A response to Dan Meyer

Following my previous post, I have been engaged in a discussion on Twitter with Dan Meyer. I like Dan. He comes across as a nice guy and has the rare ability to stick to the issues without making things personal. There are a few people out there who could learn from that.

If you are unfamiliar with Dan then you should check out his blog and his TED talk. He is a big deal.

Dan has taken issue with me about a few points on Twitter and so I thought that I would take this opportunity to expand on my thoughts a little.


I do not generally describe explicit instruction as ‘lecturing’ so why not? Well, lecturing implies a lack of interaction. It is clear to me that effective instruction involves ensuring students’ attention. In my own teaching, I attempt to achieve this by peppering any ‘lecturing’ with questions. I decide which student will answer which question (I rarely ask volunteers) and so all of my students know that they could be called upon at any time. I find that this concentrates the mind. If I am presenting something new then I will ask students to tell me how to do the non-new bits e.g. the linear algebra that drops out of the end of a transformations problem.

This looks very different from a classical university lecture where the size of the audience militates against this kind of interaction. The problem with describing explicit instruction as ‘lecturing’ is that I find people then quote studies to me that show that university-level lecturing with interactive clickers or with short review breaks is more effective than straight lecturing, thus demonstrating that explicit instruction is flawed (See papers here, here, here and here that have been forwarded to me periodically by Doug Holton – note that a common problem in interpreting these studies is trying to figure out what the “interactive” condition actually means). Clearly, explicit instruction can be a highly interactive approach and so this evidence tells us little of relevance.

“Lecturing” also does not seem to capture the phases of a lesson where students are practicing independently whereas the way that explicit instruction is defined does cover this. Explicit instruction has a long track history and is often also referred to as ‘direct instruction’. However, the latter term tends to be confused with the highly-scripted programs developed by Siegfried Engelmann and others which are basically one particular type of explicit instruction. This is why I avoid this term.

Barak Rosenshine is something of an expert in explicit instruction. He was involved in analysing the process-product research of the 1950s to 1970s that aimed to uncover the differences between more and less effective teaching. His concept of explicit instruction / direct instruction was drawn upon my Engelmann in developing his own approach. Rosenshine provides an excellent description of explicit instruction in this AFT article although he doesn’t name it as such, preferring to simply discuss ‘principles of instruction’. He goes into more detail here, this time referring to ‘direct instruction’ (paywalled).

Why do teachers seek alternatives to explicit instruction?

If explicit instruction is as effective as I claim then why do teachers seek out alternatives?

I spent 13 years feeling guilty about the way that I taught; that I should be making greater use of whistles and bells. This is because the dominant view in education asserts this. Of course, in reality, many teachers will use forms of explicit instruction because the alternatives are often unworkable. I rapidly figured-out that if I taught in certain ways then I’d have to teach the stuff again later. But I thought this was a flaw in me.

Universities and teacher training materials instruct teachers that ‘constructivist’ teaching practices are more effective, even though the evidence does not really support this. Consultants, school leaders and Dan Meyer himself are all resources that teachers could be expected to consult if they want to improve their practice and they will get a broadly similar message from each. Where could a teacher even find out about explicit instruction and its effectiveness? Well, I am trying to do my bit in a small way but it hardly compares.

The sadness is that this means that teachers often miss out on training in how to make their default explicit instruction much more effective. One light in the darkness is the work of Dylan Wiliam around formative assessment (which was basically my route into a different way of thinking).

Indeed, teaching seems to suffer from the “How Obvious” problem that Greg Yates points to in his classic paper. When presented with the findings of research, teachers tend to declare them obvious. However, when student teachers are asked to identify the attributes of effective teaching that comes from this research they generally cannot. “Not a single student cited the effective teacher’s ability to articulate clearly, or to get students to maintain time engagement.”


