going round in circles

Central to the Tiger Teachers’ model of cognitive science is the concept of cognitive load. Cognitive load refers to the amount of material that working memory is handling at any one time. It’s a concept introduced by John Sweller, a researcher frequently cited by the Tiger Teachers. Cognitive load is an important concept for education because human working memory capacity is very limited – we can think about only a handful of items at the same time. If students’ cognitive load is too high, they won’t be able to solve problems or will fail to learn some material.

I’ve had concerns about the Tiger Teachers’ interpretations of concepts from cognitive science, and about how they apply those concepts to their own learning, but until recently I hadn’t paid much attention to the way their students were being taught. I had little information about it for a start, and if it ‘worked’ for a particular group of teachers and students, I saw no reason to question it.

increasing cognitive load

The Michaela Community School recently blogged about solving problems involving circle theorems. Vince Ulam, a mathematician and maths teacher*, took issue with the diagrammatic representations of the problems.

The diagrams of the circles and triangles are clearly not accurate; they don’t claim to be. In an ensuing Twitter discussion, opinion was divided over whether or not the accuracy of diagrams mattered. Some people thought it didn’t matter if the diagrams were intended only as a representation of an algebraic or arithmetic problem. One teacher thought inaccurate diagrams would ensure the students didn’t measure angles or guess them.

The problem with the diagrams is not that they are imprecise – few people would quibble over a sketch diagram representing an angle of 28° that was actually 32°. It’s that they are so inaccurate as to be misleading. For example, there’s an obtuse angle that clearly isn’t obtuse, an angle of 71° is more acute than one of 28°, and a couple of isosceles triangles are scalene. As Vince points out, this makes it impossible for students to determine anything by inspection – an important feature of trigonometry. Diagrams with this level of inaccuracy also have implications for cognitive load, something that the Tiger Teachers are, rightly, keen to minimise.

My introduction to trigonometry at school was what the Tiger Teachers would probably describe as ‘traditional’. A sketch diagram illustrating a trigonometry problem was acceptable, but was expected to present a reasonably accurate representation of the problem. A diagram of an isosceles triangle might not be to scale, but it should be an isosceles triangle. An obtuse angle should be an obtuse angle, and an angle of 28° should not be larger than one of 71°.

Personally, I found some of the inaccurate diagrams so inaccurate as to be quite disconcerting. After all those years of trigonometry, the shapes of isosceles triangles, obtuse angles, and the relative sizes of angles of ~30° or ~70°, are burned into my brain, as the Tiger Teachers would no doubt expect them to be. So seeing a scalene triangle masquerading as an isosceles, an acute angle claiming to be 99°, and angles of 28° and 71° trading places, set up a somewhat unnerving Necker shift. In each case my brain started flipping between two contradictory representations; what the diagram was telling me and what the numbers were telling me.

It was the Stroop effect but with lines and numbers rather than letters and colours; and the Stroop effect increases cognitive load.  Even students accustomed to isosceles triangles not always looking like isosceles triangles would experience an increased cognitive load whilst looking at these diagrams, because they’ll have to process two competing representations; what their brain is telling them about the diagram and what it’s telling them about the numbers.  I had similar misgivings about the ‘CUDDLES’ approach used to teach French at Michaela.

CUDDLES and cognitive load

The ‘traditional’ approach to teaching foreign languages is to start with a bunch of simple nouns, adjectives and verbs, do a lot of rehearsal, and work up from there; that approach keeps cognitive load low from the get-go.   The Michaela approach seems to be to start with some complex language and break it down in a quasi-mathematical fashion involving underlining some letters, dotting others and telling stories about words.

Not only do students need to learn the words, what they represent and how French speakers use them, they have to learn a good deal of material extraneous to the language itself. I can see how the extraneous material acts as a belt-and-braces approach to ‘securing’ knowledge, but it must increase cognitive load because the students have to think about that as well as the language.

The Tiger Teacher’s approach to teaching is intriguing, but I still can’t figure out the underlying rationale; it certainly isn’t about reducing cognitive load.  Why does the Tiger Teachers’ approach to teaching matter?  Because now Nick Gibb is signed up to it, it will probably become educational policy, regardless of the validity of the evidence.

Note:  I resisted the temptation to call this post ‘non angeli sed anguli’.

*Amended from ‘maths teacher’ –  Old Andrew correctly pointed out that this was an assumption on my part. Vince Ulam assures me my assumption was correct.  I guess he should know.

