This is the homepage of Greg Ashman, a teacher, blogger and PhD candidate living and working in Australia. Everything that I write reflects my own personal opinion and does not necessarily represent the views of my employer or any other organisation.

I have a book out for new teachers (which some experienced teachers have also enjoyed):

The Truth about Teaching: An evidence informed guide for new teachers

Watch my researchED talks here and here

I have written for The Australian about inquiry learning (paywalled):

Inquiry-learning fashion has us running in wheel

This is my take on the “Gonski 2.0” review of Australian education for Quillette:

The Tragedy of Australian Education

Here is a piece I wrote for The Age, a Melbourne newspaper:

Fads aside, the traditional VCE subjects remain the most valuable

Read a couple of articles I have written for The Spectator here:

A teacher tweets

School makes you smarter

Read my articles for the Conversation here:

Ignore the fads

Why students make silly mistakes

My most popular blog post is about Cognitive Load Theory:

Four ways cognitive load theory has changed my teaching

To commission an article, click here


How I learnt that drama was all about talent

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At primary school we were trees. We grew up tall until the Sun spilled on our finger leaves. At secondary school we were directors, creating plays about bullying or some other social issue. This was drama until it stopped being compulsory at Year 9.

Against this backdrop were the school productions. Given that nobody ever taught us how to act, auditions were about selecting for natural talent or, as we often suspected, good looks. As I moved from primary to secondary and the pool of potential performers grew larger, my roles grew smaller until I was no longer interested and focused my attention elsewhere. After all, I wasn’t any good at drama.

I went to a working class school where we held our drama teachers in kindly contempt. They had nothing to teach us. Unlike our often boring science or history teachers, they didn’t really know anything, they just asked us to perform plays about things we knew about and made encouraging noises. Still, at least the lesson was a ‘doss’ – a break from anything approaching hard work. We could mess around.

There was never any chance of me taking drama as an elective in Years 10 and 11. And when I went to sixth form college to complete Years 12 and 13, it never even crossed my mind to take a drama-related subject. No, I chose a diet of maths and science.

Yet some of my friends decided to take Theatre Studies. They knew roughly as much about the subject as I did but had heard on the grapevine that it was an interesting, less demanding option that balanced-out some of the tougher courses.

In the common room, I learnt vicariously about Brecht and Beckett. One friend’s interest in Berkoff’s Kafka adaptations spurred me, a few years later, to pick up an English translation of The Trial.

When I landed at Cambridge, opportunities for pursuing drama were everywhere and bright young things eagerly auditioned for theatre groups, including Footlights, the incubator of BBC comedy.

As someone who was bad at drama, it wasn’t a path for me to pursue, but I did offer some support. When my college’s theatre group staged performances of The Importance of being Earnest and An Evening with Gary Lineker, I bought tickets, turned up and marvelled at the quality of the acting.

I have no complaints, but I wonder about the working-class actors who never were because of the water thin gruel they were fed as ‘drama’ at school. I don’t for a minute presume that a Year 9 diet of Beckett would turn vast swathes of kids on to acting, just as a diet of linear equations does not currently turn the vast majority of kids on to mathematics, but at least the offer is there. It’s on the table for those who feel inspired. For want of a little teaching, we may have missed out on the next Stephen Berkoff.

It would be a tragedy if, due to misguided ideas about relevance, some Drama teachers hid away the treasury of what they know, with their students therefore assuming they know nothing and that drama is all about talent.

Why would anyone want to spend time factorising trinomials?

If you have an algebraic expression of the form:


You can use the distributive property of multiplication to multiply the two brackets (i.e. multiple each term in the first bracket by each term in the second). When you do, you will usually produce a ‘trinomial’ i.e. an expression with x^2, x and unit terms. For example:


However, going in the reverse direction from a trinomial to two sets of multiplied brackets or ‘factors’ is often the more useful thing to be able to do and it is harder. For a start, if you simply dream up any old trinomial, it may not factorise at all or, if it does, the numbers that go into the brackets might be fractions or even irrational numbers such as the square root of 2.

Typically, high school students are taught how to factorise trinomials that do readily factorise and there are two levels of difficulty – those where you have only a single x^2 term and those with 2x^2, 3x^2 and so on. I prefer a strategy called ‘grouping’ for the harder kind of factorising, but this is always a cause of some debate within my department. Regardless of the approach, the ability to factorise depends a great deal on knowledge of multiplication facts (times tables).

