magic beans, magic bullets and crypto-pathologies

In the previous post, I took issue with a TES article that opened with fidget-spinners and closed with describing dyslexia and ADHD as ‘crypto-pathologies’. Presumably as an analogy with cryptozoology – the study of animals that exist only in folklore. But dyslexia and ADHD are not the equivalent of bigfoot and unicorns.

To understand why, you have to unpack what’s involved in diagnosis.

diagnosis, diagnosis, diagnosis

Accurate diagnosis of health problems has always been a challenge because:

  • Some disorders* are difficult to diagnose. A broken femur, Bell’s palsy or measles are easier to figure out than hypothyroidism, inflammatory bowel disease or Alzheimer’s.
  • It’s often not clear what’s causing the disorder. Fortunately, you don’t have to know the immediate or root causes for successful treatment to be possible. Doctors have made the reasonable assumption that patients presenting with the same signs and symptoms§ are likely to have the same disorder.

Unfortunately, listing the signs and symptoms isn’t foolproof because;

  • some disorders produce different signs and symptoms in different patients
  • different disorders can have very similar signs and symptoms.

some of these disorders are not like the others…

To complicate the picture even further, some signs and symptoms are qualitatively different from the aches, pains, rashes or lumps that indicate disorders obviously located in the body;  they involve thoughts, feelings and behaviours instead. Traditionally, human beings have been assumed to consist of a physical body and non-physical parts such as mind and spirit, which is why disorders of thoughts, feelings and behaviours were originally – and still are – described as mental disorders.

Doctors have always been aware that mind can affect body and vice versa. They’ve also long known that brain damage and disease can affect thoughts, feelings, behaviours and physical health. In the early 19th century, mental disorders were usually identified by key symptoms. The problem was that the symptoms of different disorders often overlapped. A German psychiatrist, Emil Kraepelin, proposed instead classifying mental disorders according to syndromes, or patterns of co-occurring signs and symptoms. Kraepelin hoped this approach would pave the way for finding the biological causes of disorders. (In 1906, Alois Alzheimer found the plaques that caused the dementia named after him, while he was working in Kraepelin’s lab.)

Kraepelin’s approach laid the foundations for two widely used modern classification systems for mental disorders; the Diagnostic and Statistical Manual of Mental Disorders, published by the American Psychiatric Association, currently in its 5th edition (DSM V), and the International Classification of Diseases Classification of Mental and Behavioural Disorders published by the World Health Organisation, currently in its 10th edition (ICD-10).

Kraepelin’s hopes for his classification system have yet to be realised. That’s mainly because the brain is a difficult organ to study. You can’t poke around in it without putting your patient at risk. It’s only in the last few decades that scanning techniques have enabled researchers to look more closely at the structure and function of the brain, and the scans require interpretation –  brain imaging is still in its infancy.

you say medical, I say experiential

Kraepelin’s assumptions about distinctive patterns of signs and symptoms, and about their biological origins, were reasonable ones. His ideas, however, were almost the polar opposite to those of his famous contemporary, Sigmund Freud, who located the root causes of mental disorders in childhood experience. The debate has raged ever since. The dispute is due to the plasticity of the brain.  Brains change in structure and function over time and several factors contribute to the changes;

  • genes – determine underlying structure and function
  • physical environment e.g. biochemistry, nutrients, toxins – affects structure and function
  • experience – the brain processes information, and information changes the brain’s physical structure and biochemical function.

On one side of the debate is the medical model; in essence, it assumes that the causes of mental disorders are primarily biological, often due to a ‘chemical imbalance’. There’s evidence to support this view; medication can improve a patient’s symptoms. The problem with the medical model is that it tends to assume;

  • a ‘norm’ for human thought, feelings and behaviours – disorders are seen as departures from that norm
  • the cause of mental disorders is biochemical and the chemical ‘imbalance’ is identified (or not) through trial-and-error – errors can be catastrophic for the patient.
  • the cause is located in the individual.