The Tiger Teachers and cognitive science

Cognitive science is a key plank in the Tiger Teachers’ model of knowledge. If I’ve understood it properly the model looks something like this:

Cognitive science has discovered that working memory has limited capacity and duration, so pupils can’t process large amounts of novel information. If this information is secured in long-term memory via spaced, interleaved practice, students can recall it instantly whenever they need it, freeing up working memory for thinking.

What’s wrong with that? Nothing, as it stands. It’s what’s missing that’s the problem.

Subject knowledge

One of the Tiger Teachers’ beefs about the current education system is its emphasis on transferable skills. They point out that skills are not universally transferable, many are subject-specific, and in order to develop expertise in higher-level skills novices need a substantial amount of subject knowledge. Tiger Teachers’ pupils are expected to pay attention to experts (their teachers) and memorise a lot of facts before they can comprehend, apply, analyse, synthesise or evaluate. The model is broadly supported by cognitive science and the Tiger Teachers apply it rigorously to children. But not to themselves, it seems.

For most Tiger Teachers cognitive science will be an unfamiliar subject area. That makes them (like most of us) cognitive science novices. Obviously they don’t need to become experts in cognitive science to apply it to their educational practice, but they do need the key facts and concepts and a basic overview of the field. The overview is important because they need to know how the facts fit together and the limitations of how they can be applied.   But with a few honourable exceptions (Daisy Christodoulou, David Didau and Greg Ashman spring to mind – apologies if I’ve missed anyone out), many Tiger Teachers don’t appear to have even thought about acquiring expertise, key facts and concepts or an overview. As a consequence facts are misunderstood or overlooked, principles from other knowledge domains are applied inappropriately, and erroneous assumptions made about how science works. Here are some examples:

It’s a fact…

“Teachers’ brains work exactly the same way as pupils’” (p.177). No they don’t. Cognitive science (ironically) thinks that children’s brains begin by forming trillions of connections (synapses). Then through to early adulthood, synapses that aren’t used get pruned, which makes information processing more efficient. (There’s a good summary here.)  Pupils’ brains are as different to teachers’ brains as children’s bodies are different to adults’ bodies. Similarities don’t mean they’re identical.

Then there’s working memory. “As the cognitive scientist Daniel Willingham explains, we learn by transferring knowledge from the short-term memory to the long term memory” (p177). Well, kind of – if you assume that what Willingham explicitly describes as “just about the simplest model of the mind possible”  is an exhaustive model of memory. If you think that, you might conclude, wrongly, “the more knowledge we have in long-term memory, the more space we have in our working memory to process new information” (p.177). Or that “information cannot accumulate into long-term memory while working memory is being used” (p.36).

Long-term memory takes centre stage in the Tiger Teachers’ model of cognition. The only downside attributed to it is our tendency to forget things if we don’t revisit them (p.22). Other well-established characteristics of long-term memory – its unreliability, errors and biases – are simply overlooked, despite Daisy Christodoulou’s frequent citation of Daniel Kahneman whose work focused on those flaws.

With regard to transferable skills we’re told “cognitive scientist Herb Simon and his colleagues have cast doubt on the idea that there are any general or transferable cognitive skills” (p.17), when what they actually cast doubt on is the ideas that all skills are transferable or that none are.

The Michaela cognitive model is distinctly reductionist; “all there is to intelligence is the simple accrual and tuning of many small units of knowledge that in total produce complex cognition” (p.19). Then there’s “skills are simply just a composite of sequential knowledge – all skills can be broken down to irreducible pieces of knowledge” (p.161).

The statement about intelligence is a direct quote from John Anderson’s paper ‘A Simple Theory of Complex Cognition’ but Anderson isn’t credited, so you might not know he was talking about simple encodings of objects and transformations, and that by ‘intelligence’ he means how ants behave rather than IQ. I’ve looked at Daisy Christodoulou’s interpretation of Anderson’s model here.

The idea that intelligence and skills consist ‘simply just’ of units of knowledge ignores Anderson’s procedural rules and marginalises the role of the schema – the way people configure their knowledge. Joe Kirby mentions “procedural and substantive schemata” (p. 17), but seems to see them only in terms of how units of knowledge are configured for teaching purposes; “subject content knowledge is best organised into the most memorable schemata … chronological, cumulative schemata help pupils remember subject knowledge in the long term” (p.21). The concept of schemata as the way individuals, groups or entire academic disciplines configure their knowledge, that the same knowledge can be configured in different ways resulting in different meanings, or that configurations sometimes turn out to be profoundly wrong, doesn’t appear to feature in the Tiger Teachers’ model.