The interesting stuff happens around the special cases such as the ‘difference of two squares’ or when the trinomial will not readily factorise. There is plenty of scope for exploring important ideas such as irrational numbers, linking to graphs and functions, linking to other approaches such as ‘completing the square’ and generally building a deeper, more interconnected understanding of mathematics.

It is therefore quite baffling that at some kind of forum hosted by Stanford University, Jo Boaler, a professor of mathematics education, and Professor Keith Devlin, a mathematician, came out against teaching students how to factorise trinomials:

In the ensuing Twitter discussion, Boaler and Devlin suggest there are few ‘real-life’ applications for factorising trinomials and even if they did discover one, they would let software factorise the trinomial for them, presumably no wiser about what the software was actually doing.

The justification appears to rest on drawing a distinction between knowing things like how to factorise trinomials and being a ‘creative, flexible thinker’, which seems to be some kind of generic capability that does not rest on such knowledge.

This distinction is obviously false. How can you be creative and flexible if you don’t have this kind of knowledge to draw upon? What exactly are you going to do?

The result is a paradox. I am sure, if asked, that Boaler and Devlin would make a case for students understanding the mathematics they use. Indeed, Boaler and colleagues have argued for the use of visual methods in maths specifically to aid understanding. Yet, in this case, Boaler and Devlin seem content for the understanding to lie encoded in the zeros and ones of the Wolfram Alpha software rather than in the long-term memories of mathematics students.

The argument belies an oddly functional view of mathematics education. Nobody would argue that young people do not need to learn to cook because McDonald’s or the local Greek restaurant can do that for them. Nobody says, “I know, let’s not teach children to draw any more because they can all take photos on their phones”. And yet, when it comes to maths, some people lack the imagination to see past the immediate practical uses of the subject to such an extent that once a bit of tech comes along that can factorise a trinomial or solve an integral, they suggest that we might as well pack it in and focus on vague, new age ideas about creativity instead.

Mathematics is one of the great ways of seeing the world that has been developed by human culture and is a gift from one generation to the next, whether it is initially received with enthusiasm or not. It will survive into the future, despite the best efforts of false prophets, because ordinary mathematics teachers will continue to teach their students how to factorise trinomials.

Free speech and the education faculty

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Three days before Australia’s election, a piece was published in The Conversation about a policy of one of the major parties. Oddly, the comments were locked. After contacting the editor, Misha Ketchell, today, the comments have been reopened, but not in time to reflect criticism prior to the election itself. In his response to me, Ketchell suggested that, “Sometimes we close comments on contentious topics if we are unable to spend the time we need moderating those comments.” If an organisation like The Conversation lacks the capacity to moderate comments then the obvious thing to do would be to avoid publishing articles on contentious topics.

In my Twitter timeline, on the other hand, there is an education lecturer complaining about the ‘shaming’ of academics by people disagreeing with them. This lecturer has previously taken aim at renegade professors, suggesting that disrespecting a university’s diverse range of research practices might fall foul of the university’s code of ethics. So presumably, you could not say, ‘qualitative education research sucks’ without being hauled before a disciplinary panel. I doubt this interpretation is correct, but it is interesting that a code of ethics would be deployed in this way.

I take a dim view of such arguments, having been the subject of a complaint to my university about statements I made online. Fortunately, the complaint was dealt with sensibly and dismissed, but it certainly made me pause and reflect.

The fact is that nobody particularly enjoys being disagreed with and everyone likes to think of themselves as one of the good guys. We are tempted to give a pass to the person on our side of the argument who is taking things too far while taking great offense at the inferred tone of someone we disagree with. That’s just human nature. The trouble comes when we are given the power to police the speech of others.

In recent years, it has become akin to outing yourself as fascist to declare in favour of free speech. Indeed, the free speech argument has been used by some pretty hateful people. But as a proud member of Generation X, I still remember that free speech is a progressive cause. Tyrannical regimes control what people can and cannot say. Liberal democracies generally do not, with the exception of a few kinds of speech like incitement to violence. Why? Because liberal democracies recognise human nature and its desire to abuse such controls.

I still remember the day after the 1992 general election in the UK. The polls had convinced everyone that Labour would win. Neil Kinnock, the Labour leader, had even held a rally prior to the vote that had the look and feel of a victory celebration. And yet, on that bright, cold day in April, Conservative John Major took the victory. He was the unglamorous grey man who visited every town centre and stood on his soapbox to give a speech. It worked.

The pollsters were puzzled. Voters must have been lying to them. These voters were dubbed ‘shy tories’ because they would tell others they were voting Labour, but in the privacy of the polling booth, they voted Conservative.