I have briefly mentioned that the alternative to explicit instruction may be described as ‘constructivist’ teaching. I don’t want to become bogged-down in this – I am aware that constructivism is actually theory of learning and not of teaching and I have no problem with it in this regard; we link new knowledge to old etc. If it is true then, no matter how we teach, our students will learn constructively. However, some educationalists clearly do see implications for how we should teach.

Over the years, similar approaches have been described in many ways; discovery learning, guided discovery, problem-based learning, project-based learning (see William Heard Kilpatrick for an early description), inquiry learning and so on. Many of these date from a time before the constructivist theory of learning and so reflect a broader current in educational thought, epitomised by the progressive education movement of the early 20th century. Constructivism should really be seen as part of this tradition.

As every age invents a new name for it, so a new enthusiasm develops and, without much in the way of supporting evidence, armies of evangelists go out into the world and proclaim the new ‘effective practices’. A recent example can be seen in Canada. Around the year 2000, constructivist maths was pushed heavily in schools via public policy (see the WNCP) and consultants. Since this time, Canadian results in international maths tests such as PISA and TIMSS have generally declined (and I don’t mean relative to other countries, I mean in absolute terms). It is only a correlation but if this new approach was so effective then should we not have seen the reverse trend?

I am generally cautious about comparing different countries on these measures but I do think it significant when a single participant such as Canada or Finland declines relative to itself.

On the basis of quite thin evidence (see Kamii and Dominick and a nice replication from Stephen Norton which finds the precise opposite result or look at this poorly controlled study), teachers have been urged to abandon standard algorithms or to avoid drilling students in multiplication tables and number bonds. Cognitive load theory – of which I am a student – would predict this to be a disastrous move (see my slides from prior to starting my PhD).

So, if there is a lack of evidence then what justification is there for people to continue to support constructivist approaches? One example can be seen in the various reactions to Project Follow Through and goes something like this, “OK so Direct Instruction may be good for rote memorisation of basic facts but our kind of instruction does more intangible things over a greater period of time that cannot be measured”. Or, “Direct Instruction causes criminality”. Neither of these is true (see here and here).

Another approach is to say that people who favour explicit instruction neglect motivation; that motivation is key to learning and explicit instruction is just like really boring man!

Firstly, if motivation really is so important to learning and if explicit instruction is so demotivating then surely this would render explicit instruction ineffective. The evidence suggests otherwise.

For my second point, I need to be careful. The constructivists have set a rhetorical trap here that I might fall in. I will freely admit that entertainment is not my top priority when planning lessons. My top priority is that students should learn. However, this does not mean that I want my students to be bored. If they can learn something and I can make it interesting then I would always want to do both.

It is not clear to me why explicit instruction is intrinsically more boring than any other method. Yes, it can be boring but so can problem-based learning or anything else. I’ve observed students completing one of Dan’s activities who were not particularly turned-on by it. However, I would not conclude that it was therefore intrinsically boring. Perhaps it was pitched at the wrong level or the teacher hadn’t introduced it correctly. Motivation is a complicated thing.

I have written before in the context of science and asked which activity is more boring; completing an investigation to test the strength of different wet paper towels or a whole-class discussion of whether aliens exist? Advocates of alternative methods often make life harder for themselves by also insisting that all learning be nailed to mundane aspects of everyday life. For instance, I have noted that in David Perkins’ recent book he suggests, “students plan for their town’s future water needs or model its traffic flow.” Yawn! Boring! (see, I can do it too).

I have this little proof that I like to demonstrate to show that 0.999.. = 1. Every year, it provokes heated debate. What do I do? I show the students the proof, on the board, at the front of the room and then we discuss it. I suppose that I could ask the students to get into groups and try to come up with their own proof. I suspect that most would not and would also find the activity a bit boring.

The point is that nobody owns motivation. If your explicit instruction is boring then why not make it more interesting? Why does this problem have to imply a change of method? If that’s all constructivism’s got then it’s time for a rethink.


