One year on

A year ago, I was preparing my presentation for researchED Sydney. It was exciting; I had never before given a presentation on the ideas that I write about. But it was also a fateful time.

Me and Tom B

In February 2015, I had two blogs. This blog was hardly read. I used it mainly to post quite dry pieces and to link to my columns for the TES. My other blog, “Webs of Substance” (WoS), was written under a pseudonym and was far more popular. The associated Twitter account had over 3000 followers whereas I had about 400 in my own right.

On reflection, WoS had turned into a bit of a monster. I set it up in order to shout into the void. I didn’t expect anyone to be listening. But then Old Andrew tweeted a link to a post on textbooks and I started to attract a readership. It was pseudonymous because I just wanted to be able to throw ideas around without worrying whether they might be seen as somehow representing my school. This is a good idea for bloggers who are finding their feet but, to be honest, it was hardly necessary for me. Most of my posts were technical or philosophical and rarely related to anything that happened at work.

When I spoke in Sydney, a figure sat silently in the audience, making connections. There are not many Australian teachers on social media who say what I say. He worked out that I was the author of WoS and started to troll me on Twitter about it. Then he shared this revelation with anyone who he saw me disagreeing with on Twitter. It became the story – a useful ad hominem.

I pulled the plug on WoS because I felt like I had to. And I didn’t like it much. I had given life to something that mattered to me and now I had killed it.

The year went on. I continued blogging in the same vein, posting on this site instead. I gained followers on Twitter and the loss of WoS started to bother me less. Opportunities began to arise. This year I will be speaking at the Telegraph Festival of Education at Wellington College, England, and it’s hard to imagine how I would have been able to do that as an anonymous blogger. If you’re around then come and say, ‘Hello’. I won’t be able to go out for a drink or a meal, however, because I will be in charge of sixteen youngsters who are attending the festival’s student programme.

There are other events in the offing that are yet to be announced so watch this space.

And I have written an ebook, “Ouroboros”. It’s going better than I had hoped; I’ve sold over 70 copies so far, even though it is only available through my blog site (here, if you’re interested) and it’s attracted a couple of positive reviews from David Didau and Owen Carter. Ouroboros now has a goodreads page that, at the time of writing, has no reviews or ratings at all so please feel free to vent your spleen at what a shocking waste of money it is. I also have a new facebook page.

In the debit column, I have been dropped by the TES but I am grateful to them for giving me the opportunity to write some interesting pieces which I will continue to link to from my homepage. My ambition for the next twelve months is to get something published in the Australian press. I’m not sure how I’ll go with that but it’s worth having a try. And if anyone from the Guardian or Telegraph is reading this then get in touch.

We had a sort-of wake for Harry Webb. A dinner party that had already been planned gave us the opportunity to toast the old guy and see him on his way. I wasn’t sure how it would turn-out. It seems to have turned-out just fine.

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Why is England running short of teachers?

So, according to the National Audit Office, the shortage of teachers in England is partly a retention problem. More teachers are leaving the profession. Why is this?

1. Michael Gove and the feels

Although long gone from the Department of Education, Michael Gove still casts a shadow. He famously used the term “The Blob” to describe the educational establishment and certainly there are many who feel insulted by this. And yet teachers are not the educational establishment (more’s the pity). Gove’s comments were aimed at schools of education and education quangos. Gove was always meticulously polite about practising teachers. It is therefore hard to judge how many teachers feel personally insulted by Gove or how this has affected morale.

Gove was also a man in a hurry. Former advisors such as Dominic Cummings suggest that, from the outset, the Gove team knew it had limited time to make an impact. This led to a whirlwind of curriculum reforms that added to teacher workload. This could be a factor.

2. Ofsted, accountability and Workload

Ofsted is a recently reformed institution that has taken to criticising the mad things that are sometimes done in its name. This is to be welcomed, but Ofsted cannot absolve itself of responsibility for allowing this situation to grow out of control in the first place.

