Engineering in the Leaving Cert

About 6% of those studying Engineering for the Leaving Cert are female. Why is this? First, Engineering is probably not offered in many all-girl schools. Second, the Leaving Cert engineering syllabus is bloody awful. I’m an engineer and I find it boring.

Judging from last year’s exam paper, the subject is completely dominated by mechanical engineering with a large emphasis on materials, devices and machinery. There’s no chemical or biochemical engineering (the most molecular of the engineering disciplines and traditionally the one that has the highest percentage of females), no environmental engineering and very little biomedical engineering. Bizarrely for an engineering curriculum, there is little or no computation involved and, most importantly, it looks like the  student will get no real sense that science and engineering are inextricably linked, and  that scientific advances are often possible only because of extraordinary feats of engineering.

Instead of waffling about STEM and new, supposedly ‘engaging’,  pedagogies, we should be injecting a bit of excitement into the curriculum of each of the STEM subjects and, most importantly, ensuring that these subjects are taught by passionate teachers with the required content knowledge.

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It’s official: STEM is a thing and it’s all about real world problems and stuff

From the recently launched STEM Education Policy Statement (emphasis mine):

STEM is about igniting learners’ curiosity so they participate in solving real world problems and make informed career choices [sic].

STEM is interdisciplinary, enabling learners to build and apply knowledge, deepen their understanding and develop creative and critical thinking skills within authentic contexts.

STEM education embodies creativity, art and design.

So STEM is now officially a sort of super-discipline, designed to enable young people  to become real-world problem solvers and to develop thinking skills. Oh, and it involves a bit of art and design.

This has to be a document written by non-scientists; spoofers who don’t understand what it takes to master one of the STEM disciplines, never mind a STEM super-discipline; who seem to have no interest in the value of science and mathematics for their own sake; who are in thrall to technology; who see education in purely instrumentalist terms; who believe that education should mimic the world of work;  who have forgotten where they have come from and forgotten how they have come to be where they are; people who believe that skills have an existence independent of knowledge; people who believe that even STEAM is a thing.

It’s a depressingly bad document and it makes me angry.

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Is coding really the future?

I’ve done some coding (aka computer programming but that sounds less sexy) throughout my career. As a student (undergrad and postgrad) I did lots of coding in FORTRAN and a few years ago I did an Open University module in which I had to code in the AI language, Prolog. Most recently, any programming I’ve done has been in MATLAB.

My view of coding is this: coding is a tool that can be used to solve problems and if the problem is interesting, so is the coding.

So I find the clamour to introduce coding into primary school a bit odd. What problems do we want kids to able to solve with their new found coding skills? We teach young people to read and write and do sums because these are skills that they will use throughout their lives. But can we say these things about coding? Is coding really going to be the equivalent of writing? Somehow I doubt it and it seems to me that we have developed a sort of fetish around coding and most of the evangelists for coding have never coded and never experienced that feeling when you want to smash your computer to bits because your code is churning out nonsense.

A lot of education policy these days seems to be driven by a sense that the 21st century world is very ‘sciencey’ and so our students should be learning lots of ‘sciencey’ stuff, whether it’s coding or building robots. I’m not convinced and anyway, won’t the robots who many claim are coming and about to take away our jobs, not be able to do our coding for us?

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David McWilliams, education and group think

The weird thing about the David McWilliams show on TV3 tonight was that David seemed to think that he was saying something new.  (For international readers, David McWilliams is to Irish economics what Brian Cox is to physics and astronomy.)

In fact, in a talk in which he bizarrely blamed our secondary school system for the groupthink that led to the financial crisis, he was a living example of groupthink. He presented (backed up by an obviously cherry-picked audience with a few notable exceptions) a mish-mash of the decade-old ideas of Ken Robinson and Howard Gardner, sprinkled with the fairy dust of “jobs that don’t exist”, “21st century skills”, “critical thinking” and “learning styles”. It was all depressingly jaded and derivative stuff and very much part of the education orthodoxy that has designed Project Maths and the new Junior Cycle, all inspired by the belief that knowledge is dead because we’ll always have Google and all we need are ‘skills’.  It was the snake oil that education consultants have been peddling for years – and making lots of money out of it.  It was the stuff of the TED talker, the spoofer and the person who thinks he/she is an expert on education because he once went to school.