When you ban views either overtly, through laws, regulation and codes, or by making them unacceptable in genteel society, you don’t make those views go away. People still hold them, it’s just that you don’t know that they hold them and so you cannot challenge them. This does not matter so much if you live in a totalitarian regime with an iron grip on power, but in a democracy that has regular elections, it’s useful to know what people think.

When you label the UK’s Leave voters as racists, you make them less inclined to declare themselves at polite dinner parties or to pollsters, but don’t be surprised when they turn out in large numbers to vote for The Brexit Party.

We have been reminded of this again in Australia this weekend. The pollsters got it wrong and so did much of the media. Without missing a beat, on the day before the election people were marking the passing of Bob Hawke by declaring that it was a shame he would not be around to see a Labor election win. It was a given. Ignoring the lessons of history, we all knew what would happen. But we were wrong. The Coalition won. The media had been listening to itself again, giving us the middle-class view of reality.

Just like every other area of public policy, education needs its debates. If I am wrong about something then demonstrate that I am wrong. I may never quite accept you have succeeded – that takes a pretty big person – but others who may be inclined to think like me may shift position as you expose the hollowness of my claims.

By trying to silence, you put as all in the deep freeze, with no possibility of progress and nobody any the wiser.

Democracy sausage

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Today, Australia votes in a general election that will determine who forms the next government. The campaign has been tiresome, with both sides prone to making deeply misleading claims.

Exhibit A is the claim made by the Liberal-National Coalition (our main centre right party) that plans by the centre left Australian Labor Party to scrap a tax rebate on share dividends – a rebate no other country seems to have – is a tax increase.

Exhibit B is Labor’s repeated claim that the Coalition have ‘cut’ spending to schools. They have actually increased spending. The claim seems to rest on the idea that the Coalition have not increased spending by as much as Labor planned to do just before it last left office, but that’s not a ‘cut’, it’s less of an increase.

It’s valid to be angry about either of these measures and prosecute your case accordingly, but this kind of spin is disrespectful towards voters.

Australia has a complicated preferential voting system that few people seem to understand, particularly when it comes to the ballot paper for the Senate. Outside every polling station, alongside the charity sausage sizzle, volunteers from each of the parties hand out ‘how to vote’ cards. The game is to try to send second, third, fourth etc. preferences in a direction that disadvantages a party’s main rival. The unfortunate result is a Senate where a bunch of fruitcakes with a tiny number of votes end up holding the balance of power.

I voted Labor today but I voted ‘below the line’ and made all my own preference selections from the main political parties. I have far more in common with the left of the Coalition than most of the tiny electoral oddities. How do I know? I’ve done a bit of homework.

In Australia, voting is compulsory. If you don’t turn out, you attract a fine. If the state requires Australians to perform this duty then what duty does the state owe in return? Education.

The trite solution to politicians making misleading statements is to teach the population ‘critical thinking skills’. However, regular readers of this blog will know that this is something of a red herring. General purpose critical thinking skills don’t really exist.

Instead, Australian electors need to posses relevant knowledge. It would not be possible to attempt to teach all knowledge relevant to an election in school – it would rapidly date and would risk placing educators in a position of advocacy. Instead, we need to equip voters to be able to obtain this knowledge themselves in adult life from a range of reputable sources. I think we sometimes assume that those who disengage from political news always do so as a matter of taste, but it is hard to comprehend sources such as the ABC unless you have a good base of foundational knowledge. That is what schools could and should provide through a knowledge-rich curriculum.

In the meantime, all that remains is to take a bite out of Australia’s democracy sausage and wait for what the night has in store.

To all the creative lovers in the world

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Are you a creative person? Really? So that means you can garden creatively, are a creative lover, are a creative structural engineer and you can write songs just like Oasis? All of those things? At the same time? Definitely? Maybe?


To my friends and family, I am quite a good cook. I am no chef but I am reasonably competent. Am I creative? Well, here’s the thing – I have invented a few dishes, but others are dishes that I have adapted from recipes or from other people. Even the dishes I have invented make use of common combinations of ingredients. Is that creative? Is that derivative? Can you be creatively derivative? Noel Gallagher is hoping you think so.

So is creative genius Isaac Newton, who only saw further because he was standing on the shoulders of giants such as Galileo and Halley. Giant’s shoulders are also known as culture, a lot of which is taught in school.

I quite like Sir Ken Robinson’s definition of creativity as, “…the process of having original ideas that have value,” because it highlights the need, no matter how subjective, for value. Anyone can create a scribble on a piece of paper that nobody has created before, but it will have little value. I suspect that a lot of the efforts at fostering creativity in schools have a similar quality – the production of artifacts that are novel yet meritless.

