Conjuring motivation, just like that

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I used to do an act when teaching air resistance. I would write ‘A’ on one piece of A4 paper and ‘B’ on another. I’d then say that I was going to drop them from the same height and ask the class to vote for which one they thought would hit the floor first. Whichever one they chose, I’d say I was backing the other. Then I’d screw that one up into a ball and let them both go. I always won.

I’ve never considered if this was motivating. It was intended as a bit of fun. I would only do it with a class I knew well because, otherwise, it’s a risk. You risk implying that you think the students are stupid and some may take offence.

I thought about this when reading Dan Meyer’s latest post. He’s been touring maths conferences, asking maths teachers to take a bet: he thinks of a number between 1 and 100 and they get ten guesses. Each time they get it wrong he tells them if the real answer is higher or lower. The catch is that it’s not a whole number and so Meyer always wins.

I’d groan if someone played this trick on me. But there are many other ways it could go down if a teacher did it in class. Students might conclude that their maths teacher is an otherworldly geek; a definitional pedant. They may be annoyed by the trick because, again, it potentially implies that they are stupid.

According to Meyer, it is intended to build motivation by giving a reason to students for why we might have different categories of number such as natural numbers and rational numbers. This fits with Meyer’s pet theory about maths motivation which is the idea that maths is an aspirin and students need to experience the headache to appreciate it.

If we think about the specifics, what are we trying to motivate these kids to do here? Do we want them to learn the names of different classes of numbers? If so, that’s pretty low level and at best incidental to the maths I’m keen for students to learn. It’s also not hard to convince kids of the need for labels because categorising things is human. And for interest I tend to go with a schtick about infinities of different sizes; the infinity of natural numbers is smaller than the infinity of real numbers and so on.

Do we perhaps think that the trick will motivate students about maths more generally? If so, they’re going to be disappointed when they get to quadratic functions.

Ironically, Meyer’s game seems like a solution in search of a problem.

This is a reflection of a much bigger issue in maths education. Some folks are holding on to motivation for dear life. If you believe in constructivist maths teaching, for instance, then that can be hard to maintain when the evidence stacks up against its effectiveness. So you can rationalise your position by claiming it’s motivating.

But the theories of motivation that these claims rest upon tend to be homespun. They fail to distinguish between a passing or ‘situational’ interest in a specific activity and a long term or ‘personal’ interest in mathematics. You also have to swallow that solving problems is inherently more fun than listening to people explain things. But problems can be frustrating and explanations can be interesting.

To really sort this out we would need to run robust trials. That’s a problem because the literature is full of research where students are asked if they found the new thing interesting. And that’s not robust.

So anyone can grow their own unproven theory of motivation. For what it’s worth, I’m not convinced that you can ensure students develop a personal interest in any subject. That’s because we are humans with independent tastes and desires. However, I believe that the greatest threat to developing a personal interest is a lack of success. I reckon that constantly being hit with the fact that you can’t do something would bum you out. In that case, we need to avoid gratuitous struggle and instead teach maths really well so that our students experience success. That, if anywhere, is the place instructional theories and motivational theories intersect.


The man from Opposite Land

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My daughters have a game. One of them will declare, “Opposite Land!” and from then on, everything that either of them says must be the opposite of what is true. I used to think this was just a child’s game but I am now starting to wonder whether Opposite Land actually exists. I think I’ve spotted one of their citizens doing the rounds of education conferences and he is Andreas Schleicher of the OECD, the organisation that runs the Programme for International Student Assessment (PISA).

Today, Mr Scheicher is quoted as claiming, “Actually in China you will find more emphasis on conceptual understanding, on creativity, on those kinds of non-routine skills, than in Australia.” And he suggests that Australia suffers from a ‘crowded curriculum’ with ‘lots of content’.


I would like to see the evidence to support these claims. I have previously looked at claims about memorisation based on  PISA. The construct that was used to measure memorisation was flawed and seemed to have virtually no relationship to PISA results. Moreover, the idea that Australia’s denuded, knowledge-lite curriculum is somehow ‘overcrowded’ beggars belief.

From his comments, Schleicher’s claims about memorisation seem to be based upon the fact that Australian students do better on the easier PISA questions than they do on the harder ones. If the reverse was true in East Asia then this would be a striking finding but I suspect that East Asian students simply do better on all of the questions.