Disrupting Education

Education is a strange, looking-glass world where conservatives pose as radicals. It is not a progressive education utopia, even if the ideas of the progressive education movement are drawn upon heavily by educational academics. Schools are intensely practical places and children pose myriad problems which educators have to muddle-through on a daily basis.

Instead of providing solutions to such problems, education academics are generally committed to some sort of an ‘approach’. Typically, academics construct complicated-sounding nouns and then try to rationalise why these ‘things’ are important. ‘Reification’ is the complicated-sounding noun that describes this process.

Educationalists would do better to adopt part of what is recognised as the scientific method. They should ask, ‘What would be the case if I were wrong?’ and then seek that evidence. This is what scientists do. This is why science is the best magic available at present and why we haven’t yet benefited from The Sociological Revolution. A good theory echoes Pat Benatar. “Hit me with your best shot,” it says, “fire away!”.

And so we must welcome the disruptors. And I’m not on about those who are giving kids iPads or anything as daft as that. I am talking about those who are now holding received educational wisdom up to the light and seeing right through it.

They ask whether learning styles or multiple intelligences exist. They wonder whether ‘skills’ such as ‘collaboration’ or ‘creativity’ are really skills and whether they look the same in different contexts. Perhaps these skills have just been made-up – ‘socially constructed’ if you will – and are not really ‘things’ at all.

The disruptors wonder whether teachers really are to blame for children’s deep-seated behavioural problems. They challenge the narrative that these are caused because teachers don’t listen or don’t plan engaging enough lessons. Instead, they question whether there are other causes and other solutions.

Indeed, they wonder about the notion of engagement, sanctified as it may be. Perhaps there are many kinds of engagement of which relatively few lead to learning. Perhaps hard work can in fact cause the right kind of engagement. Perhaps defining engagement in ‘active’ behavioural terms risks circular reasoning, particularly if we wish to promote behaviourally active teaching methods. Other kinds of engagement are possible, after all. 

The disruptors ask what is wrong with telling kids things. They challenge the idea that inquiry/discovery/constructivist/insert-new-name-for-it-here methods are better and point to the empirical evidence that they are not.

Of course, those who inhabit the current landscape are not going to welcome the disruptors. They are the conservatives who wish to preserve the way of things. They are likely to dismiss, patronise and even openly insult the new punks who are insisting on thinking for themselves.

But they can’t stop it. These are revolutionary times.


Why I loved linear A Levels 

I recall walking to my secondary school one day. I can remember the exact spot on that journey where it occurred to me that I would like to study physics at Cambridge. It was where I left a road and turned right into an alleyway. I remember thinking that Newton was at Cambridge, he was a great physicist and so it would be great to study physics there.

I hadn’t really gained this insight at school. My dad was an engineer and so questions and storytelling at home had led to this train of thought. My school was a bit of a tough place. It had recently gone through some bad times but it had a relatively new headteacher who was determined to sort things out. However, part of this strategy was to jump on new initiatives. My school was pushing all students through the new Double Science GCSE whilst the neighbouring schools all still retained separate science.

However, I loved my science lessons. I had a good teacher. I can’t remember as much about maths. The only thing that really stands out was being taught quadratic equations for the first time in the final lesson before GCSE study leave. It was only likely to be one question on the exam, so the thinking went, and so I could get it wrong and still get an A grade.

The schools in Dudley at that time did not have sixth forms and so I went on to a sixth form college. In a past life, it had been a grammar school and still retained a traditional feel.

I started out badly. I hadn’t a clue what was going on in chemistry class. I just didn’t know any of the words my teachers were using. In maths, I was on a D grade. So I made a decision. From Monday to Thursday I would do two hours of work each evening, whether I had homework to fill that time or not.

My sixth form had an Oxford and Cambridge club for those thinking of applying. I didn’t join. That would be absurd. I focused on my studies.