Some in education are extremely ideological about accountability and will claim that tests do not assess what is important and what is important cannot be tested. Therefore, they suggest, we should abandon testing and testing-based accountability. However, I think that most teachers are pragmatists. They are quite happy to be held to account for their students’ results provided that they think the measure is fair.

What teachers really dislike are arbitrary accountability measures that seem to have little link to improved student learning. Think of all the onerous marking policies, form-filling and invalid lesson observation judgements. This could be a contributor to teachers chucking it all in.

3. Behaviour

Nobody wants to work in an unsafe or stressful environment. I once taught in a school where behaviour was very poor and I remember the feeling of anxiety I experienced on the bus every morning.

That school turned itself around by adopting a strong, whole-school policy. A challenging school without a proper behaviour policy is a disaster for ordinary teachers, and especially so for new teachers and substitute teachers.

There is a philosophy out there that teachers needs to manage all their own behaviour issues because it is all about individual teacher-student relationships. If teachers are expected to run and manage their own detentions then a quick back-of-an-envelope calculation will show just how impractical this is in a challenging school. This means that teachers often give up, take to tolerating poor behaviour and lower academic standards.

Yes, teacher-student relationships are important and teachers should work hard at promoting positive relationships. They should be given professional development and support to do this. But the school-student relationship is also vital. Abusing a teacher or disrupting a lesson should be seen as disrespectful of the school community and the school needs to take action. Leaders who won’t step-up here are dodging their responsibilities and I have no doubt that this leads to teachers departing the profession.

4. The Economy

As the economy dips, people move into the safe-haven of teaching. It is a stable role that is largely protected from recession. When the economy starts to pick-up again, teachers look to pastures new. The push factors become more significant, particularly if a prolonged squeeze on public finances has led to teaching becoming relatively less well paid. You might be prepared to tolerate a poor working environment if the alternative is insecurity or perhaps no job at all but when there are more attractive jobs around, teachers may consider leaving.

Conclusion

I think the main factor is the economy but this doesn’t mean that schools have no role to play. Schools should review the push factors. They should conduct a bonfire of silly policies and focus on ensuring that they create a safe environment for their teachers to work in. When teaching works well, it is a fantastic, rewarding job. Teachers will forego the prospect of higher pay or a swanky office for a job that they love.

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Maths anxiety – a ouroboric process?

In my recent book, I discussed ‘ouroboric’ processes in education. I suggested that some relationships that people think are linear – that motivation leads to learning or that conceptual understanding must come before learning procedures – are actually cyclical.

The examples that I gave were of positive processes. However, a new paper by Cambridge University researchers suggests that the negative relationship between maths anxiety and maths achievement is also cyclical.

I have written about maths anxiety before. The model that I used would be called ‘the deficit theory’ by the Cambridge researchers. This basically posits that maths anxiety is caused by a lack of ability. The teaching implication of this is that we should teach maths in the most effective way possible in order to improve competence and reduce anxiety. We might also consider giving students experience of success with some relatively straightforward work rather than asking them to struggle for extended periods.

The alternative explanation for maths anxiety is ‘the debilitating anxiety theory’. People who worry about their maths performance have to devote some of their working memory to the worrying. They therefore have fewer working memory resources to devote to problems. Jo Boaler is a prominent populariser of the debilitating anxiety theory amongst maths teachers and she advises that we avoid timed tests because they have been shown to induce anxiety. However, she also advocates open-ended problem-solving which is likely to overload working memory and which would not provide the routine competence that the deficit theory implies students need.

There exists powerful evidence for both theories. Longitudinal studies support the idea that poor levels of achievement lead to future maths anxiety. A range of lab-based studies such as those that induce stereotype threat – reminding a group that there is a negative perception of that group’s mathematical ability – show that maths anxiety leads to poorer performance.

The Cambridge researchers propose that the interaction works both ways. They also point out that while the deficit theory is supported by long term studies, the debilitating anxiety theory is supported by short-term experiments. So the two interactions work at different scales.