This is not the first instance of strange pronouncements from PISA. The overwhelming finding from PISA 2012 was that their measure of ‘student-orientation’ correlated negatively with PISA maths results in every country. And the story from PISA 2015 was that the more ‘enquiry-based’ science students were exposed to, the worse their results.

What has Schleicher had to say about this?

Nothing. Nada. Crickets.

It’s almost as if there is some kind of ideological bias that affects the way the OECD report their findings.

The teacher perspective

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I admire academics and specialist practitioners. The education system has been particularly well served by those with an interest in special educational needs such as dyslexia. Often, the programmes and techniques that speech pathologists develop for one-to-one teaching present the best archetype for standard classroom instruction. Students with difficulties often don’t need something qualitatively different; they just need the best possible version of what everyone needs. So I want these voices in the education debate just as I want the voices of parents, employers and politicians.

Nonetheless, there is nothing quite like being a teacher. Teachers think in systems in a way that others often do not. Unfortunately, teachers are so busy teaching that their voices are often left unheard. And that’s a problem.


Light switches in the corridors

A few years ago, the U.K. government decided to rebuild many of its schools. The first wave of rebuilding was under the Private Finance Initiative (PFI). This was basically a way of keeping borrowing off the government’s books; a private business would borrow the money to rebuild a school and the government would guarantee to rent it back off them for a long period of time.

I worked in one such school. As teachers, we were not allowed to comment on how it should be designed. Instead, the school leadership had to come up with a ‘specification’ for what the school should be able to do. We ended up with light switches in the corridors, an open plan art department and various other silly ideas that few teachers would have endorsed. Under the later Building Schools for the Future programme (BSF), many schools were built with impractical designs requiring later mitigation. It may make perfect to an architect to design break-out spaces for classrooms but it will immediately occur to a teacher that he or she cannot be in two places at once and so break-out spaces will hardly, if ever, be used.


The inability for teachers to be in two places at once is something that is both obvious and frequently neglected by people who don’t teach. Recently, I spoke at a conference attended by many speech pathologists and I was largely positively received. However, I felt my comments on differentiation did not go down as well.

It seems reasonable to suggest that children will benefit from teaching targeted at their own, individual needs. To an extent, I agree. As Benjamin Bloom suggested, the ultimate form of teaching is one-to-one instruction where learning objectives and progress can be negotiated and honed in real time.

This is not the situation that most teachers are confronted with. Instead, we typically teach classes of 20-30 students, sometimes more. If we intend to tailor everything to individual students then we need to divide the teacher’s time accordingly. If, as often happens in attempts at differentiation, we group students into, say, five groups, each group will receive a maximum of 12 minutes of direct teacher input per hour. And this is before we deduct time for classroom management, something that increases in this situation as students who are not currently interacting with the teacher may become distracted.

Whole-class teaching will not be perfectly tailored to each student, but it is far more efficient and this is difficult to explain to non-teachers because it pits a functional argument against an emotive one about valuing individuality. Perhaps it’s a teacher’s professional duty to make within-class, differentiation-by-grouping work? Perhaps. But we certainly haven’t figured out how to do that yet. There is simply no body of evidence showing the effectiveness of the practice.


And it is the same empathy gap that plagues discussions of behaviour. When teachers think about behaviour management and school systems and procedures, they visualise flows of children passing through corridors and classrooms full of students who teachers have a duty to engage with academic content.

Imagine a busy school with a behaviour policy in which a senior member of staff is ‘on-call’ at any given time. Imagine a student is disrupting a class, refusing to cooperate. The first thing a teacher will notice is the effect on other students. It is hard to engage in challenging academic content at the best of times and a disruptive peer is the ultimate distraction. So the teacher calls for the senior member of staff who takes the student away.

A non-teacher might find this appalling. The student has been excluded from the classroom! Why was no attempt made to engage the student? Why didn’t the teacher attempt to find out what the student was communicating? There may be trouble at home or the student might not have had breakfast or… the possibilities are endless.

Firstly, teachers do engage in these discussions every day. In fact, they often go far beyond the expectations of their contracts. I have known a teacher take a child out to the shops in order to buy him clothes. This was because she found out that he didn’t want to go to the school disco and, when she probed a little, she realised this was because the only clothes he had were his school uniform. Teachers do this stuff. We have our sleeves rolled-up and take on far more than many people might imagine.

But how do you deal with the disruption I have described in the middle of a lesson? What are the other students meant to do while you engage the disruptive student in a discussion about what he or she is communicating? This is why we have systems and rules.

