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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 written two books:

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

Ouroboros – an ebook

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

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Registered problem solvers

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The clock ticked in the waiting room. The clients sat quietly. Most were scrolling through mobile phones. Some just sat and stared blankly into the middle distance.

Tick, tick, tick, went the clock.

Ms Jackson had a blocked drain. Mr Ahmed wanted to know the best investment plan to help him support his children if they decided to go to university. Ms Peters had recently moved to the city and was finding it hard to break into the tight-knit friendship groups she encountered.

The sign on the consulting room door read, “K. Solomon: Registered Problem Solver.” It creaked open. A young woman appeared. She turned back to talk to someone inside, “Thank you, Dr. Solomon,” she said before turning and striding confidently across and out of the waiting room.

Then, a kindly face appeared. Dr Solomon wore an open neck shirt and a broad smile. “Mr Ahmed?” he asked.

There is no such thing as a registered problem solver. The closest to it is probably the Citizen’s Advice Bureau charity. However, if you visited a Citizen’s Advice Bureau, they would be unlikely to be able to help you with your blocked drain unless it was part of some legal or consumer dispute.

There are plenty of experts who we can consult. There are family doctors, solicitors, accountants and so on. However, each of these has a carefully delineated field of expertise, with the professional associations that provide accreditation for each of these occupations taking a great interest in defining this field and ensuring practitioners have the required knowledge.

However, if problem solving were a general skill as the Australian Curriculum suggests, we should expect to see experts in this skill offering their services to the public. Those with superior general problem solving skills would presumably be able to make a good living by offering a problem solving service. We do not see this.

For a general skill of problem solving to exist, it would need to be something different to the accumulation of specific knowledge. Presumably, a skilled problem solver would not need to begin with any specific knowledge about a given situation because they could gain all the knowledge they need from secondary sources such as books, interviews and the ubiquitous internet. In fact, the rise of the all-knowing internet from the mid 1990s onwards should perhaps have corresponded to an explosion in people offering generic problem solving services.

Why has this not happened?

Because this logic is built upon a misunderstanding of the role of knowledge in the human mind. Knowledge does not sit in a set of filing cabinets, waiting to be consulted when a skill is activated. A better picture of long term memory is a tool shed. Knowledge is what you think with. We can only process about four items in our working memory at the same time, but one of these items can be an entire connected web of ideas held in long term memory known as a ‘schema’.

You cannot think with knowledge that is stored in secondary sources and, in fact, as you try to make use of knowledge from secondary sources, you will encounter working memory limits.

This is why registered problem solvers do not exist and why those who solve problems in specific fields need to acquire a large body of knowledge in order to be able to do so.

 

An open book?

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I teach two Year 12 classes that have an external exam at the end of the year. One is the Victorian Certificate of Education (VCE) exam in Physics and the other is VCE Mathematical Methods. Despite all the claims made about standardised testing in Australia, the VCE and its equivalents in other states, are really the only high stakes tests that students sit. They are high stakes because entrance to university can depend upon the results. For that reason, I am minded to take a low risk approach.

VCE exams are not the exams that I would design. They have been influenced by constructivist ideas which have worked to both water-down and decohere the curriculum and the way it is assessed. For instance, Maths Methods has two exams. Exam 2 is worth twice as many marks as Exam 1 and students are allowed to bring in one bound A4 sized book of notes and a sophisticated calculator. In Physics, there is only one exam, but students are allowed to bring a sheet of A3 paper with both sides covered in notes – this is popularly known as a ‘cheat sheet’. Furthermore, part of the VCE grade comes from tasks that students complete in class and that are then cohort-referenced against the exam grades. These have lots of regulations around them that, in some cases, include the explicit instruction that students must be able to refer to notes.

I am not a fan of open-book assessment. Firstly, it does not fit with my preferred model of learning which is about maximising long-term memory. Instead, it seems to be based on the idea that mere facts are unimportant and that learning is about developing mysterious skills that are somehow independent of knowledge. On a more prosaic level, I worry that students will be misled. They will be lulled into a false sense of security by thinking they have everything then need to know written down. However, if they haven’t actually learnt the content, they will be plagued by all the problems associated with reading content when you lack background knowledge.