The whole programme was conducted in an evidence-free zone. The fact that the financial benefits of higher education are higher in Ireland that anywhere else in the world was ignored (and I’m not saying that’s necessarily a good thing), that entrepreneurship is highly correlated with educational  achievement (see here, here and here), that Ireland is the 10th most innovative country in the world, that it is employers not the ‘system’ who are driving the need for youngsters to acquire a third level education, was all ignored. It was all anecdote, prejudice, anti-intellectualism and reverse snobbery.

When the programme veered into AI, self-directed leaning, student empowerment (students learn what they want!) I could see that we were heading into the territory of the deluded.

To be honest the whole programme was pathetic and beneath David McWilliams who is a smart guy and normally a fine communicator. It presented ill-defined solutions to ill-defined problems and all in all, it was an unholy mess.

I teach university students who are in the top 15% of school-leavers as measured by the Leaving Cert. More than anything, they have a proven work ethic – to get 480 points in the Leaving, you have to work hard. They are (in the main) bright, enthusiastic, modest and willing to learn. We take them from school where they are assessed by a final written exam and we assess them in at least 10 different ways over the course of their university career. They respond brilliantly and it is an absolute pleasure and privilege to work with most of them.

What bugs me the most about all of this cynicism is that it belittles the efforts of the thousands of youngsters who take on the challenge that is the Leaving Cert – for many the biggest challenge that they will have faced in their lives – and live to tell the tale.  They will have shown remarkable work ethic and resilience in doing so. Then, with our guidance and support, the majority of them overcome the many challenges presented by third level education and become the extraordinarily talented scientists, lawyers, doctors, nurses, engineers, teachers and all of the other professions that make such a contribution to our country.

What is it about our history that has made us so cynical?

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10 of the best popular science books

Given that it’s science week, here are 10 books that I have read and would do so again:


Cosmos by Carl Sagan

The story of everything brilliantly told by the first science communication superstar.

The lonely hearts of the cosmos – Denis Overbye

The story of astronomy; not just the facts but the personalities and the rivalries.

Man on the Moon – Andrew Chaikin

The best book about the Apollo missions that you’ll read.

Prime Obsession by John Derbyshire

The connections between seemingly unrelated branches of mathematics are brilliantly revealed but you’ll need to like maths for this one.

Chaos by Jonathan Gleick

The story of the young pioneers of nonlinear dynamics and chaos theory. Really conveys the excitement of being in at the beginning.

Quiet by Susan Cain

In an increasingly extrovert world, this is a great reminder that some people just like a bit of peace and quite. Educators take note.

Why don’t children like school – Daniel Willingham

We’re in cognitive science territory here and this is the book that really started my education journey.

The Elegant Universe by Brian Greene

The story of string theory taught by a current superstar of science communication, and the author’s modest part in it. Conveys the excitement of scientists who thought they were on the verge achieving the holy grail of physics: the unification of the forces.

When breath becomes air by Paul Kalanithi

Really belongs in the ‘illness narrative’ category (a genre I usually hate) but it brilliantly and heartbreakingly conveys the shear brutality of terminal cancer.

A tear at the end of creation by Marcelo Gleiser

The basic message here is: the universe is complicated and messy – not reducible to a single over-arching theory – and maybe we just have to live with that.

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Mathematical Mindsets by Jo Boaler – A review of Chapter 5

I have tons of lab reports to mark so naturally enough I decided the spend last hour reading Chapter 5 of Jo Boaler’s Mathematical Mindsets book. This chapter has the title Rich Mathematical Tasks.

The overall impression I got from the chapter is that mathematics classes in which Jo Boaler’s methods are used would indeed be very engaging for students. There is a big emphasis on inquiry, creativity and independent thinking and it is quite easy to imagine kids enjoying the whole experience.

But there is no real context provided and in some ways the whole thing reminds me of the Project Maths initiative in Ireland. Project Maths is designed to make maths more engaging and more ‘authentic’ and to make students better at problem solving and critical thinking. Taken on its own merits, it’s not a bad course although it does seem to present particular challenges to people with reading difficulties (it’s very ‘wordy’). But the thing is; there is growing evidence that Project Maths does not prepare students for mathematics study at university. Students seem to lack basic skills and the narrowness of the Project Maths curriculum has left big holes in their mathematics knowledge.

And that’s the thing about education – you always have to ask the question: does the new approach, engaging and all as it is, prepare students for the next rung on the education ladder? Evidence from Canada, in particular, would suggest that methods such as those proposed by Boaler, seductive as they might be, ultimately lead to a decline in performance at higher levels.

So while I think that aspects of Boaler’s approach have merit when used in moderation, I can’t really seem them as a blueprint for the future of maths education.