From the comfort of an armchair, it may seem heartless to insist, as some schools do, that children walk in silence between lessons on the left hand side of the corridor. It is an insult is to assume that this is simply authoritarianism on the part of teachers. They’re just being little tinpot dictators, right? Not at all. Why do you think such a rule exists? What do you think those corridors were like before that rule was put in place? Do you think it was a safe environment? Do you think that all students enjoyed their freedom to walk between classes as they saw fit or do you think some dreaded lesson changeover?

Teachers must speak for themselves

I have noticed a change since I first started blogging in 2012 and it is that the teacher perspective is now taken more seriously. Teachers should defer to experts in their genuine areas of expertise but the online community is perhaps a little less deferential than it once was and that’s a good thing. I suspect it is far harder to be an education charlatan these days.

And this is because, through blogging and social media, teachers have found a way to make their voices heard. They have found a way around traditional gatekeepers by talking directly to each other and the wider public.

If you haven’t made your own voice heard yet, and if you think it is safe to do so, then the world will benefit from your perspective too. Come, join the discussion.

Recommended reading 

I have a nonlinear approach to my reading list, generally reading several books in parallel, looping back and sometimes waiting a long time before getting to a particular text. So I thought it would be worth recommending some books that I am reading at the moment.

1. The Writing Revolution. Judith Hochman and Natalie Wexler

I have been working with my school’s English department for a while, examining ways of making the teaching of writing more explicit. I was late to the Hochman method, an approach that is outlined in this book. And yet I recognised many of the ideas from our own process of trial and error. Hochman and Wexler present plausible strategies that have been used successfully in schools and are informed by their understanding of research. We should really have a variety of explicit approaches to teaching writing to choose from, but the reality is that the overwhelming majority of schools and teachers teach writing implicitly by asking children to do lots of it and then trying to put it right through feedback. This make The Writing Revolution even more valuable as one of the few alternatives. 

2. Bringing words to life. Isabel Beck, Margaret McKeown & Linda Kucan

Vocabulary is another body of knowledge that is often built implicitly. In many ways, it is better to do it this way because there is evidence that simply teaching lists of words is ineffective. This book presents a systematic approach to introducing and teaching new words in context so that children will be able to use them. This is especially important for children from disadvantaged backgrounds who may not be exposed to these words at home.

3. Making Good Progress? Daisy Christodoulou

I returned to this book after reading The Writing Revolution. Although The Writing Revolution discusses assessment, I think that Making Good Progress adds a great deal more about the interplay between short components and complex products. It will make you think about assessing writing in an entirely new way.

4. Making Sense of Interventions for Children with Developmental Disorders. Caroline Bowen & Pamela Snow

When I received this book, I imagined that it would be a worthy and thorough treatment of developmental disorders and the many programmes that have mushroomed in order to treat them. It certainly does this and, as such, is an invaluable reference for teachers and parents. What I hadn’t realised was how witty and erudite it would be. I particularly enjoyed the brief section on ‘psychological astrology’.

5. The Academic Achievement Challenge. Jeanne Chall.

Published in 2000, this book flew under my radar for a long time. Since discovering it, I have returned to it repeatedly. It is an essential guide for anyone who wants to know the history of evidence in education since the second half of the 20th century and the powerful forces arraigned against proponents of explicit teaching.


It would be remiss of me, at this point, to fail to mention my own ebook, Ouroboros, which is still available very cheap via this link.

An interesting flaw in Cognitive Load Theory

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A new paper has been published by Ouhao Chen and colleagues that points to a flaw in one of the assumptions of Cognitive Load Theory (CLT); a flaw with some potentially interesting implications.

One of the central ideas of CLT is that the working memory in which we consciously process new (biologically secondary) information is limited, but these limits fall away once dealing with knowledge stored in long term memory. I used to think of this as a design flaw; that you could perhaps improve on humans by expanding our working memories but CLT assumes there is a reason for this limit: Given that information passes through working memory into long term memory, it prevents rapid and disruptive changes to long term memory.

Apart from when dealing with knowledge stored in long term memory, CLT assumes that the working memory capacity of an individual is fixed. This may be wrong because the Chen et. al. paper suggests a new ‘depletion effect’ where working memory capacity reduces further after a period of use.

The authors point to a few previous studies that show that a taxing task led to an impaired performance on a subsequent task designed to measure working memory capacity. However, this was not in a learning context. So the authors set up a context where primary school students learnt about fractions or basic algebra.