The most transparent example of this that I can think of is the two ‘split ring commutators’ in the Physics syllabus. One is associated with a Motor and the other with a certain kind of generator. When the assessors ask students to explain the role of a split ring commutator in a generator, those who are over-reliant on their cheat sheet are likely to explain the role of a split ring commutator in a motor. Fortunately, I know about this booby trap and warn my students about it in an animated fashion.

However, I don’t quite have the courage of my convictions. I don’t really know what the evidence says about open-book assessments and so I follow a low risk approach by replicating the final exam as much as possible. For instance, in class work and assessments, if I am giving Maths Methods students Exam 2-style questions to complete, I let them refer to their notes and I let my Physics students refer to their cheat sheets throughout the course.

Should I?

Perhaps not. A new study involving university students learning cognitive psychology seems to suggest that students who are not allowed access to their notes perform better overall. Unusually for a trial of this kind, it is not a quasi-experiment but a full randomised controlled trial and so the evidence it provides is pretty strong. It is only one study, so we probably shouldn’t give too much weight to it, but it has made me pause.

Perhaps I need to change my approach.

Ontario takes a fresh view of maths teaching

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Maths teaching in Ontario has featured regularly on this blog over the years. People used to point to it as an example of good practice and yet, in recent years, Ontario’s scores on standardised assessments such as the Programme for International Student Assessment (PISA) have declined.

I have not taught maths in Ontario, but it does appear to represent a large-scale implementation of ‘fuzzy maths’. I use this term because the name used by proponents constantly shifts. To some, it is ‘reform maths’, to others it is ‘constructivist’. However, if you go around calling it ‘constructivist’ then someone else is likely to appear and inform you that constructivism is a theory of learning and not a teaching method.

However, there are a few essential points. Fuzzy maths is not a fully explicit teaching approach. No matter how scaffolded or guided it is, students are still required to figure some things out for themselves. This is the key pivot point away from explicit teaching, because the latter tends to over-explain and re-explain concepts. As such, fuzzy maths is subject to the the criticism that it overloads working memory. Fuzzy maths is perhaps epitomised by the old strapline to Dan Meyer’s maths teaching blog, “less helpful”, although this seems to have disappeared in recent times.

Fuzzy Maths proponents take relatively simple ideas and, through the application of much beard-stroking, turn them into pseudo-deep discussion points. Should we call a mistake a mistake? How do we know if students really understand the principle of equivalence, deeply? I mean, like really deeply, dude?

They also disdain what they would characterise as the rote learning of procedures and the memorisation of maths facts. Given that doing maths involves performing procedures and that knowledge of maths facts is helpful when performing procedures, fuzzy maths represents a form of maths-in-denial. The effects on students should be fairly obvious and probably do account to some degree for Ontario’s decline.

It is therefore heartening to see a change of approach from Ontario’s government. We do not yet know the details, but the Toronto Sun is reporting that memorising times tables is back on the agenda, alongside training for teachers and a generally more traditional approach. There is also an emphasis on employability. Yes, students do need to be able to read a tape measure, but I wouldn’t want maths to be reduced to just the functional.

Unfortunately, the Toronto Star, and perhpas the politicians they have been talking to, have described this reform in the language of ‘back to basics‘. This may play well with many parents, but it makes it hard to bring academics along who can dismiss it as part of a politically conservative agenda. I understand why people use this term – they mean that we must not ignore the fundamentals. However, it also has the unfortunate connotation that teaching maths is basic when it most certainly is not.

No matter, gripes aside, it looks like Ontario’s fuzzy maths experiment has finally come to a welcome end.

On beard-stroking

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Back in 2005, Harry Frankfurt of Princeton University published an essay on the topic of – and forgive me if you have a nervous disposition – ‘bullshit’. Frankfurt’s description is interesting:

“The bullshitter may not deceive us, or even intend to do so, either about the facts or about what he takes the facts to be. What he does necessarily attempt to deceive us about is his enterprise. His only indispensably distinctive characteristic is that in a certain way he misrepresents what he is up to.”

It is not about lying. It is about an indifference to the truth. The central claims may be true or false. That’s not the point. The point is that the bullshitter is a fake, a phoney.