On the other side of the debate is what I’ll call the experiential model (often referred to as anti-psychiatry or critical psychiatry). In essence it assumes the causes of unwanted thoughts, feelings or behaviours are primarily experiential, often due to adverse experiences in childhood. The problem with that model is that it tends to assume;

  • the root causes are experiential and not biochemical
  • the causes are due to the individual’s response to adverse experiences
  • first-hand reports of early adverse experiences are always reliable, which they’re not.


Kraepelin’s classification system wasn’t definitive – it couldn’t be, because no one knew what was causing the disorders. But it offered the best chance of identifying distinct mental health problems – and thence their causes and treatments. The disorders identified in Kraepelin’s system, the DSM and ICD, were – and most still are – merely labels given to clusters of co-occurring signs and symptoms.  People showing a particular cluster are likely to share the same underlying biological causes, but that doesn’t mean they do share the same underlying causes or that the origin of the disorder is biological.

This is especially true for signs and symptoms that could have many causes. There could be any number of reasons for someone hallucinating, withdrawing, feeling depressed or anxious – or having difficulty learning to read or maintain attention.  They might not have a medical ‘disorder’ as such. But you wouldn’t know that to read through the disorders listed in the DSM or ICD. They all look like bona fide, well-established medical conditions, not like labels for bunches of symptoms that sometimes co-occur and sometimes don’t, and that have a tendency to appear or disappear with each new edition of the classification system.  That brings us to the so-called ‘crypto-pathologies’ referred to in the TES article.

Originally, terms like dyslexia were convenient and legitimate shorthand labels for specific clusters of signs or symptoms. Dyslexia means difficulty with reading, as distinct from alexia which means not being able to read at all; both problems can result from stroke or brain damage. Similarly, autism was originally a shorthand term for the withdrawn state that was one of the signs of schizophrenia – itself a label.  Delusional parasitosis is also a descriptive label (the parasites being what’s delusional, not the itching).


What’s happened over time is that many of these labels have become reified – they’ve transformed from mere labels into disorders widely perceived as having an existence independent of the label. Note that I’m not saying the signs and symptoms don’t exist. There are definitely children who struggle with reading regardless of how they’ve been taught; with social interaction regardless of how they’ve been brought up; and with maintaining focus regardless of their environment. What I am saying is that there might be different causes, or multiple causes, for clusters of very similar signs and symptoms.  Similar signs and symptoms don’t mean that everybody manifesting those signs and symptoms has the same underlying medical disorder –  or even that they have a medical disorder at all.

The reification of labels has caused havoc for decades with research. If you’ve got a bunch of children with different causes for their problems with reading, but you don’t know what the different causes are so you lump all the children together according to their DSM label; or another bunch with different causes for their problems with social interaction but lump them all together; or a third bunch with different causes for their problems maintaining focus, but you lump them all together; you are not likely to find common causes in each group for the signs and symptoms.  It’s this failure to find distinctive features at the group level that has been largely responsible for claims that dyslexia, autism or ADHD ‘don’t exist’, or that treatments that have evidently worked for some individuals must be spurious because they don’t work for other individuals or for the heterogeneous group as a whole.


Oddly, in his TES article, Tom refers to autism as an ‘identifiable condition’ but to dyslexia and ADHD as ‘crypto-pathologies’ even though the diagnostic status of autism in the DSM and ICD is on a par with that of ADHD, and with ‘specific learning disorder with impairment in reading‘ with dyslexia recognised as an alternative term (DSM), or ‘dyslexia and alexia‘ (ICD).  Delusional parasitosis, despite having the same diagnostic status and a plausible biological mechanism for its existence, is dismissed as ‘a condition that never was’.