All students completed a series of learning tasks, a series of working memory tasks and a test. Roughly half completed this in one massed block whereas the others completed this is spaced-out blocks. Interestingly, the test for this latter group was on a different day to any of the learning tasks and we might think would impair performance even if it led to better learning in the long term.

Not so. Instead, there was a classic spaced practice effect where students in the spaced group did better on the test than those who completed the single massed block. So far, this is unremarkable although the authors do note that relatively few experiments have tested the effect of spaced practice in an authentic classroom environment with authentic learning goals in the way that they did.

But that’s not the interesting part. They also noticed a poorer performance on the working memory tasks for the massed group. Previously, explanations of the effect of spaced practice have relied on ideas such as that the process of trying to retrieve something that is starting to be forgotten improves its retrieval strength. This study suggests another, possibly additional, mechanism: spaced practice avoids cognitive depletion.

The study was quasi-experimental. Rather than being randomly selected into the conditions, for practical reasons children completed them in their usual classes. This was mitigated slightly in the second experiment by running two sequences and switching the conditions from the first to the second sequence i.e the class that did massed practice in the first sequence did spaced practice in the second and vice versa. The results held.

This potentially expands the scope of CLT to act as a theoretical basis to explain other effects like spaced practice.

The authors also note hints in previous experiments that depletion might be highly domain specific. If so, this would have implications for teachers because we could avoid depletion by switching task types.

Teachers should have university degrees

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There is an interesting debate raging in the U.K. after the government proposed a wholly vocational route into teaching. Although it is intended to be a ‘degree equivalent’, trainee teachers would not graduate from university in the traditional way and would instead learn on the job. The initial reaction from many teachers on Twitter was that this would deprofessionalise teaching and suspicions were raised that it is intended as a cheap solution to the problem of teacher supply. Under current arrangements apprentices may be paid as little as £3.50 per hour, which is far less than paying for proper teachers. Schools that are struggling to manage their budgets might find this attractive.

Others then weighed-in to the discussion, sensing hypocrisy. Backing the government, Sean Harford of the English schools’ inspectorate, Ofsted, accused teachers of preaching the equivalence of vocational and academic routes yet not wanting it for their own profession.

I think this term ‘equivalence’ is a problem here. I don’t see much value in vocational courses prior to the end of formal schooling, and this is as someone involved in attempting to set-up such courses in a previous role. They are a poor alternative to basic academic learning. The theory is that students will be so motivated by hairdressing or vehicle maintenance that this will push them through the contextualised key skills courses in English and maths that they complete on the side; the stuff that they really need. But it doesn’t work like that. Kids need the basics first and the best way to learn this is not as an afterthought in a complex context.

I recently tweeted about the fact that Germany has improved in PISA over the last 17 years whereas Finland has declined. Dylan Wiliam then linked to a blog post explaining the changes that Germany has made in that time. One of these has been a move away from sorting kids at the age of ten into vocational and academic streams.

Perhaps for some students, the school system and their personal circumstances have failed them and they would be better off starting work or training as a traditional apprentice. But this is not because they are not ‘academic’, it is not an intrinsic property of the student.

After compulsory education has ended, vocational routes make more sense. But are they ‘equivalent’ to academic ones? I have no problem with a parity of esteem; that we hold them in as high regard. Even so, this is manifestly not the case in England where the general public think of degrees as superior. What is absolutely clear is that they are different to academic routes. You learn on the job, focusing on the tasks involved in doing that job. Academic learning does not have the same focus. Instead, it is built around growing and applying discipline knowledge, wherever that leads.

Teachers teach these disciplines, even generalist primary school teachers. And so teachers need an understanding of them. It is therefore essential that they have reached a recognised threshold of academic learning themselves. If anything, we should be pursuing this with greater vigour, not watering it down. I cannot prove that this will make teachers more effective but this is about our values as a society. And by raising the status of teaching we probably will end up with better teachers.

However, I am not making an argument for teaching degrees. I think all teachers, including primary teachers, would be better served by studying an academic subject at university and simply focusing on that for a few years. I can’t point to any studies but I can point to the fact that, just as with those hairdressing students, learning vocational aspects of teaching alongside learning your subject is incoherent. Once students have finished a degree in a subject, there should be a variety of routes open to train as a teacher. I still believe that university-based teacher education courses have the potential to deliver the best mix of theory and practice but I don’t think they do a brilliant job at the moment. That’s why I believe that school-based alternatives, as have already emerged in the U.K., offer an opportunity to improve the whole sector through competition.