At the end of the lower sixth we had a series of exams in all of our subjects. I did quite well. My chemistry teacher asked if I had considered applying to Oxbridge. I froze a little. She suggested that I go on a trip that was running to the open day and then promptly organised this before I could object. I still feel emotional about this. 

I then went to maths class. Mr Hill, the old, crusty head of maths appeared at the door and asked if any students were thinking of applying to Oxford or Cambridge. Well, I had to raise my hand now. He marched us down the hallway to where the maths results were posted. “Point to where you are,” he said. I pointed at my name. “Third in the year,” he noted, “that’s OK.”

In the October of the upper sixth I made my application. The story of this process is for another day but, in short, I got into Cambridge and was able to pursue my dream of studying physics there. I was the only student from my sixth form to do so that year. I have my chemistry teacher to thank but also a system of A Levels where I had a whole year to find my feet.


Practice or Drill?

There are a couple of terms that are often used pejoratively in education discussions and yet possess an interesting relationship with reality. “Drill” and “Memorisation” are generally considered to be bad things; the kind of stuff that puts children off education. However, if we replace the term “drill” with “practice” then it is trivially true that it is a desirable thing. Who ever mastered anything without sufficient and sustained practice? Similarly, would we not also want our students to remember what they have learnt? If they do not, then can we even say that they have learnt anything at all? So, “memorization” is perhaps not all that bad.

Of course, deployment of these terms is part of the romantic education-as-an-awakening-from-within narrative that sets itself against attempts to transmit knowledge and skills from experts (teachers) to novices. And yet, as we have seen, the logic is hard to sustain.

It therefore sparked my interest to be involved in an exchange with Jo Boaler where she sought to draw some kind of a distinction between ‘drill’ and ‘practice’:

Boaler Tweet - Drill or Practice

At first sight, it also seems trivially true that being ‘thoughtful’ is a good thing and that if this distinguishes drill from practice then practice is, indeed, more desirable. However, this reminded me of Alfred North Whitehead’s prescient words that I have quoted before on this blog:

“It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.”

Whitehead is right. My research is in the area of Cognitive Load Theory (CLT) and, as with much educational theory, CLT bears a striking resemblance to common sense. Certainly, Whitehead was anticipating CLT with this quote.

The point is that we have limited processing capacity; a limited ‘working memory’ with which to solve problems. This becomes easily overloaded – cognitive overload. To circumvent this limit, we may (largely unconsciously) draw upon our long term memory. The fact that items can be pulled into the working memory from the long term memory with little conscious effort causes us, I believe, to underestimate this facet of how the mind works. In turn, this leads to the sorts of statements that we see about knowledge being unimportant or that students can just look things up when they need to.

To give an example from maths, the area that Jo Boaler and I were discussing, it is unhelpful to have to devote precious working memory resources to calculating 6 x 8 or to apply a ‘strategy’ to find the sum of 11 and 7. It is far better to just know these basic maths facts – i.e. retrieve them from long term memory – and therefore free working memory to interpret the problem or to produce a mental model of the situation.

Drill, especially timed drill, is excellent for promoting the swift retrieval of such facts from the long term memory. It utilises the testing effect which has been demonstrated to be highly effective, particularly for relatively simple items such as these. If there really is a distinction between drill and practice such that practice is the more flatulent kind of a thing then drill is what we should aim for.



I’ve got a plan. See what you think.

I’m going to invent something called “Ashmaths”. It’s an intervention for those students who are making below-average progress in numeracy by the end of year one. Of course, it’s not suitable for all of these children and there needs to be some kind of selection process. Perhaps those children who aren’t suitable will need to be moved out of the intervention once this becomes clear (i.e. they don’t seem to be making much progress). I’ll come up with some sort of criteria.