Tom is entitled to take a view on diagnosis, obviously. He’s right to point out that reading difficulties can be due to lack of robust instruction, and inattention can be due to the absence of clear routines. He’s right to dismiss faddish simplistic (but often costly) remedies. But the research is clear that children can have difficulties with reading due to auditory and/or visual processing impairments (search Google scholar for ‘dyslexia visual auditory’), that they can have difficulties maintaining attention due to low dopamine levels – exactly what Ritalin addresses (Iversen, 2006), or that they can experience intolerable itching that feels as if it’s caused by parasites.

But Tom doesn’t refer to the research, and despite provisos such as acknowledging that some children suffer from ‘real and grave difficulties’ he effectively dismisses some of those difficulties as crypto-pathologies and implies they can be fixed by robust teaching and clear routines  –  or that they are just imaginary.  There’s a real risk, if the research is by-passed, of ‘robust teaching’ and ‘clear routines’ becoming the magic bullets and magic beans he rightly despises.


*Disorder implies a departure from the norm.  At one time, it was assumed the norm for each species was an optimal set of characteristics.  Now, the norm is statistically derived, based on 95% of the population.

§ Technically, symptoms are indicators of a disorder experienced only by the patient and signs are detectable by others.  ‘Symptoms’ is often used to include both.


Iversen, L (2006).  Speed, Ecstasy, Ritalin: The science of amphetamines.  Oxford University Press.

learning styles: how does Daniel Willingham see them?

In 2005, Daniel Willingham used his “Ask the cognitive scientist” column in American Educator to answer the question “What does cognitive science tell us about the existence of visual, auditory, and kinesthetic learners and the best way to teach them?

The question refers to the learning styles model used in many schools which assumes that children learn best using their preferred sensory modality – visual, auditory or kinaesthetic. Fleming’s VARK model, and the more common VAK variant, frame learning styles in terms of preferences for learning in a particular sensory modality. Other learning styles models are framed in terms of individuals having other stable traits in respect of the way they learn. Willingham frames the VAK model in terms of abilities.

He summarises the relevant cognitive science research like this; “children do differ in their abilities with different modalities, but teaching the child in his best modality doesn’t affect his educational achievement” and goes on to discuss what cognitive science has to say about sensory modalities and memory. Willingham’s response is informative about the relevant research, but I think it could be misleading. For two reasons; he doesn’t differentiate between groups and individuals, and doesn’t adequately explain the role of sensory modalities in memory.

groups and individuals

In the previous post I mentioned the challenge to researchers posed by differences at the population, group and individual levels. Willingham’s summary of the research begins at the population level “children do differ in their abilities with different modalities” but then shifts to the individual level “but teaching the child in his best modality doesn’t affect his educational achievement” [my emphasis].

Even if Willingham’s choice of words is merely a matter of style, it inadvertently conflates findings at the group and individual levels. Group averages tell you what you need to know if you’re interested in broad pedagogical approaches or educational policy; in the case of learning styles, there’s no robust evidence warranting their use as a general approach in teaching. It doesn’t follow that individual children don’t have a ‘best’ (or more likely ‘worst’) modality, nor that they can’t benefit from learning in a particular modality. For example, Picture Exchange Communication System (PECS) and sign languages are the only way some children can communicate effectively and ‘talking books’ gives others access to literature that would otherwise be out of their reach. On his learning styles FAQ page, Willingham claims this is a matter of ‘ability’ rather than ‘style’; but ability is likely to have an impact on preference.

memory and modality

Willingham goes on to explain “a few things that cognitive scientists know about modalities”. His first claim is that “memory is usually stored independent of any modality” [Willingham’s emphasis]. “You typically store memories in terms of meaning — not in terms of whether you saw, heard, or physically interacted with the information”.

He supports this assertion with a finding from research into episodic memory – that whilst people are good at remembering the gist of a story, they tend to be hazy when it comes to specific details. His claim appears to be further supported by research into witness testimony. People might accurately remember a car crashing into a lamppost, but misremember the colour of the car; they correctly recall the driver behaving in an aggressive manner, but are wrong about the words she uttered.

