance and markets, with others spearheading research on gravitational waves. Our Leaving Certificate studies were just the first step on our mathematical journeys but gave us a flavour of the challenge and endeavour we might enjoy in further study.

As a secondary-school teacher, and now teacher educator, I try to ensure all children will have the opportunity to enjoy learning mathematics and see the value of the subject that is so prevalent and important in many aspects of life. Although only a handful might choose to continue their direct study of the subject, most learners entering further or higher education will continue doing mathematics. Others may never write another mathematical equation after secondary school, but they will use their mathematical knowledge and numeracy skills in all aspects of life, from calculating the best energy rates to managing colleagues’ work schedules. Having a mathematically literate society is an important part of empowering people to engage in democratic processes through calling out inaccurate claims and questioning data.

Levels of mathematical achievement correlate with higher incomes in later life but, unfortunately, not all learners have the opportunity to study mathematics at higher level. Schools that are designated as socioeconomically disadvantaged, or Deis, are significantly less likely to offer higher-level maths than non-Deis schools. With 25 bonus points available for those studying higher level, this inequity locks many young people out of further and higher education.

Worryingly, mathematics education in Ireland also seems to exacerbate a gender gap. Historically, girls were as likely as boys to achieve top marks in the subject, but since the curriculum reform of 2012 girls are less likely to achieve a H1 than boys. A similar gap does not exist with the Junior Cycle and work done by the Society of Actuaries of Ireland suggests the Leaving Cert maths exam favours students with more practised spatial-reasoning and problem-solving skills, strengthened through subjects such as applied mathematics (which is studied by twice as many boys as girls). This is not a problem with girls; it’s a problem in how we construct and assess our mathematics curriculum.

It was a privilege to be invited to contribute to a review of the Leaving Certificate mathematics curriculum by the National Council for Curriculum and Assessment (NCCA) and I looked forward to working with colleagues to design a syllabus that would allow all young people, of all levels of achievement, to develop the knowledge and skills that would benefit their futures.

Conversations within the NCCA group were collegial and professional, with a shared objective in designing curricula that would work for students. While there were disagreements of opinion, these were professional, respectful and constructive. Unfortunately, group decisions were not always recorded, handpicked opinions appeared in drafts and input from some members was consistently ignored.

The potential to design an additional assessment component that would allow students to think more deeply and communicate their mathematical understanding in creative ways was wasted. Decision- making processes were opaque and I found the structures of work to be flawed in design, governance and output. I do not believe these draft curricula serve the mathematical or numeracy needs of students sitting foundation or ordinary level and, even though Ireland already underserves high-achieving students, this proposed curriculum will not enhance student learning at higher level.

While errors in a draft curriculum can be amended, the fact that corrections from separate group members were consistently ignored points to a systems- design issue. Teachers and pedagogy experts are, and should be, involved in curriculum design, as is common practice around the world. Where Ireland differs is the formalised and constant involvement of subject-matter experts. Across the globe research academics and representatives of subject associations are consistently involved in curriculum drafting. This ensures secondary-school subjects can evolve to incorporate new knowledge and skills, engaging young people in subjects that are relevant and that prepare them for an ever-changing world.

A structure for curriculum design that maintains content coherence, makes evidence-informed decisions and supports teachers to translate this to the classroom is necessary. A dilution of such subject expertise in our current system may be why our biology curricula have, in a time of biodiversity crisis, dramatically less plant-based science, why our agricultural science curricula have little mention of forestry, or why academics resigned from the chemistry and construction study groups.

Mathematics is a human endeavour, continually developed and expanded through international collaboration, characterised by rigour, abstraction and proof. In a world where machines increasingly perform routine procedures for us, the value of mathematics in teaching students to reason, abstract, interrogate assumptions, construct arguments and determine whether conclusions are justified becomes more important. Unfortunately, these skills are precisely the aspects of mathematics that the draft curricula are eroding.

Had I studied one of the proposed curricula, it is unlikely I would have continued to do mathematics at third level. Considering another curriculum review may not happen for 15 years, I worry these curricula will discourage students from pursuing Stem.

Our children and young people deserve to learn in ways that are equitable and prepare them for their futures. I believe our current systems of curriculum reform are failing them. In an age where disciplinary knowledge and trusted experience are more necessary than ever, a systems review of how we design and incorporate subject-matter expertise, alongside important pedagogy and teaching practice, is required.

Dr Aoibhinn Ní Shúilleabháin is associate professor of mathematics education at DCU

Little publicity in change of payment of Household Benefits

Since September 8, 2025 all new applicants for the State Household Benefits Package are paid the allowance to their nominated bank account or post office.