Now what we are going to do is give a one-to-one intervention to these students for 30 minutes a week for about eight to twelve weeks. It will include like… er.. some maths. I will create proprietary training and charge people lots of money for it. Perhaps we’ll hold conferences and the like. Maybe we’ll make a thing about being able to solve problems lots of different ways. Or perhaps I’ll follow the fashion and go all traditional, drilling them in times-tables and maths facts. It doesn’t matter really; the point is that I’ll control all of that and you’ll have to pay for it if you want to call what you do “Ashmaths” which you will, because…

…next, we’ll start with the research. We’ll run my expensive one-to-one intervention against business-as-usual i.e. no intervention at all. I’m pretty sure that this will lead to positive results. After all, twelve one-to-one, half-hour maths sessions must be better than none, right?

Once we’ve got the evidence then we can start selling politicians and administrators on the benefits of my program. Moreover, people are likely to think that it’s my proprietary strategies that have had the effect. Why not? Let’s encourage them to think that. With a bit of luck, I might be able to sell materials into mainstream classrooms and perhaps influence how maths is taught there too. Pretty soon, even standard classroom teachers will want to come to my conference to see what it’s all about.

Sounds like a good plan.


Freedom to Educate

This post is circuitous because it reflects the journey that my thinking has taken.

I happen to be in Cambridge at the moment, with a school tour. Whilst here, I was reminded of the sordid little tale of the Wyverns’ garden party from a few weeks ago and their ill-fated attempt to include bouts of jelly wrestling. They had previously abandoned this practice due to claims of sexism but they thought they had found a wheeze this time that would get them over the line; men would wrestle too. It didn’t wash. Rowan Williams who is now the Master at Magdalene College put his foot down and banned it. I am all in favour of Williams’s action. The drinking society members are likely to be the kind of rich, entitled boors who I grew to dislike at university and the college has a right to protect its image when confronted with such seediness perpetrated – at least in part – in its name.

So a good result then.

However, a couple of issues arise from the sound and fury. Why do none of the articles about this little episode question why women would participate in such an event? I cannot imagine saying anything at all at university that would have convinced any of my female friends to jelly wrestle for my entertainment. What’s going on? Well, did I mention that there is a cash prize? I don’t know how much it is. And the guys who organised it are probably loaded. Might women be swayed into participating in order to gain their favour; to seem cool? Perhaps the participants just think it’s fun; perhaps they are the kind of party girl that I have never met in my entire life? Perhaps they start out with one motivation but then retrospectively apply another – I think much of human reasoning is like that. To me, this is an interesting aspect of the story and yet none of the potential participants, or former participants, are asked for their thoughts.

Seedy, sordid, bad for the college image; all of these I understand. But I also happened to stumble upon another set of reasons why such an event should not go ahead. According to this commentator in The Cambridge Student:

“I believe that jelly wrestling, as it stands in the context of a male drinking society’s garden party, is damaging to the mental health of women with body image issues and eating disorders (EDs). It’s not surprising that EDs are a big problem in Cambridge as one of the main risk factors is perfectionism, which is a very common trait in students here. When I tried last year to raise awareness of EDs by producing an informative video, I was quickly flooded with messages from girls just like me – who felt that being academic was no longer enough, they had to be physically perfect too (and by any means necessary). I’m sure male drinking societies don’t mean to add to the pressure felt by these girls, but the fact is that they do. It’s common for male drinking societies to openly judge women on their appearance – if you don’t believe me try going to a swap dressed in something loose that covers you up and see how long it takes for you to be called frigid or be completely side-lined by the group.”

This is clearly thoughtful, pertinent and borne of personal experience. I have no difficulty picturing how these oafish lads – whom I am already predisposed to dislike – would judge women in loose clothing. But I am a little squeamish about the idea that jelly wrestling is damaging to the mental health of women with body image issues and eating disorders and that this is a reason to ban it. I believe that we need to think long and hard before we start to accept such arguments. We have crossed a Rubicon of sorts where one person’s vulnerability to a mental health issue can be used as an argument for restricting the freedoms of others. To an extent, this has always been the case. Nobody has unfettered liberty; showing disturbing videos to a child, for instance, would be considered irresponsible by most reasonable people. However, remember that in this situation, nobody is compelled to attend the Wyvern’s garden party. It is more that we just don’t like the thought of it. And how far are we willing to extend this principle? What about sexy music videos? What about bikinis on the beach?