The charge of hypocrisy is perhaps valid for those teachers who have spent years preaching the equivalence of vocational and academic routes. I am not one of those teachers. Vocational learning and academic learning are different and nothing good ever comes of trying to pretend that they are the same.

Ask them what they stand for

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I am one of education’s debunkers. I challenge arguments and research. I don’t just restrict myself to obvious targets such as learning styles, I question a whole range of claims, observations and experimental designs.

Yet I don’t sit aloof. Everyone has an agenda and it’s transparent what my agenda is.

I advocate for access to a rich, unashamedly academic curriculum for all students. I advocate for explicit teaching. And let me be clear about this; I don’t mean that all of every lesson should involve a teacher stood at the front of the room explaining and asking questions. I do mean that new concepts are fully explained to novice learners from the outset and that there is then a gradual release from teacher-directed to independent work. I value students being able to tackle complex problems on their own. The subjects I teach, mathematical methods and physics, have VCE exams which always involve novel questions of a form that students will not have experienced before and so the ability to tackle such problems is the goal of my teaching.

I see a pivot point about which explicit teaching and alternatives such as inquiry learning turn in different directions. That pivot point is roughly the first, everyday explanation of a phenomenon that a teacher can articulate. Alternatives to explicit teaching will deliberately miss out some or all of this explanation. Explicit teaching will add to it, breaking it down further; including the why and addressing the common misconceptions and errors.

I don’t have such strong views on schools structures. I want more schools that give ordinary kids access to a rich academic curriculum and explicit teaching but I can’t honestly say I am certain of the best way of achieving this. Recently, I have become more convinced that models like Charter Schools in the U.S. and Free Schools in the U.K. are the best chance because they relax the control of central bureaucracies that tend to disapprove of the schools I want to see. Only a small number of schools of this type emerge under these structures, but this does give them the chance to prove the principle and so influence other schools in the system.

More broadly, I am socially liberal and politically left-of-centre. I would be inclined to nationalise monopolies such as water and electricity utilities. But I won’t go toe-to-toe in an argument with you about this because I don’t know as much about the issue as I know about education.

So that’s where I stand. It should be familiar to anyone who regularly reads my blog because I’ve written all of this before.

Yet there are some debunkers, some critics, who won’t make it clear where they stand. It’s not transparent what they are advocating. We see this whenever the term ‘progressive education’ comes up. People try to deny it is a thing, despite its long, well-documented history. Why?

I think there are a number of reasons why people try to obscure their agendas. Firstly, it is human to think that other people are ideological and doctrinaire whereas you are balanced and can see all sides of the argument. However, if I can name the ideology that you subscribe to then this undermines that view. It’s the power held in a name, if you will.

Secondly, I think some people believe that it is a sign of intelligence to be nuanced and to point to the incomplete nature of any models that others propose. But models are models. By nature they are incomplete abstractions. So although at best this kind of critique can shed new light on a subject, at worst it is an irrelevant parlour game.

Thirdly, obscuring your own view is a good strategy for winning arguments. The socratic questioner does not have a position that can be refuted, creating a power imbalance. After all, you can keep asking, ‘why,’ until it’s just turtles all the way down.

Finally, some people may have a view, but it might not be based on much or it might not be very well supported with evidence. So they hold back, like I would with an argument about nationalisation. However, I can’t imagine myself then becoming involved in the minutiae of a debate about the subject. If anything, I would watch and learn.

I am not convinced that anyone is entirely neutral. Even in ignorance we have a preference. This is why we have science and the scientific method. It doesn’t stop scientists from having human biases; you can’t. But the scientific process is bigger than any scientist and, when it is working properly, involves checks and balances that should mean we edge ever closer to the truth. We should treat debate in a similar way. The teaching community is not generally made-up of scientists but we should see our debates as having a similar aim. I am probably wrong in many of the positions that I take but in order to refute them you need a better argument. That moves us all forward, if slowly.

Here is what I suggest. When you next find yourself arguing with someone whose own position is obscure then ask them outright what they advocate. They can put it in their own words and don’t have to accept someone else’s labels. Let them define what they believe. If the terms are very general then ask for specifics; ‘So what precisely do you mean when you say you are in favour of inclusion? How is an inclusive school different to one that is not?’ Establishing people’s positions serves the wider discussion. It aids clarity, letting us know which options are being compared.

And if you can’t get a straight answer then that’s probably a sign that genuine discussion is not going to happen.