Up until that date the allowance was credited to one's gas or electricity account.

Why the change? It seems it works out cheaper and easier for the State to manage.

But did the older system not give better protection to poorer and more vulnerable people? It seems to have been a safer method in helping people with their gas and electricity bills.

Did the change get much publicity? It would appear not. Why?

How can we stop the vacuous 'like'?

It seems in ordinary conversation in Ireland today it is next to impossible for anyone to put a sentence together without saying the word 'like' or the expression, 'like you know'.

It has become nonsensical. Younger people, people of school age, cannot put a sentence together without saying 'like' five or six times; every sentence begins with like. But it is not  exclusively used by younger people.

And it cuts across all classes, indeed its genesis maybe well be with the middle classes.

Someone has said it is a word-filler; what exactly is that? The way it is being used it has no meaning whatsoever, it is vacuous.

Yes, 'I like cycling' or 'he looks like his mother', perfect meaning of the word. But 'Like I went to town today and I bought a book, like. Gosh, the town was busy, like.'

It seems to be the first word foreigners learn when they arrive in Ireland.

How did this madness get such a life and how can it be ridiculed and stopped?

How do level crossings prioritise cars?

The letter below appeared in The Irish Times yesterday and below that the article to which the letter is referring. Anyone who reads the article is sure to ask the same question Peter O'Gorman asks.

The relevant sentence is underlined. 

Sir, – I read the article “Irish Rail seeks to close five level crossings” (August 31st) in a state of some confusion.

That confusion centred on the assertion by the Rail Users Ireland group that the level crossings “prioritise cars”.

When the train is coming, the gates close, and the cars wait. The trains do not wait. Perhaps the group could elaborate and explain exactly how this arrangement favours cars. – Yours, etc,

PETER O’GORMAN,

Sandymount,

Dublin 4.

TIM O’BRIEN

Irish Rail has confirmed it wants to close all five level crossings along the south Co Dublin train line, as recommended by consultants employed to oversee the Dart+ improvement project.

An unpublished report, prepared by Arup for Irish Rail, notes that the “emerging preferred option” for the Coastal South section of Dart+ would involve the permanent closure of the crossings at Lansdowne Road, Serpentine Avenue, Sandymount Avenue, Sydney Parade and Merrion Gates.

It recommended that an underpass for vehicular traffic be built north of the existing Merrion Gates, which link Merrion Road with Strand Road and is regarded as one of the worst traffic bottlenecks in Dublin, along with pedestrian and cycle crossings to replace the other four gated level crossings for vehicles.

The report, which runs to 681 pages, was delivered to Irish Rail in May 2022, but its conclusions have not yet been subject to public consultation. It focuses on Dart+ Coastal South.

The overall project would see the length of electrified rail lines increase from 50km – between Greystones, Co Wicklow, and Malahide, Co Dublin – to 150km. The extended network would serve Drogheda, Co Louth, and Maynooth, Co Kildare, and the M3 Parkway near Dunboyne, Co Meath.

The report acknowledges the closure of the level crossings “in the absence of suitable mitigation may have an impact on traffic in terms of connectivity, additional delays or queuing in the wider area”.

The four-year delay in progressing the report’s recommendations was criticised by the Rail Users Ireland campaign group, which obtained a copy under Freedom of Information laws.

Mark Gleeson, the group’s spokesman, said the closure of the Merrion Gates crossing “was first discussed in the late 1970s”.

Cars over train

“Dart passengers have suffered for 42 years from a compromise which prioritises private cars over the train,” he said. “The proposals from Irish Rail/Arup offer a once-in-a-lifetime opportunity to replace Merrion Gates and to dramatically improve rail performance and capacity.

“While some of the recommendations will clearly raise concerns, Irish Rail sitting on the report for over four years without starting public consultation is ridiculous.”

A spokesman for Irish Rail said Dart+ was a phased project, with the Bray to Greystones element of the Coastal South section progressing first.

“The remainder of the route, including the level crossings element, will not progress until 2030 at the earliest,” he said.

“The long-term goal to include the closure of the road/rail interface at the level crossings on the southside.”

The report notes that the five level crossings are closed to vehicular traffic between 41 per cent and 83 per cent of the time from 8am to 9am. The most frequently closed was Sydney Parade and the least was the Merrion Gates.

It notes that there were 28,000 vehicle movements across the five level crossings in a single day, with almost half of these (11,400) through the Merrion Gates. There were 4,900 at Serpentine Avenue, followed by Sydney Parade Avenue (4,600), Sandymount Avenue (3,900) and Lansdowne Road (3,200).