What has this to do with education? Well, we have seen the rise of this type of argument, particularly in higher education and particularly in the United States. Course materials may now feature trigger warnings (although I recently read that the term “trigger” could be triggering and so should be avoided). The idea is that students who have suffered abuse, for example, might be disturbed by reading a text in which abuse is discussed. This would be damaging to their mental health.

A recent anonymous blog by a Midwest professor discussed how this movement has changed the higher education landscape. The post went viral. I cannot imagine the professor writing this post under his real name, a point that he also makes in the piece. So this simultaneously reveals the value of the web for facilitating anonymous comment whilst providing his critics with a lazy line of attack. Given the source, it is hard to know exactly how much weight to place on an assertion such as, “I once saw an adjunct not get his contract renewed after students complained that he exposed them to “offensive” texts written by Edward Said and Mark Twain.” There may have been more to it than this and we cannot ask for the other side of the argument. However, I believe that this is both worrying and plausible given some of the incidents that have made it into the press (e.g. the Laura Kipniss saga).

What has this to do with P-12 education? Well, at the moment, not much. It seems to be restricted to the liberal arts in American universities and with a bias towards issues involving gender and race. However, there are a number of factors that could mean that school teachers will soon have to pay attention to these issues.

One of the driving forces seems to have been students seeing themselves as consumers and therefore able to make demands of their institutions on this basis. We are seeing an increasing consumerism in education across the English-speaking world. Schools that will live or die by the choices that students and parents make will find it increasingly difficult to tell them things that they don’t want to hear.

I remember when I was training as a science teacher, I asked my mentor about how to approach teaching The Big Bang, given that some students might have religious objections. She said, “I always tell them that it’s just a theory.” This is a neat pivot around the word ‘theory’ that plays on its ambiguous nature. In normal discussion, ‘theory’ is synonymous with ‘idea’ or ‘hypothesis’; a theory could begin, “I reckon…” And yet in science, a theory is something supported by empirical data; quite a different kind of thing. I have never used my mentor’s formulation, preferring to say, “This is what the science says but you are free to believe whatever you want.” So there have always been sensitive areas but never ones that could not be mentioned.

However, at the very outset of the UK academies program there were worries about academies teaching creationism at the behest of their sponsor. It concerned me at the time and I wonder how the issues will play in the years to come. Will consumer-empowered parents and students object to The Big Bang, evolution, learning about other religions (they already do), climate science, sex education (they already do) or any positive discussion of homosexuality? Will they object to learning about dead, white, male authors or seek to approve the books on a school’s reading list? Perhaps an art teacher might run into trouble by discussing Vincent Van Gogh’s likely suicide without providing a trigger warning for those students who might be at risk of self-harm.

It has taken us a long time to develop the enlightenment culture that we currently enjoy; a culture in which we are generally free to express our views and to debate. The fruits of this culture have been unprecedented technological and cultural advances. Education is the regenerator of the enlightenment. It passes knowledge on to the next generation but it also passes attitudes and dispositions. By being prepared to tackle difficult subjects, criticise views, highlight historic differences and errors, we show our young people that the world is messy and complex and that blind faith in the dear leader is probably unwarranted. We give our students permission to think for themselves and to think differently. But we cannot do any of this without being able to professionally and appropriately range over a great many difficult and challenging issues. We should not be trying to wrap our young people in mental cotton wool. Instead, we should exhort them to, “Open your eyes! Look!”

The enlightenment is young, fragile and under attack on several fronts. We shall miss it when it’s gone.