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A review of Mathematical Mindsets by Jo Boaler: Part I

At the second attempt I returned to Jo Boaler’s book Mathematical Mindsets. I really wanted to get an insight into what she is proposing because I have no doubt that the curriculum designers are planning to incorporate Boaler’s ideas into what will be Ireland’s revised primary school curriculum. And what happens at primary school level eventually affects us in higher education.

Before reviewing the book in detail I think it’s important to state what I believe about maths teaching.

I believe that mathematics is best seen as a language in which the ‘grammar’ is not arbitrary but follows logically from a small number of axioms.

I believe that all rules of the mathematical language should be explained and justified when first encountered, and not just presented as arbitrary rules to be ‘learned off’. However, I believe that mathematical fluency can be (and usually is) achieved by remembering and applying those rules even when the proof of those rules has been forgotten. If you are bothered by a lack of understanding at any time, then you can always go back and refresh your memory.

I believe that mathematical fluency is an essential component of mathematical problem-solving. A lack of fluency leads, in my opinion, to cognitive overload and frustration.

I believe anyone can become competent at mathematics through effective, enthusiastic teaching and a lot of practice but I’m not sure how far you can push this. Is everyone capable of getting a degree or a PhD in engineering or physics, not to mention maths? Perhaps, but maybe for most people the process would be so slow that the opportunity cost involved in pursuing maths-intensive study might be too great. But I also believe that only some people – perhaps a small fraction of the population – have the innate talent for the abstract thinking required to become high-achievers in math.  I think maths is like singing or painting or writing or any other academic, athletic or artistic endeavours. Most of us can reach some degree of competence but true excellence is likely to be beyond us no matter how hard we practice.

I think it’s understandable and no great mystery that many people just don’t like mathematics. In my view it is hard to construct an evolutionary argument as to why human beings would have evolved to the extent that most of us were able to think in the abstract way required to progress in maths (see this paper by Steven Pinker).

I think people are turned off by maths for two reasons: (i) they didn’t really like it in the first place (and shouldn’t have to explain themselves for not doing so) or (ii) they fell behind at some stage of their learning, failed to catch up, and lost all motivation. Maths is a very hierarchical and unforgiving subject.

People who really like mathematics love what many modern maths gurus describe disparagingly as ‘drills’. Every problem is seen as a challenge. Every problem is there to be solved whether it is ‘authentic’ or not. ‘Maths people’ need to be nurtured and challenged just as much as the people to whom maths has to be ‘sold’.


Anyway, given that background, I set off on the Boaler book which despite the name is really about the teaching of arithmetic and basic geometry. It’s not about algebra or calculus or differential equations. My impression from leafing through the book was that Boaler was over-complicating things in the name of enhancing ‘understanding’ but I was willing to be convinced otherwise. I should say that Boaler seems to advocate a very visual approach to mathematics and visualisation wouldn’t be my default way of thinking about anything. So I do have to acknowledge my own built-in biases

I also have to say that when I first encountered Jo Boaler it was through this article in Scientific American in which she seems to seriously misinterpret the PISA 2012 findings on the teaching of mathematics (See Greg Ashman’s analyses which begin here.) So I have some trust issues!

Anyway here is what I thought of the first three chapters.


Chapter One: The brain and mathematics learning

The purpose of this chapter seems to be to present the proposition that, with the right mindset, everyone can become expert at mathematics. “Mindset” here is the growth mindset of Carole Dweck fame and to me it seems to be little more than a ‘sciencey’ way of talking about what you or I might call a positive attitude. It seems to be a very American concept, an idea that you can accomplish anything if you just try hard enough and are not fazed by failure.

Chapter One is fundamentally about making the case for the primacy of nurture over nature. It’s inspired by ideas like brain plasticity which most of us have heard about, but also a curious thing called “brain growth”. My impression of the chapter was that the discussion was superficial and ignored vast swathes of literature in which nature versus nurture has been debated, often quite ferociously. A lot of the argument in Boaler’s book seems to be based on anecdotes, opinion and a few fMRI experiments, many of which seem to be a bit on the old side.

The key point in the chapter for me was this anecdote:

The PISA team not only administer maths tests; they also survey students to collect their ideas and belief about mathematics and their mindsets. I was invited to work with the PISA team after some of the group took the online class I taught last summer. One of them was Pablo Zoldo, a soft-spoken Spaniard who thinks deeply about math learning and has considerable expertise in working with giant data sets. Pablo is an analyst for PISA, and as he and I explored the data, we saw something amazing – that the highest-achieving students in the world are those with growth mindset, and they outrank the other students by the equivalent of more than a year of mathematics.