How many of us blindly follow the prevailing fashions?

This week's column in The Kerryman newspaper.

Michael Commane

Over the weekend I visited three people, two with developed stages of dementia and one with a brain tumour.

It depressed and shocked me; I have known two of the people ever before they were struck down with dementia and I know the other person since she was first diagnosed with cancer.

The experience forced me to ask what is it all about. It selfishly prompted me to ask myself how will I end up. 

We prance about thinking we are invincible; at the blink of an eye we can be struck down in myriad ways. We never know what’s around the corner. 

The new school term has begun, I’ve done my first few days of teaching post primary students. It’s most unlikely the ideas I am expressing here cross the students’ minds, that is, unless, they have had to deal with tragedy in their own lives. And at this age most of them have fortunately been spared the vagaries of life.

Why am I being so despondent, maybe even dark?

By chance on Saturday I watched something on YouTube that set my mind in a downward spiral; something that is forever haunting me. It was an interview with Markus Wolf. 

I imagine most readers have never heard of him; he was the chief spymaster in the former German Democratic Republic, better known to us as East Germany. The interview took place in 1990. 

He comes across as an intelligent, articulate, urbane man, whom I can imagine was a loving father and husband, though he did have three wives, not at the same time. 

He was enemy number one to the western world and feared and hated in his own country. Wolf was at the top of the hated East German secret service, known as the Stasi.

I recommend you watch it on YouTube, you can pull down the English subtitles.

John Banville once said that if he had his way he would remove the word evil from the dictionary and replace it with circumstance. How many people we know in management jobs, whether in private industry, state companies, the church, could as easily have found themselves working in similar jobs in Hitler’s Germany, Stalin’s Russia, Mao Zedong’s China? What would I have done? I think my incompetency would have made me a non-runner from day one; otherwise, I’m scared to think about it.

It’s not just in areas of health that we are fragile, surely that word fragility, maybe circumstances, cuts right across our lives from the day we are born until the moment of our death.

Just think of our school system and the race to score high in the world of CAO points. Our postcode plays a major role; just check the results from the various schools and it’s game set and match who wins and who loses.

And that’s part of the story that keeps me on my toes, even wondering how do we form moral opinions, how do we really decide what is right and wrong. 

How many of us simply follow the prevailing fashions, run along with the crowd. Do we all simply feel comfortable in our own particular bubble?

Whatever about Markus Wolf, who am I? Who are you?

Remembering the first day of six years of barbarity

On this day, September 1, 1939 Germany invaded Poland; the first day of World War II in Europe. The war lasted six years and one day and in that time between 6o and 75 million people lost their lives as a result of the barbarous conflict.

We are living in dangerous times; each of us has a role to play in making sure we don't drift towards war.

World War II did not happen overnight; conflicts were  breaking out across the world, fascism was on the rise, Germany felt it had been humiliated as a result of the outcome of World War I. Hitler offered them a strong man, he would make Germany 'great again'; the people, rich and poor, fell for his empty, evil words.

While Nasa reaches to the stars Trump behaves as Trump

A new Nasa space telescope, the Nancy Grace Roman Telescope was launched on Sunday from the Kennedy Space Center in Florida, USA.

It will help scientists probe the nature of dark matter, dark energy, and other mysteries of the universe.

The satellite will travel, covering over 1.5 million kilometres in approximately three months.

Some  short few days earlier US President Donald Trump renamed Lake Ontario Lake America; he did this because of a breakdown on discussions between the US and Canada on tariffs. Once again he threw the toys out of the pram.

Google has already renamed the lake, calling it Lake America; what sycophants, anything for a few extra dollars.

What would have happened had Donald Trump applied for a job at Nasa?

The world becomes a more confusing place every day. Maybe the Nancy Grace Roman telescope will help us get some answers.

The telescope is called after US astronomer Nancy Grace Roman (1925 - 2018), who was the first woman executive at Nasa; she was the chief astronomer at the administration in the 1960s and '70s.

Discover where you might be on the political/social compass

This is well worth a try. It's an interesting questionnaire to discover where you might be on the political/social compass.

It takes less than 10 minutes.

https://www.politicalcompass.org/test/en?page=1 

'Creeping like snail unwilling to school' - Shakespeare

Treat people as if they were what they ought to be and you help them to become what they are capable of being.  -   Johann Wolfgang von Goethe  (1749 - 1832)

Saw this on a notice board in an Educate Together school, where I have begun teaching. One week down and impressed with what I've experienced. 

Classes begin in earnest on Monday; happy learning and good fortune to all who are going back to school on Monday and a special word to those, who are beginning in a new school and indeed, to the little ones who are going to school for the first time.