Skills: to transfer or not to transfer?

Tiger Teachers see higher-level skills as subject-specific. That hasn’t stopped them applying higher-level skills from one domain inappropriately to another. In her critique of Bloom’s taxonomy, Daisy Christodoulou describes it as a ‘metaphor’ for the relationship between knowledge and skills. She refers to two other metaphors; ED Hirsch’s scrambled egg and Joe Kirby’s double helix (Seven Myths p.21).  Daisy, Joe and ED teach English, and metaphors are an important feature in English literature. Scientists do use metaphors, but they use analogies more often, because in the natural world patterns often repeat themselves at different levels of abstraction. Daisy, Joe and ED are right to complain about Bloom’s taxonomy being used to justify divorcing skills from knowledge. And the taxonomy itself might be wrong or misleading.   But it is a taxonomy and it is based on an important scientific concept – levels of abstraction – so should be critiqued as such, not as if it were a device used by a novelist.

Not all evidence is equal

A major challenge for novices is what criteria they can use to decide whether or not factual information is valid. They can’t use their overview of a subject area if they don’t have one. They can’t weigh up one set of facts against another if they don’t know enough facts. So Tiger Teachers who are cognitive science novices have to fall back on the criteria ED Hirsch uses to evaluate psychology – the reputation of researchers and consensus. Those might be key criteria in evaluating English literature, but they’re secondary issues for scientific research, and for good reason.

Novices then have to figure out how to evaluate the reputation of researchers and consensus. The Tiger Teachers struggle with reputation. Daniel Willingham and Paul Kirschner are cited more frequently than Herb Simon, but with all due respect to Willingham and Kirschner, they’re not quite in the same league. Other key figures don’t get a mention.  When asked what was missing from the Tiger Teachers’ presentations at ResearchEd, I suggested, for starters, Baddeley and Hitch’s model of working memory. It’s been a dominant model for 40 years and has the rare distinction of being supported by later biological research. But it’s mentioned only in an endnote in Willingham’s Why Don’t Students Like School and in Daisy’s Seven Myths about Education. I recommended inviting Alan Baddeley to speak at ResearchEd – he’s a leading authority on memory after all.   One of the teachers said he’d never even heard of him. So why was that teacher doing a presentation on memory at a national education conference?

The Tiger Teachers also struggle with consensus. Joe Kirby emphasises the length of time an idea has been around and the number of studies that support it (pp.22-3), overlooking the fact that some ideas can dominate a field for decades, be supported by hundreds of studies and then turn out to be profoundly wrong; theories about how brains work are a case in point.   Scientific theory doesn’t rely on the quantity of supporting evidence; it relies on an evaluation of all relevant evidence – supporting and contradictory – and takes into account the quality of that evidence as well.  That’s why you need a substantial body of knowledge before you can evaluate it.

The big picture

For me, Battle Hymn painted a clearer picture of the Michaela Community School than I’d been able to put together from blog posts and visitors’ descriptions. It persuaded me that Michaela’s approach to behaviour management is about being explicit and consistent, rather than simply being ‘strict’. I think having a week’s induction for new students and staff (‘bootcamp’) is a great idea. A systematic, rigorous approach to knowledge is vital and learning by rote can be jolly useful. But for me, those positives were all undermined by the Tiger Teachers’ approach to their own knowledge.  Omitting key issues in discussions of Rousseau’s ideas, professional qualifications or the special circumstances of schools in coastal and rural areas, is one thing. Pontificating about cognitive science and then ignoring what it says is quite another.

I can understand why Tiger Teachers want to share concepts like the limited capacity of working memory and skills not being divorced from knowledge.  Those concepts make sense of problems and have transformed their teaching.  But for many Tiger Teachers, their knowledge of cognitive science appears to be based on a handful of poorly understood factoids acquired second or third hand from other teachers who don’t have a good grasp of the field either. Most teachers aren’t going to know much about cognitive science; but that’s why most teachers don’t do presentations about it at national conferences or go into print to share their flimsy knowledge about it.  Failing to acquire a substantial body of knowledge about cognitive science makes its comprehension, application, analysis, synthesis and evaluation impossible.  The Tiger Teachers’ disregard for principles they claim are crucial is inconsistent, disingenuous, likely to lead to significant problems, and sets a really bad example for pupils. The Tiger Teachers need to re-write some of the lyrics of their Battle Hymn.