Back to my cooking. As a fourteen-year-old in a single parent household, I shouldered some responsibility for peeling potatoes and grilling chops. I even used a Schwartz spice mix to make chilli con carne on a Friday night. So I’ve been cooking for nearly thirty years. This means that I can move a knife pretty swiftly and I can anticipate the effect of removing, adding or replacing an ingredient to a dish – something I do largely without thought. Nobody taught me to be creative.

In contrast, I was never really taught to draw or paint. At the schools I attended, these were activities that you just did, with little to no instruction in how to do them any better. So my artistic skills are still at the novice level where I left them and the probability of me ever producing an original artwork that has value is small.

Is creativity useful, desirable, vital to our economic and aesthetic futures? Yes. Are there a few generic tricks that can help the muse locate you in the twilight? Perhaps. But that does not mean creativity is monolith that can be carved out from the laborious process of gaining expertise.

If creativity is the destination then expertise is the turnpike, whatever it is you want to be creative at doing.

The Non-Conversation

With Australia’s general election looming on Saturday, it is certainly worth debating one of the few policies put forward by the ruling Coalition government: the offer of over $10 million to fund a voluntary phonics health check similar to the UK’s compulsory phonics screen.

While I suggest it is worth debating, that’s not what is happening over at The Conversation. Instead, The Conversation has published an article critical of the Coalition’s promise which, at the time of writing, provides no opportunity to comment. – less of a conversation and more of a lecture.

So what are the arguments against spending a relatively modest amount of federal funding on a voluntary check? Let’s take a look.

“The government would be better investing its millions in initiatives that support an approach to teaching that targets inequality, as well as supporting students at the intermediate benchmark to develop the skills to rise to the high benchmark.”

Really? How do we do these things? It’s not clear. In contrast, it is pretty clear how a phonics screen would work – it would alert us early to children who are struggling to decode.

“The proposal to fund a voluntary online open-access phonics “health check”… assumes teachers aren’t assessing children’s early reading knowledge and skills. This is wrong. Early years teachers implement a range of ongoing checks, including phonics checks… an independent inquiry into the UK phonics screening check found 94% of participating teachers said that the phonics check did not provide any information on individual children which they did not already know.”

We have plenty of evidence that many teachers in Australia lack the knowledge to teach phonics. It may be the case that 94% of participating UK teachers said the phonics check provided no new information, but only 58% of students passed the first phonics check, despite teachers saying they were teaching phonics, so we have to treat such self-reports with some scepticism.

The problem is that ‘teaching phonics’ is a slippery term that is not well understood. A teacher who asks children to analyse the sound made by the first letter in a word may well think they are teaching phonics, particularly if their own training was deficient.

“Australian teacher educators must abide by the Australian Institute for Teaching and School Leadership (AITSL) Program Standards, which states all literacy teacher educators teaching in accredited initial teacher education programs are required to teach the Australian Curriculum: English… The Australian Curriculum: English devotes a whole substrand – phonics and word knowledge – to teaching phonics.”

Unfortunately, it doesn’t really matter what it says in the standards or the Australian curriculum, it matters what teachers know and what children learn.

It’s a shame nobody can make these points over at The Conversation.

Learning to count to sixteen

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We were never clear what to do with the days. They were stunted grunts of days anyway, because we woke around lunchtime. We would eat, then my friend would go to the pool while I read a book about the history of beer.

So we decided to go for a lesson one afternoon. Our teacher spoke like you might expect a detached house with a kitchen garden in Henley-on-Thames to speak, cruising through her introductory remarks as the sea breeze gently beat on her sail of a dress.

“The important thing is to count to sixteen,” she explained. “All records can be broken up into sixteens.” Then she demonstrated counting as she played through some of her funk house collection. We took turns at beat-matching and mixing. It was too short.

Despite some music training as a child, I had never heard about counting to sixteen. It made the records speak clearly. I could parse them like our grandparents were taught to parse text.

That evening, my friend and I were in a sticky-floored bar when the DJ played Love Story by Layo & Bushwacka. We turned to each other. “One-two-three-four…”

The rhythm of Ibiza, the pulse of sunset cafes, bars and super-clubs, had a new way of counting.

Summer turns to autumn, and one crisp Saturday I was stood on the Tottenham Court Road holding a huge box, standing out. A stripe of a man with creosote teeth and wide eyes approached. “I live near here,” he suggested. “You can bring that to my place and I can set it up and show you how to use it,” he suggested through a lupine smile.

“Nah, mate. It’s alright,” I replied. “I already know how to count to sixteen.”