Good luck to all.

An Australian airport chaplain on steroids, good ones

The link below is well worth watching; it's how an airport chaplain does a good job.

https://youtu.be/8nSAV8097Vg?si=rNwCfgRMpPOYF3oX

Back to school, shorter daylight, leaves on the ground

Did we ever think in Ireland we would be relieved to see rain?

It's back to school time; ever before the clock goes back the days are getting shorter, the magic of a 04.30 brightness is gone for another year and it's time to turn on the light shortly after 20.00.

Have you noticed there are far more fallen leaves on the paths this August than in previous years and flowers exhausted.

A Carlow man farming 100 cattle told The Irish Times that he is spending €3,500 per week to feed them due to drought conditions.

It seems the older we get the more difficult it is to face into winter; but at least we have autumn to prepare.

Remembering Warrenpoint and Mullaghmore

On this date, Monday, August 27, 1979 the IRA killed 18 British soldiers near Warrenpoint in County Down. On the same day an IRA bomb killed four people, including Lord Mountbatten, at Mullaghmore in County Sligo.

Thankfully we have come a long way from those dark days; all those who helped stopped the carnage deserve our gratitude.

Bus drivers deserve our praise in both word and deed

This week's column in The Kerryman newspaper.

Michael Commane

The carnage on our roads is appalling; it’s a horror show, and has been for far too long. Are they really accidents? 

When it comes to slaughter on our roads is it not a misnomer to call them accidents? If I get into my car, drive my motorbike or indeed cycle my bicycle having consumed alcohol surely it’s not an accident if I kill or maim someone? Indeed, you might say it was an accident I didn’t kill a person.

Most of us have no time for those who misbehave on our roads; at least we have no trouble expressing those views to friends and neighbours and certainly in public. 

But how often do we actually flagrantly break the rules of the road? Every day I see people on their phones while they are driving their cars. I’m inclined to believe people are so slow to move off when lights change to green because they are occupied with their phones.

And I’m no saint on the road. I believe the story below may have a cathartic role in my telling it and I certainly hope it has.

I have been gifted with the great ability of sound sleeping; alas one night last week I slept for a mere four hours. I spent the night thinking and worrying about something I had done earlier in the day.

I was cycling in Dublin’s city centre, to be precise on Dorset Street, heading towards Mountjoy Jail; I was in a hurry. I had been asked to deliver a book to someone and wanted to catch him during his lunch break. 

When I came to the junction of Dorset Street and Blessington Street the traffic light had turned red for me. I saw a stationary bus on Blesinngton Street and decided I could shoot across before the bus moved. But what I didn’t see was another bus which was moving. 

Had that bus not slowed down most likely I would now be in hospital with broken bones, indeed, I could be dead. It was the careful driving of the bus driver that saved me. He/she beeped their horn but at that stage I was on the far side of the street. I was somewhat shaken for a second or two but brushed it off and got on with my business. Yes, I was in time to make my delivery.

It was later that night in bed I thought of my appalling behaviour. What had I lost my legs and been wheelchair-bound for the rest of my life? It would have been no accident; every moment of it was my fault and no one else’s. And what about the driver, the trauma I would have caused her/him? I can well imagine I did give them a terrible shock.

I often chat with bus drivers and hear first-hand what they have to put up with every day. They do an extraordinary job for the travelling public.

It’s easy to blame everyone else for the road carnage. I hope and pray I’ve learned my lesson and practise what I preach. I wish I were in a position to apologise to the bus driver who was far more careful than I.

Newly partly-erected lampposts disappear in south Dublin

Some weeks ago Dublin City Council began erecting new concrete lampposts in Rathgar Village with the intention of removing the older metal lamp stands. The partly-erected three or four new lamp stands have  been removed, no sign of them. Where are they, what's happened them? Who pays for this apparent inefficiency?

The wealthiest again destroying the most disadvantaged

Due to an oversight, this post is late appearing today, apologies.

The slaughter on the carriageway near Middlesborough in the UK on Saturday is a copybook repeat of what happened on an Irish motorway earlier in the week. Indeed, in both cases five boys and young men were in both cars while driving in the wrong direction on fast roads.

These boys and young men are troubled people, some of them under the care of social services.  They have all been killed, they have also killed two police officers and seriously injured four adults and a child. They had done unimaginable damaged pain  to the families of those who they have killed.

There are myriad reasons for this behaviour but it is beyond a shadow of doubt they have been coaxed on to do this by TikTok.

The wealthiest people in the world fooling the most disadvantaged in society.

It's shocking.