Willingham then extends the role of meaning to the facet of memory that deals with facts and knowledge – semantic memory. He says “the vast majority of educational content is stored in terms of meaning and does not rely on visual, auditory, or kinesthetic memory” and “teachers almost always want students to remember what things mean, not what they look like or sound like”. He uses the example ‘a fire requires oxygen to burn’ and says “the initial experience by which you learned this fact may have been visual (watching a flame go out under a glass) or auditory (hearing an explanation), but the resulting representation of that knowledge in your mind is neither visual nor auditory.” Certainly the idea of a fire requiring oxygen to burn might be neither visual nor auditory, but how many students will not visualise flames being extinguished under a glass when they recall this fact?

substitute modalities

Willingham’s second assertion about memory and sensory modalities is that “the different visual, auditory, and meaning-based representations in our minds cannot serve as substitutes for one another”. He cites a set of experiments reported by Dodson and Shimamura (2000). In the experiments a list of words was read to participants by either a man or a woman. Participants then listened to a second list and were asked to judge which of the words had been in the first list. They were also asked whether a man or woman had spoken the word the first time round. People were five times better at remembering who spoke an item if a test word was read by the same voice than if it was read by the alternative voice. But mismatching the voices didn’t make a difference to the number of words that were recognised.

Dodson and Shimamura see the study as demonstrating that memory is highly susceptible to sensory cues. But Willingham’s conclusion is different; “this experiment indicates that subjects do store auditory information, but it only helps them remember the part of the memory that is auditory — the sound of the voice — and not the word itself, which is stored in terms of its meaning.” This is a rather odd conclusion, given that almost all the words in the experiments were spoken, so auditory memory must have been involved in recognising the words as well as identifying the gender of the speaker. I couldn’t see how the study supported Willingham’s assertion about substitute modalities. And substitute modalities are widely used and used very effectively; writing, sign language and lip-reading are all visual/kinaesthetic substitutes for speech in the auditory modality.

little difference in the classroom

Willingham’s third assertion is “children probably do differ in how good their visual and auditory memories are, but in most situations, it makes little difference in the classroom”. That’s a fair conclusion given the findings of reviews of learning styles studies. He also points out that studies of mental imagery suggest that paying attention to the modality best suited to the content of what’s being taught, rather than the student’s ‘best’ modality, is more likely to help students understand and remember.

the meaning of meaning

Meaning is one of those rather fuzzy words that people use in different ways. It’s widely used to denote the relationship between a symbol and the entity the symbol represents. You could justify talking about memory in terms of meaning in the sense that memory consists of our representations of entities rather than the entities themselves, but I don’t think that’s what Willingham is getting at. I think when he uses the term meaning he’s referring to schemas.

The sequence of a series of events, the gist of a story and the connections between groups of facts are all schemas. There’s no doubt that in the case of complex memories, most people focus on the schema rather than the detail. And teachers do want students to remember the deep structure schemas linking facts rather than just the surface level details. But our memories of chains of events, the plots of stories and factual information are quite clearly not “independent of any modality”. Witnesses who saw a car careering down a road at high speed, collide with a lamppost and the driver emerge swearing at shocked onlookers, might focus on the meaning of that series of events, but they must have some sensory representation of the car and the driver’s voice in order to recall those meaningful events. And how could we recall the narrative of Hansel and Gretel without a sensory representation of two children in a forest, or think about a fire ceasing to burn in the absence of oxygen without a sensory representation of flames and then no flames?

I found it difficult to get a clear picture of Willingham’s conceptual model of memory. When he says “the mind is capable of storing memories in a number of different formats”, and “some memories are stored visually, some auditorily, and some in terms of meaning“, one could easily get the impression that memory is neatly compartmentalised, with ‘meaning’ as one of the compartments. That impression wouldn’t be accurate.

mechanisms of memory

In the brain, sensory information (our only source of information about the outside world) is carried in networks of neurons – brain cells. The pattern of activation in the neural networks forms the representations of both real-time sensory input and of what we remember. It’s like the way an almost infinite number of images can be displayed on a computer screen using a limited number of pixels. It’s true that sensory information is initially processed in areas of the brain dedicated to specific sensory modalities. But those streams of information begin to be integrated quite near the beginning of their journey through the brain, and are rapidly brought together to form a bigger picture of what’s happening that can be compared to representations we’ve formed previously – what we call memory.