I think there is a similar phenomenon that we might describe as ‘beard-stroking’. In this instance, the beard-stroker’s claim is essentially true, but it is a relatively small, perhaps trivial, claim. The beard-stroker then inflates it with much intellectual methane until the claim can suitably fill some vessel or other.

As an example, let me give the inflation of the relatively simple idea of children learning that an odd number plus an odd number is an even number. It is a straightforward piece of declarative knowledge that can be demonstrated in a number of ways, but to the authors of a new paper on early maths teaching, it swells to blimpish proportions:

“…as students operate on particular whole numbers, they might notice—either spontaneously or through teacher scaffolding—that the action of adding two odd numbers results in an even number. This compression of their observation about multiple instances of adding two particular odd numbers can be represented in a unitary or generalized form through natural language (e.g., ‘‘The sum of two odd numbers is even’’). In turn, the action of representing a generalization is a socially mediated process whereby one’s thinking about symbol and referent are iteratively refined (Kaput et al., 2008), leading to a mediation of the generalization itself…

…consider a representation-based argument (Schifter, 2009) that students might construct through either physical objects, such as cubes, or a drawing that depicts such objects. They might reason that since an odd-numbered set of cubes can be separated into pairs of cubes with one cube left over, the combination of two odd-numbered sets of cubes results in no cube without a ‘‘partner’’ cube. That is, since the leftover cube in each of the two sets combines to form a new pair, the resulting sum is even…”

This discussion continues at some length and is typical of many discussions in education research papers. In much the same way that an analogy is the extended form of a simile, beard-stroking is perhaps the extended form of the deepity – a phrase that is true on a trivial level and which is then used to add weight to a implied meaning on a different level that is false.

As with bullshit, the question of the intention behind beard-stroking is an interesting one. We fool nobody like we fool ourselves and I doubt it is a conscious strategy as much as a habit. Regardless, it is the enemy of clarity because we have to let  the gas out in order to see clearly what remains.

The avoidance of doubt

It was 1997 and we were sat at a stream. I think we were washing our clothes, but this part of the memory is weak and could be a later projection. The part that has stuck with me over the years is being told that I would go to hell.

The name of the person I was talking with has gone. She had dark hair and an unfussy middle-class English manner. Even so, her words did not come easily. Her brow peaked, her eyes widened and her voice softened.

“So let me get this straight,” I asked, “even if I live a good life and do good things in the world, just because I happen to have made a mistake over this issue – a very human mistake – just because I have got it wrong and chosen the wrong religion to follow or I have chosen no religion, I am going to go to hell?”

“Yes,” she said and then turned her face away from me. I did not pursue it further. It feels to me now like it was time to go back to camp.

I am always puzzled by people who lack doubt and I am starting to think they are a problem.

Perhaps you think I lack doubt? I certainly have strong views and I am pretty sure about a few things, but doubt is always there. I have plans for my year at work and I worry that they won’t succeed. Even on the issue of education – on which I have written more than my fair share of polemics – I have always acknowledged that I am likely to be wrong on at least some of it. Which bits? I cannot know.

Certainty is a different condition. It afflicts its victims with a Manichean view of a polar world neatly dichotomised into good and evil. It allows people to tweet obscene and insulting images about politicians they don’t like on the grounds that the politician is an evil person with evil intent who deserves it. But of course, to the recipient of such slurs and his or her followers, this is yet more evidence that they are the good guys and their opponents are the evil ones who will use any underhand tactic to slander them.

But the truth is that few people think they are evil. Most believe they are doing some good in the world. They have to believe this in order to get to sleep at night. Most people are not psychopaths, they have a conscience and they tell themselves stories to assuage that conscience. The conscious evil-doer seeking evil for evil’s sake is relatively rare.

Certainty leads to, and maybe even requires, cultish behaviour. Adherents become defined by their adherence. The more strongly held the view, the more bizarre it is, the greater the faithfulness of the believer. And this is as true for the wacky evangelical offshoot of the Anglican church I encountered in Africa as it is for devotees of identity politics.