The Tiger Teachers’ model of knowledge: what’s missing?

“If all else fails for Michaela at least we’re going to do a great line in radical evangelical street preachers.” Jonathan Porter, Head of Humanities at the Michaela Community School was referring to an impassioned speech from Katharine Birbalsingh, the school’s head teacher at the recent launch of their book, Battle Hymn of the Tiger Teachers: The Michaela Way.

Michaela Community School’s sometimes blistering critique of the English education system, coupled with its use of pedagogical methods abandoned by most schools decades ago, has drawn acclaim, criticism and condemnation. There’s a strong, shared narrative about the Michaela Way amongst the contributors to Battle Hymn. If I’ve understood it correctly, it goes like this:

There’s a crisis in the English education system due to progressive ideas that have dominated teacher training since the 1960s. Child-centred methods have undermined discipline. Poor behaviour and lack of respect makes it impossible for teachers to teach. Subject knowledge has been abandoned in favour of higher-level skills wrongly claimed to be transferable. The way to combat the decline is via strict discipline, teacher authority, a knowledge-based curriculum and didactic teaching.

Knowledge is power

“Knowledge is power” is the Michaela motto. Tiger Teachers are required to have extensive knowledge of their own subject area in order to teach their pupils. Pupils are considered to be novices and as such are expected to acquire a substantial amount of factual knowledge before they can develop higher-level subject-specific skills.

Given the emphasis on knowledge, you’d expect the Tiger Teachers to apply this model not only to their pupils, but to any subjects they are unfamiliar with.   But they don’t. It appears to apply only to what pupils are taught in school.

A couple of years ago at a ResearchEd conference, I queried some claims made about memory. I found myself being interrogated by three Tiger Teachers about what I thought was wrong with the model of memory presented. I said I didn’t think anything was wrong with it; the problem was what it missed out. There are other examples in Battle Hymn of missing key points. To illustrate, I’ve selected four. Here’s the first:


Rousseau is widely recognised as the originator of the progressive educational ideas so derided in the Michaela narrative.   If you were to rely on other Tiger Teachers for your information about Rousseau, you might picture him as a feckless Romantic philosopher who wandered the Alps fathering children whilst entertaining woolly, sentimental, unrealistic thoughts about their education.   You wouldn’t know that he argued in Émile, ou de L’Éducation not so much for the ‘inevitable goodness’ of children as Jonathan Porter claims (p.77), but that children (and adults) aren’t inherently bad – a view that flew in the face of the doctrine of original sin espoused by the Geneva Calvinism that Rousseau had rejected and the Catholicism he (temporarily) converted to soon after.

At the time, children were often expected to learn by rote factual information that was completely outside their experience, that was meaningless to them. Any resistance would have been seen as a sign of their fallen nature, rather than an understandable objection to a pointless exercise. Rousseau advocated that education work with nature, rather than against it. He claimed the natural world more accurately reflected the intentions of its Creator than the authoritarian, man-made religious institutions that exerted an extensive and often malign influence over people’s day-to-day lives.   Not surprisingly, Émile was promptly banned in Geneva and Paris.

Although Jonathan Porter alludes to the ‘Enlightenment project’ (p.77), he doesn’t mention Rousseau’s considerable influence in other spheres. The section of Émile that caused most consternation was entitled ‘The Creed of a Savoyard Priest’. It was the only part Voltaire thought worth publishing. In it, Rousseau tackles head-on Descartes’ proposition ‘I think, therefore I am’. He sets out the questions about perception, cognition, reasoning, consciousness, truth, free will and the existence of religions, that perplexed the thinkers of his day and that cognitive science has only recently begun to find answers to. I’m not defending Rousseau’s educational ideas, I think Voltaire’s description “a hodgepodge of a silly wet nurse in four volumes” isn’t far off the mark, but to draw valid conclusions from Rousseau’s ideas about education, you need to know why he was proposing them.

Battle Hymn isn’t a textbook or an academic treatise, so it would be unreasonable to expect it to tackle at length all the points it alludes to. But it is possible to signpost readers to relevant issues in a few words. There’s nothing technically wrong with the comments about Rousseau in Battle Hymn, or Robert Peal’s Progressively Worse (a core text for Tiger Teachers) or Daisy Christodoulou’s Seven Myths about Education (another core text); but what’s missed out could result in conclusions being drawn that aren’t supported by the evidence.