Russia needs Europe as Europe needs Mother Russia

On this day, August 23, 1942 the German Army began the battle at Stalingrad. It was expected Stalingrad would be taken in two weeks. In February 1943 the Germans surrendered and it was the beginning of the end of Hitler's Germany.

On the same date the following year, 1943 the Red Army liberated Kharkiv, having defeated the Germans at Kursk, which was history's biggest ever tank battle. 

August 23, 1990 Armenia declared indepence from the Soviet Union.

And on August 23, 1990 the Federal Republic of Germany and the German Democratic Republic announced they would reunite/unit on October 30, 1990.

The moral of the story? Russia has an important part to play in the life and times of Europe.

Germany seen through the eyes of a BBC camera in 1955

This is a fascinating clip from the BBC archives.

It's filmed in Germany in 1955.

https://youtu.be/1s42PbmGWyI?si=OIr0ppNzSx3Wk32U

Attachments area

Preview YouTube video 1955: What Next for Germany? | Special Enquiry | BBC ArchivePreview YouTube video 1955: What Next for Germany? | Special Enquiry | BBC Archive

'You said Nato would not move one inch to the east'

This is a link to a press conference President Vladimir Putin gave seven months ago. He is answering questions put to him by BBC Russian correspondent Steve Rosenberg.

Rosenberg tells Putin all power is in his hands. One might ask how come Rosenberg is permitted to remain in Russia. Rosenberg's wife is Russian.

 https://youtu.be/y5kllN0U7nY?si=deE_lxY_hMaVP9yV

Free advertising TV bonanza for the Healy-Raes

Three nights in a row RTÉ has given hours of prime time television to events in Kerry; Monday and Tuesday the Rose of Tralee and then Wednesday the Healy-Rae show.

What would a political party pay for such free advertising.

The Healy-Raes have that special thing that grabs attention.

What exactly did Ivan Yates and Terry Prone add to the programme?

Michael can make some howlers. Last night he told us all that sleep is a useless exercise. A touch of Trumpism about that. It's doubtful the medical profession would agree.

Both Michael and Danny say they are not cash millionaires. What's a cash millionaire?

There was not too much sweat, blood and tears on the programme. An upfront interview with both Michael and Danny would have been interesting.

Great television. More votes for the Healy-Raes? Most likely. Isn't that their life blood.

A hitchhiker’s story on a busy German motorway fadó fadó

This week's column in The Kerryman newspaper.

Michael Commane

Last week Frank McNally wrote in his Irishman’s Diary in The Irish Times a piece about his hitchhiking days. It reminded me of the many years I spent hitchhiking. Indeed, up until the introduction of the Local Link service across Kerry two years ago I was often to be seen with my thumb out on a number of Kerry roads. 

Hitching is dead and gone and with O’Leary in the grave. I can well believe there are people under 40 who may not know what the word means.

In the 70s, and 80s there was not an exit to a city or town in Ireland where there were not young people sticking out their thumbs hoping someone might stop to give them a lift.

How Ireland has changed; I knew a young German Dominican who came on holidays to Ireland in the late 1960s with a fellow student. They hitched all across the country, wearing their roman collars. Until his death some years ago he was still talking about how they were never standing on the road more than five minutes before a car stopped. 

I had a mix of good and bad experiences, mostly good. It was summer 1972, the Olympics were taking place in Munich and I was hitching from Cologne to Worms, which is about 216 kilometres. 

I took a bus from the city centre to a motorway ramp. The ramp was crowded with hitchhikers; I decided to move up as far as possible, most of them were couples, I had the advantage of being on my own. 

Surrendering was on the horizon when a car pulled up, inside a young woman and her dog. I told her in very poor German I was going to Worms, she said she was going to Munich and that was on her way. 

Off we went; her English was slightly better than my German, I’m not sure how we communicated. Maybe an hour into our journey she told me she had a spare ticket to the Olympics, where she was going, and asked me would I like to go with her. 

I was 23, Irish and maybe shy, and immediately said no. We passed my exit and I explained I’d like to get off at the next possible exit or motorway rest spot. 

She kept driving. I again asked her to stop at the next ramp. At that, she pulled into the hard shoulder and told me to get out. I was relieved, jumped out, she drove off. 

As she did, I realised I had left one of my two  bags on her back seat. I was on a busy German motorway, scared. I walked to the next bridge, where I managed to scramble down on to a road. I had no option but to continue hitching. 

After a few minutes a huge truck pulled up, driver wearing a vest. I still remember he was a big man, for a second or two I did not know what to do. That man went out of his way and brought me to the hall door of our priory in Worms.

I often wonder what might have happened had I gone to the Olympics in Munich that summer in 1972.