In education, our goal is to produce critical thinkers who can engage fully in civil society. We need to be alert to certainty and we need to inoculate our students with a healthy dosage of doubt. We must also catch ourselves before we start teaching our own questionable certainties as immutable truths, because when we do, we become part of the problem. We probably don’t think we are doing evil, but…

An open letter to Theresa May on the link between free school meals and knife crime

Dear Mrs May

We know you’ve probably got a lot on right now, but we would like to draw your attention to something.

The depressing rise in youth knife crime has been well documented, but did you know that children who commit knife offences are four times as likely to be claiming free school meals than children who don’t commit these offences?

Clearly, this means that although this is a complex and nuanced issue, free school meals are certainly a factor in knife crime.

We are not saying that all free school meals should be banned. Of course not. There are some extreme cases where the issuing of free school meals is warranted. We are just suggesting that we get rid of all the entirely frivolous cases of free school meals – all those instances when free school meals have been doled out without much thought, perhaps for the lols.

This is not an attack on teachers and schools. They do a great job, but they could do a better one, and we think we are best placed to explain to them how to do it.

Sincerely,

A credulous mayor

A journalist

The people whose job it is to actually tackle knife crime


If you really want to understand the wicked problem of knife crime then this confronting BBC podcast is a good place to start.

How to avoid pointless debates on Twitter

I have been on Twitter since 2012. In the early years, I felt it was my duty to try to engage with anyone who wanted a discussion. I thought that this would help me to form a more balanced perspective. To be fair, sometimes it did and sometimes it still does. This is when disagreement reaches the higher levels of Graham’s hierarchy of disagreement, when those involved in the discussion are genuinely trying to figure something out. As Graham suggests, “You don’t have to be mean when you have a real point to make. In fact, you don’t want to. If you have something real to say, being mean just gets in the way.”

Unfortunately, too many people are mean. If anyone insults you, I suggest blocking them. I didn’t block anyone in my first few years, but if someone calls me a name then they are now gone from my timeline immediately.

Most people don’t just hurl insults around. Instead, they rely on bad arguments. The whole set of logical fallacies are often displayed in Twitter debates, but there are two key things to remember. Firstly, most people will never concede that they are wrong and, secondly, some people start an argument without having the intellectual grunt to finish it.

Once you understand these points, two kinds of bad argument naturally flow. The first is to start arguing about definitions and the best way to explain this is with an example. I recently wrote a piece pointing out that a maths education professor had argued against a focus on teaching maths facts, such as that 5 x 5 = 25, and that she had also argued against timed tests. I then pointed to an article the professor co-authored that favourably referenced a paper where students with learning difficulties are taught maths facts with the aid of speeded practice.

In the real world, this is a direct contradiction. On Twitter, however, there is infinite scope for trying to tease out differences between ‘timed tests’ and ‘speeded practice’ – some of this even made it into the blog comments. It seems it is preferable to twist yourself up into semantic knots than to consider reevaluating your world view. My advice for any argument that descends into this kind of stuff is to mute the argument. If an individual continually engages in arguing about definitions then I also recommend muting that individual.

The surest sign that someone is out of their depth is that they will stop making any kind of case and suggest you read something. Often, this is a book that you don’t own. Nevertheless, even if it is an article that is available on line, why would you read it? Individuals who make such a gambit rarely explain what this piece can add to the argument. Instead, they hope to divert you down a rabbit hole and avoid having to defend their views themselves.

Do not be shamed by the suggestion that it is anti-intellectual to refuse to read the link. There is a lot to read in this world and much of it is dross. If someone wants you to spend your time reading something then the least they can do is explain exactly why you should read it and exactly what parts of your argument it refutes. Again, if people indulge in this practice then I suggest you mute them. Nothing good is likely to come of it.

But you may be concerned. How will I convince people if I don’t engage with them?

As I have suggested before, you are highly unlikely to ever convince someone you are arguing with on Twitter. Instead, the debate is for the benefit of those silent onlookers who can see both sides of an argument and then make up their own minds. Once the debate descends into one about definitions or ‘you should read x’ then nobody is going to benefit from it being extended. Cut your losses. Find someone else to talk to or focus on expounding your own ideas as clearly as possible on a blog.