An interesting ouroboric process.

Ouroboros Motif

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Teaching Creativity

Creativity is one of “the four C’s” identified by The Partnership for 21st Century Learning (P21) as “learning and innovation skills”. P21 want us to somehow teach this skill in K-12 education.

I have long suspected that there is no one thing we can call ‘creativity’. It is a reification; we have conjured something into being and then decided to treat it as if it actually exists. We have considered processes that have superficial similarities as if they are aspects of the same underlying ability.

Creativity in science might involve designing a new experimental procedure or formulating a new hypothesis. Artistic creativity, on the other hand, might involve subverting rules and norms to produce something aesthetically unique. What do these processes have in common? Very little. What kind of training will improve both kinds of creativity? None. This is important because the use of the word ‘skill’ implies something that can be improved and developed with practice.

On the other hand, domain-specific creativity might be trainable. There might be heuristics that we can use to generate more novel tech innovations, for instance (although they won’t work for creating pieces of music). However, I suspect that a lot of creativity simply comes with increasing expertise. It is hard to be creative in a domain about which you know little. First, learn the basics; then, the more difficult or abstract stuff; finally, we can be truly creative. Little inventive tasks might be a fun diversion along the way but they will be limited in scope by the expertise of their creator.

I was therefore interested to read two very different articles on the subject of creativity that both happened to have come to my attention today. The first article, by Eric Weiner, is a taster of his book, “The Geography of Genius” and was Tweeted out by @polymathish. I found myself nodding along in agreement as it busted a few myths about our current preoccupation with creativity:

“There is no such thing as free-floating, untethered “creative thinking.” All creativity, like all athletics, exists only in context. You can teach someone tennis. You can teach them basketball. You cannot teach them athletics. Likewise, you cannot teach creative thinking (whatever that means) but only creative approaches to certain subjects. Furthermore, psychologists have yet to identify a single “creative personality-type,” and it’s doubtful they ever will. Geniuses can be sullen introverts like Michelangelo or garrulous extroverts like Titian.”

Weiner goes on to explain that creativity requires discernment; something that you need lots of domain knowledge to apply.

The second article was a piece by Dr Sacha DeVelle for the Australian Council for Educational Research’s (ACER) teacher magazine. It focuses on ‘creative insight problems’ and treats creativity as if it is a general skill, links into to collaboration, innovation and problems solving – similar to P21 – and notes that it is a required component of the Australian Curriculum.

There is a section on, “Neuroscience and creative insight,’ and I don’t really understand the point of this. However, the main thing that I wish to highlight is the issue of ‘routine’ versus ‘non-routine’ problems. DeVelle notes:

“Geoff Masters points out in his recent Teacher article on 21st Century skills, the solution of standard problem types continues to prevail within school curricula.”

Then she concludes:

“The Australian Curriculum states that students should be able to recognise creative problems and actively participate in their solutions. Identifying routine and non-routine problem types is integral to that process. Our research focuses on the teaching strategies that facilitate the solution to creative insight problems. These strategies include recognising domain specificity (for example, verbal, spatial or mathematical) and facilitating a change in how the problem is perceived.”

How could you hope to recognise domain specificity without substantial knowledge of the relevant domains? How could you hope to identify which problems are routine and which are non-routine without a substantial knowledge of routine problems? First, learn the basics.

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Example-problem pairs

Over the past year, I have been thinking a great deal about the implications of the following section from “Cognitive Load Theory” by Sweller, Kalyuga and Ayers*:

“Trafton and Reiser found that for an example to be most effective, it had to be accompanied by a problem to solve. The most efficient method of studying examples and solving problems was to present a worked example and then immediately follow this example by asking the learner to solve a similar problem. This efficient technique was, in fact, identical to the method used by Sweller and Cooper (1985) and followed in many other studies. It was notable that the method of showing students a set of worked examples followed later by a similar set of problems to solve led to the worst learning outcomes.”