That text was followed by a figure like this:


And that was it. That was the PISA evidence presented. There was no mention of methodology or controls or uncertainties – no scatter plots, no correlation coefficients. The idea that mindset could be worth a year of mathematics teaching is an extraordinary claim and as Carl Sagan said, extraordinary claims require extraordinary evidence. And I saw none.

Chapter 2: The Power of Mistakes and Struggle

The key idea being presented in this chapter is that making mistakes is good because they make your brain “grow”. I’m not quite sure what this means but, to be honest, I’m always wary of claims made about learning on the basis of experiments in which parts of the brain are seen ‘lighting up’ after some event or other.

The idea that making a mistake can be a useful learning experience is incontestable but a core assumption in this chapter seems to be that traditional maths teachers abhor mistakes and create a climate of fear and anxiety which is exacerbated by relentless drilling, repetition and testing designed to eliminate errors. If that’s what maths teacher sdo, then Boaler is quite right to be concerned. But whatever about primary school, the teaching of mathematics at higher levels often involves not so much drilling as simply solving lots of problems; not problems of the same type or of uniform difficulty but a variety of problems of escalating difficulty. This approach to the teaching of advanced mathematics (in Russia) is well described in Mashsa Gessen’s fascinating book on Grigori Perelman , an extremely introverted character who solved the Poincare Conjecture, after which he withdrew from the world without claiming his million dollar Millennium Prize.

So while the basic point being made in this chapter is that maths classes should be ‘safe spaces’ where students are not afraid to make mistakes and where mistakes are seen as an opportunity to learn, I think the impact of the chapter depends to a large extent on presenting a caricature of maths teaching, one that I don’t recognise either in the “Mental Maths” books used currently in Irish primary schools or in the way I was taught maths at all levels of the system.

Chapter 3: The Creativity and Beauty in Mathematics

I completely agree with Boaler’s claims that mathematics can be a wonderful discipline and if I were to recommend one book that shows the deep connections that exist between the different sub-disciplines of maths, it would be this one.

Anyway, Chapter Three moves away from primary school arithmetic to advanced mathematics. The late (and tragically so) Maryam Mirazakhani, Fields Medal winner for her work on that most abstract of maths disciplines – topology – is mentioned, and the general point is made that mathematics often involves exploration, journeys down blind allies and admissions of ignorance. But later in the chapter the signals become a little mixed.

Boaler says that “over the years, school mathematics has become more and more disconnected from the mathematics that mathematicians use and the mathematics of life”. I would have thought that the reason for this is that mathematicians are forging ahead, creating whole new fields of mathematics, and new computational tools, while primary school pupils still have to learn the basics. But Boaler’s solution to this ‘problem’ is to seek advice from someone who is the polar opposite of Maryam Mirazakhani, namely Conrad Wolfram. Wolfram’s main achievement has been to create the Mathematica computation package (and it is fantastic to be fair) and, like Lego executives who advocate for more learning through play, he advocates the following recipe for maths education::

  1. Posing a question
  2. Going from the real world to a mathematical model
  3. Performing a calculation (using computational software)
  4. Going from the model back to the real world to see if the original question is answered.

This is utilitarian mathematics, it’s not the doing of maths because maths is a beautiful and worthwhile thing in itself.  Indeed, if truth be told, a lot of mathematical models are pretty ugly; they often contain ‘fudge factors’ that destroy any beauty there might have been in the original, simplest version of the model.

The chapter spends a little bit of time on those lists of 21st century skills that the World Economic Forum regularly churns out, before ending with what seems like a call for maths teaching to mimic how maths is used in the real world. This idea is commonplace in education these days especially in the sciences where it is widely believed that to learn science, students should spend their time behaving like scientists, i.e. by conducting research and enquiry-based activities rather than acquiring scientific knowledge.

It is hard to understand why this belief has become so popular in education because it has not gained traction in most other areas of life including sport, music, painting, sculpture, acting, writing and singing. In all of these endeavours, it is accepted that practice and performance can take very different forms. Rugby players practice individual and small-group skills far more than they play 15-a-side full contact rugby; the great renaissance painters spent many years drawing in pencil before being allowed to come within a mile of paint, and most actors have to undergo all sorts of embarrassing training exercises in acting school even before getting a bit part in a dodgy TV series.

For me, the take home point from the first three chapters is this: teachers should be nice to kids, create an encouraging and supportive class environment, and make sure that the kids are not afraid to get answers wrong. And that’s about it.

Next time: Chapters 4 and 5

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