Teacher qualifications

Another example is teacher qualifications. Michaela teachers don’t think much of their initial teacher training (ITT); they claim it didn’t prepare them for the reality of teaching (p.167),  it indoctrinates teachers into a ‘single dogmatic orthodoxy’ (p.171), outcomes are poor (p.158), and CPD in schools is ‘more powerful’ (p.179). The conclusion is not that ITT needs a root-and-branch overhaul, but that it should be replaced with something else; in-school training or … no qualification at all. Sarah Clear says she’s “an unqualified teacher and proud” (p.166) and argues that although the PGCE might be a necessary precaution to prevent disaster, it doesn’t actually do that (p.179), so why bother with it?

Her view doesn’t quite square with Dani Quinn’s perspective on professional qualifications. Dani advocates competition in schools because there’s competition in the professional world. She says; “Like it or not, when it comes to performance, it is important to know who is the best” and cites surgeons and airline pilots as examples (p.133). But her comparison doesn’t quite hold water. Educational assessment tends to be norm-referenced (for reasons Daisy Christodoulou explores here) but assessments of professional performance are almost invariably criterion-referenced in order to safeguard minimum standards of technical knowledge and skill. But neither Dani nor Sarah mention norm-referenced and criterion-referenced assessment – which is odd, given Daisy Christodoulou’s involvement with Michaela. Again, there’s nothing technically wrong with what’s actually said about teacher qualifications; but the omission of relevant concepts increases the risk of reaching invalid conclusions.

Replicating Michaela

A third example is from the speech given by Katharine Birbalsingh at the book launch. It was triggered by this question: “How would you apply Michaela in primary? Could you replicate it in coastal areas or rural areas and how would that work?”

Katharine responds: “These are all systems and values that are universal. That could happen anywhere. Of course it could happen in a primary. I mean you just insist on higher standards with regard to the behaviour and you teach them didactically because everyone learns best when being taught didactically … You would do that with young children, you would do that with coastal children and you would do that with Yorkshire children. I don’t see why there would be a difference.” She then launches into her impassioned speech about teaching and its social consequences.

You could indeed apply Michaela’s systems, values, behavioural expectations and pedagogical approach anywhere. It doesn’t follow that you could apply them everywhere. Implicit in the question is whether the Michaela approach is scalable. It’s not clear whether Katharine misunderstood the question or answered the one she wanted to answer, but her response overlooks two important factors.

First, there’s parent/pupil choice. Brent might be one of the most deprived boroughs in the country, but it’s a deprived borough in a densely populated, prosperous city that has many schools and a good public transport system. If parents or pupils don’t like Michaela, they can go elsewhere. But in rural areas, for many pupils there’s only one accessible secondary school – there isn’t an elsewhere to go to.

Then there’s teacher recruitment. If you’re a bright young graduate, as most of the Michaela staff seem to be, the capital offers a vibrant social life and  a wide range of interesting alternative career alternatives should you decide to quit teaching. In a rural area there wouldn’t be the same opportunities.  Where I live, in a small market town in a sparsely populated county, recruitment in public sector services has been an ongoing challenge for many years.

Coastal towns have unique problems because they are bounded on at least one side by the sea. This makes them liminal spaces, geographically, economically and socially. Many are characterised by low-skilled, low-paid, seasonal employment and social issues different to those of an inner city. For teachers, the ‘life’ bit of the work-life balance in London would be very different from what they could expect in out-of-season Hartlepool.

Of course there’s no reason in principle why a replica Michaela shouldn’t transform the educational and economic prospects of coastal or rural areas.   But in practice, parent/pupil choice and teacher recruitment would be challenges that by definition Michaela hasn’t had to face because it’s a classic ‘special case’.  And it’s not safe to generalise from special cases. Again, there’s nothing technically wrong with what Katharine said about replicating Michaela; it’s what she didn’t say that’s key.  The same is true for the Tiger Teachers’ model of cognitive science, the subject of the next post.


Birbalsingh, K (2016).  Battle Hymn of the Tiger Teachers: The Michaela Way.  John Catt Educational.

Christodoulou, D (2014).  Seven Myths about Education.  Routledge.

Peal, R (2014).  Progressively Worse: The Burden of Bad Ideas in British Schools.  Civitas.

Rousseau, J-J (1974/1762).  Émile.  JM Dent.