It is something that we have discussed as a maths department as we try to improve our planning documents and resources. How best can we utilise this effect when teaching our students new concepts? I admit that my standard practice has often be to present a set of worked examples and this does not seem to be the most effective strategy.

One approach might be to present an example alongside a similar problem.

Example-problem pairs I

I know some people are PowerPoint-phobic but please don’t be put-off by that. It could just as easily be presented in a booklet or on an iPad screen. I like PowerPoint slides because I can project them onto a standard whiteboard and then scribble over and annotate them.

The above example is useful for illustrating the idea but it is abstract. I have been wondering exactly how close to the original problem a ‘similar’ problem must be. In the statistics example-problem pair below I have change the context. In other respects, the problem is very similar to the example. For instance, the information is presented in the same order. Could such an example-problem pair have an impact on transfer? It certainly highlights the deep structure.

Example-problem pairs II

My other concern cuts to the heart of cognitive load theory. There are those who posit that we can lower cognitive load too far and that some load is necessary for learning. This led to the introduction of the notion of ‘germane’ cognitive load – productive load – into cognitive load theory. It has caused problems because it makes the theory potentially unfalsifiable. Sweller explains why in an email comment for a post on my old blog:

Concerning germane cognitive load, once we get into the details of cognitive load theory, we run out of accessible work. Here is a brief history of germane cognitive load. The concept was introduced into cognitive load theory to indicate that we can devise instructional procedures that increase cognitive load by increasing what students learn. The problem was that the research literature immediately filled up with articles introducing new instructional procedures that worked and so were claimed to be due to germane cognitive load and other procedures that didn’t work and so were claimed to be due to extraneous cognitive load. That meant that all experimental results could be explained by cognitive load theory rendering the theory unfalsifiable. The simple solution that I use now is to never explain a result as being due to germane cognitive load. Cognitive load theory is not a theory of everything and some results are due to factors unrelated to working memory load and should be explained by those factors rather than working memory factors.”

However, the potential issue remains. We could possibly have activities that are too fully guided and that therefore lead to little learning. Example-problem pairs seem to minimise the amount of struggle and so you might think that they would qualify as such activities. They certainly don’t seem to induce any ‘desirable difficulties’. Yet the evidence suggests that they are effective.

And fully guided strategies such as Engelmann’s Direct Instruction also seem to work. I have heard anecdotal reports that students and teachers sometimes even don’t notice the progress that is made until they conduct a new assessment. How can this be if they are making an effort to learn? Surely there must be a limit to how far we can reduce load?

If we substitute activities with ones that involve students thinking about something other than the targeted learning then they won’t learn much. This is what happens when we ask students to complete wordsearches to learn key words or in Dan Willingham’s famous example of baking biscuits to learn about The Underground Railroad.

But I wonder whether, as educators, we have a systematic bias towards providing too much load. Therefore, anything that we come up with that reduces load seems to work (with novice learners). There might potentially be a lower limit – it seems reasonable to suggest that optimal learning will take place when we have a full but not overloaded working memory. It’s just that we haven’t reached it yet. Even with example-problem pairs, there is still plenty for a novice to think about.

*Sweller and Kalyuga are my PhD supervisors.

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Six signs that you’re a progressive educator

Recently, I was told by an academic that I should be pursuing a career in journalism rather than academia. My crime was that I referred to ‘the left’. You see, to the more enlightened among us, there is no such thing. It’s far more complicated than simple labels such as ‘left’ and ‘right’.

This argument is interesting because there manifestly is a set of positions that most reasonable, educated people would recognise as ‘left wing’. It doesn’t mean that any one individual has to adopt all of them. In fact, I regard myself as centre-left and I am fine with that, picking and choosing, issue by issue. But left versus right is not a false choice.

Yet there are those who seem to think that a similar divide in education – progressive versus traditional – is a false choice, even though we can clearly identify differences in the two philosophies that have practical significance in the classroom. Some people may be unaware that progressive education has a long history and isn’t just something made up by bloggers to argue against. Alfie Kohn has even had a go at defining it.

I completely agree with some of the tenets of progressive education. I don’t think education should be stratified by social class – liberal arts for posh people, cooking and metalwork for the proles. And I don’t believe in corporal punishment. So to that extent, I am a progressive.

Are you wondering whether, like me, you are a bit of a progressive too? Here are some signs to look out for.

1. You believe that learning should be natural

This is probably the fundamental tenet of progressivism and it leads to some of the others. Have you ever noticed how children effortlessly learn to speak or walk? Have you noticed how they figure out how to play with a new toy? Do you think that education should be like that; joyful and natural?

If so, you will be suspicious of activities that look forced and unnatural such as drill and practice. You will be skeptical of phonics instruction in reading, not because you think children shouldn’t learn letter-sound relationships but because you don’t think they should be drilled in them. They should instead pick this up by reading real, authentic books; a more natural method.

[Why this view is wrong]

2. You believe in learning by doing

This leads on from the first point. Real mathematicians solve open-ended problems and so that’s what students should do. They should be creating, making things and applying their knowledge. You also think that this aids understanding – students understand things better when they figure things out for themselves rather than simply being told.

[Why this view is wrong]

3. You don’t think children should be punished

You believe that children’s behaviour is largely a product of their circumstances. It is therefore cruel to punish them for poor behaviour. It is controlling and undemocratic. Punishment is also counterproductive and will not fix the problem. Instead, students should explore their behaviour through discussion. They should be led to conclude for themselves that their actions were antisocial.

[Why this view is wrong]

4. You think that content is interchangeable

You see your role as one of developing myriad skills such as the skill of ‘critical thinking’ or ‘collaboration’. These are more important than specific content because they can be transferred to different contexts and applied to any content. This is particularly important because we don’t know what the future holds (see final tenet). It also means that we do not have to trouble students with difficult texts like Shakespeare – they can think critically or make inferences about any texts.

[Why this view is wrong]

5. You believe that learning must be relevant and authentic

This is closely linked to the previous point. You think that it’s wrong to teach children about dead, white males, their history and their science. Instead, learning should be closely matched to the interests and lived experience of the learners. Perhaps they can do project work based around an issue in the local community.

[Why this view is wrong]

6. You think that the future fundamentally changes everything

The advent of Google means that a traditional knowledge-based education is no longer of any use. In the future, many people will be doing jobs that don’t exist yet and so we need to prepare them for these jobs by developing the previously mentioned transferable skills.

[Why this view is wrong]

Back to the argument

It is interesting to contemplate why, periodically, folks pop up to denounce the debate between traditional and progressive teaching methods as a false dichotomy. I have a hypothesis as to why this is. Most of those who make this argument have written blogs that express support for some of the tenets that I have outlined above. Perhaps instead of defending their views in a open debate they prefer to suggest that there is no debate to be had.

Four_students_working_on_the_preliminary_sketches_of_a_mural_depicting_the_history_of_Peru8d23055v

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In real life

“Numbers are not objects of study just because they are numbers already constituting a branch of learning called mathematics, but because they represent qualities and relations of the world in which our action goes on, because they are factors upon which the accomplishment of our purposes depends. Stated thus broadly, the formula may appear abstract. Translated into details, it means that the act of learning or studying is artificial and ineffective in the degree in which pupils are merely presented with a lesson to be learned. Study is effectual in the degree in which the pupil realizes the place of the numerical truth he is dealing with in carrying to fruition activities in which he is concerned. This connection of an object and a topic with the promotion of an activity having a purpose is the first and the last word of a genuine theory of interest in education.” John Dewey, Democracy and Education, 1916

Maths teachers are often exhorted to teach mathematics through real-life contexts. This is a key part of the progressive tradition and a feature of reform mathematics teaching. There appear to be two main reasons, the first is affective and the second cognitive.

We presume that real-life contexts will be motivating for students. Most maths teachers will have had a student ask if the maths that they are learning will be useful in real life. There is a tendency to accept the premise of the question and conjure a lame response, something that I am not prepared to do. We don’t tend to judge other subjects in this way. Education is not a purely utilitarian pursuit; a means for producing future employees. Even if it were, we are terrible at predicting the future. The key principles that inhabit the mathematical canon have endured and this is why we teach them. We cannot know how or when or to whom they might prove valuable.

The idea of motivation is also fraught. How far must we stray from optimal learning in order to accommodate it? I can engage a group of 12-year-olds in a poster making activity but they won’t be learning any maths and when they realise this then they are likely to view the subject less favourably. In my new book, I show that the linear idea that you must first motivate students in order to get them to learn is simplistic and flawed.

The other reason for the use of real-world contexts is cognitive. There is a body of research that suggests that students do not transfer what they learn in maths class to situations where they really could apply this knowledge in real-life. Jean Lave is probably one of the foremost researchers in this area. Perhaps if we used real-life contexts more in mathematics classrooms then students would be able to transfer their learning better to problems they meet elsewhere? It seems reasonable.

It was therefore with interest that I read a comment on my previous blog post by a regular contributor known as “Chester Draws” – I assume it’s not his real name. He linked to this paper in the journal, “Frontiers in Psychology: Cognition”. It details a set of experiments where content was held the same but the degree of contextualisation was varied. The more contextual the instruction, the less able students were to transfer the learning to new situations. This may be because the contexts added more information for the students to process. It’s only one paper but it should at least raise some doubt about the reform narrative.

I was reminded of Dan Willingham’s comments that learning tends to adhere quite strongly to the context in which we first learn it. Furthermore, I recalled research that showed that maths teachers in China are much more comfortable working in the abstract than maths teachers in the U.S. When you contemplate the idea of transfer then it becomes quite clear that this is the purpose of creating abstract rules and generalisations in the first place. An abstraction can potentially be picked-up and dropped down somewhere else. Concrete examples do not lend themselves to transfer in the same way.

Yet I must avoid presenting a false choice here. I think that many traditional maths teachers will relate concepts to contexts. It’s more a question of the degree to which this is a priority. Reform advocates will argue against ‘pseudo-contexts’ that are meant to represent real-life but are not credible. I think that traditionalists would be more relaxed about these examples provided that they furthered an understanding of the maths. So it’s more a case of a kind of fundamentalism versus a more pragmatic approach. Indeed, just last week I was teaching some abstract theory regarding binomial random variables and I gave an example of what one might be, “You have a biased coin with a probability of 0.7 of tossing a head. You toss it 50 times. The number of times you get a head would be a binomial random variable.”

Is this useful? Can it be applied to a real-life contexts that my students will experience? Who cares.

penny

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What’s the point?

It is natural to focus on the differences between us. This is productive when it comes to analysing approaches to teaching because such discussions allow us to clarify our own thinking or the thinking of others. These arguments often throw light on unexamined assumptions and allow the possibility – and it usually is just a possibility – of changing minds.

Publicly, I often found myself disagreeing with the late Grant Wiggins. We differed on the validity of E D Hirsch’s arguments and specifically those around reading comprehension strategies. I also criticised Wiggins’ views on the nature of understanding.

Yet Wiggins will most be remembered for his work on ‘backwards design’. Forget designing lessons on the basis of activities that you would like to do. Instead, think of what you want to achieve and select your activities according to that. As is the case with many powerful ideas, it is deceptively simple and yet you can quickly find many examples of practices that ignore this principle.

I found myself reaching for the concept of backwards design when contemplating the approach that Jo Boaler sets-out in her latest book, “Mathematical Mindsets”. There is a lot to analyse in this book, not least the application of Carol Dweck’s mindset theories to maths teaching. This is perhaps for another post (although I can’t help remarking that Boaler’s argument that Einstein was slow to learn to read is not supported by his official biographers). Instead, I will focus on Boaler’s views on maths teaching.

In a chapter called “Rich Mathematical Tasks”, Boaler introduces us to a lot of cool activities. She talks of visiting a Silicon Valley startup and knocking the socks off the bright young entrepreneurs by asking them how to solve 18 x 5. Apparently, they did this in many different ways and were so amazed by this fact that they wanted to make “18 x 5” t-shirts. The focus here is on the activity. The activity continues to hold centre-stage throughout this section. We read, for instance, of a task that requires students to draw different rectangles with the same fixed area.

The mathematical objectives behind these activities are never clear. Instead, the implication is that they will show students that maths is a creative subject that isn’t all about right answers. It will help them with the aforementioned mindsets and things like that. It is also suggested that these tasks are highly motivating. I am deeply sceptical that this kind of activity-based ‘situational’ interest will necessarily lead to long-term motivation in mathematics and I wrote about it here.

I think it is relatively simple to come up with cool maths activities and that this is something that is valorised a lot more that perhaps it should be. It is far more valuable to be able to structure instruction so that students can learn and understand complex, abstract concepts. Such instruction will not necessarily be cool and funky but it will allow students to grow their expertise and, perhaps, their sense of their own ability or ‘self-concept’.

Boaler also promotes productive failure: students should struggle with trying to solve a problem before being given explicit instruction in how to solve it. There is some evidence for this idea but I am not convinced that it is sufficient to support this as a general maths teaching strategy. We have lots of evidence to support explicit instruction and even the most casual of observers will see that the concept of productive failure could backfire. The productive failure studies tend to have problems with the controls that they employ, specifically in their interpretation of explicit instruction. There is nothing disingenuous about this – it really is hard to design well-controlled trials that do equal justice to the different conditions that they try to compare. Read the paper cited by Boaler for yourself and see what you think.

The other evidence that Boaler cites are her own studies in the UK and US. These have generated much comment and so I will make just a few observations. In the UK research, Boaler studied two schools. One used a traditional approach and the other used more of a problem-based learning approach. We don’t know the identity of these schools and it is quite possible that one or both are outliers. We could have simply happened upon an unusually effective problem-based learning school and an unusually ineffective traditional one. We don’t know whether the maths instruction was more important than other environmental factors, classroom behaviour and so on. The sample size of N=2 is not really sufficient for drawing any firm conclusions. The US study was of three schools which hardly improves the situation.

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Could teachers run their own affairs?

One of the interesting aspect of the College of Teaching debacle in England is that it has thrown a harsh light on the differences between teaching and other professions. Lawyers, surgeons and accountants are largely trusted to set-up and regulate their own affairs. Yet we don’t seem to be thought capable of doing the same and instead need input from professional development providers and higher education institutions. Perhaps we are just less capable? I’m not sure. I wonder if we can achieve more than we think.

For instance, let’s imagine a different kind of school.

Models of school provision are now changing across the English-speaking world. We have free schools and academies in England and charter schools in the U.S. It’s possible that the same kinds of schools will emerge in Australia. And yet the schools that we have seen so far all follow a fairly traditional structure, even if they are experimenting with new approaches to teaching.

Visualise, instead, a school run as a partnership between teachers. It would need to be pretty small – the limit on partnerships in Australia is about 20 individuals, I think. And these boutique partnership schools would probably have quite a limited offering within their walls – student choice would come from whether to attend a particular school or not rather than through the subjects on offer at an individual school, which is probably a more efficient way of providing options.

The teachers would employ their own support staff. They might contract-out timetabling and other administrative functions. They would have to deal with behavioural issues themselves and you might think this would distract them from focusing on teaching. However, the prevailing philosophy in many schools is that teachers largely should deal with behaviour issues themselves. So there may be no net change.

Such a school would struggle to offer a full range of extra-curricular opportunities but then why should it need to? Could it not link up with local sports clubs or drama societies and have specialists offering this provision? And the size of the school would be a bonus. Everyone would know everyone.

I think that as we awake as a profession, we will start to realise that we might be capable building all sorts of new ways to educate.

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