The underlying biological mechanism appears to be essentially the same for all sensory modalities and for all types of memory – whether they are of stories, sequences of events, facts about fire, or, to cite Willingham’s examples, of Christmas trees, peas, or Clinton’s or Bush’s voice. ‘Meaning’ as far as the brain is concerned, is about associations – which neurons are activating which other neurons and therefore which representations are being activated. Whether we remember the gist of a story, a fact about fire, or what a Christmas tree or frozen pea looks like, we’re activating patterns of neurons that represent information associated with those events, facts or objects.

Real life experiences usually involve incoming information in multiple sensory modalities. We very rarely encounter the world via only one sensory domain and never in terms of ‘meaning’ only – how would we construct that meaning without our senses being involved? Having several sensory channels increases the amount of information we get from the outside world, and increases the likelihood of our accessing memories. A whiff of perfume or a fragment of music can remind us vividly of a particular event or can trigger a chain of factual associations. Teachers are indeed focused on the ‘meaning’ of what they teach, but meaning isn’t divorced from sensory modalities. Indeed, what things look like is vitally important in biology, chemistry and art. And what they sound like is crucial for drama, poetry or modern foreign languages.

In his American Educator piece, Willingham agrees that “children do differ in their abilities with different modalities“.  But by 2008 he was claiming in a video presentation that Learning Styles Don’t Exist. The video made a big impression on teacher Tom Bennett. He says it “explains the problems with the theory so clearly that even dopey old me can get my head around it”.

Tom’s view of learning styles is the subject of the next post.

Dodson, C.S. and Shimamura, A.P. (2000). Differential effects of cue dependency on item and source memory. Journal of Experimental Psychology: Learning, Memory and Cognition, 26, 1023-1044.

Willingham, D (2005). Ask the cognitive scientist: Do visual, auditory, and kinesthetic learners need visual, auditory, and kinesthetic instruction? American Educator, Summer.

synthetic phonics, dyslexia and natural learning

Too intense a focus on the virtues of synthetic phonics (SP) can, it seems, result in related issues getting a bit blurred. I discovered that some whole language supporters do appear to have been ideologically motivated but that the whole language approach didn’t originate in ideology. And as far as I can tell we don’t know if SP can reduce adult functional illiteracy rates. But I wouldn’t have known either of those things from the way SP is framed by its supporters. SP proponents also make claims about how the brain is involved in reading. In this post I’ll look at two of them; dyslexia and natural learning.


Dyslexia started life as a descriptive label for the reading difficulties adults can develop due to brain damage caused by a stroke or head injury. Some children were observed to have similar reading difficulties despite otherwise normal development. The adults’ dyslexia was acquired (they’d previously been able to read) but the children’s dyslexia was developmental (they’d never learned to read). The most obvious conclusion was that the children also had brain damage – but in the early 20th century when the research started in earnest there was no easy way to determine that.

Medically, developmental dyslexia is still only a descriptive label meaning ‘reading difficulties’ (causes unknown, might/might not be biological, might vary from child to child). However, dyslexia is now also used to denote a supposed medical condition that causes reading difficulties. This new usage is something that Diane McGuinness complains about in Why Children Don’t Learn to Read.

I completely agree with McGuinness that this use isn’t justified and has led to confusion and unintended and unwanted outcomes. But I think she muddies the water further by peppering her discussion of dyslexia (pp. 132-140) with debatable assertions such as:

“We call complex human traits ‘talents’”.

“Normal variation is on a continuum but people working from a medical or clinical model tend to think in dichotomies…”.

“Reading is definitely not a property of the human brain”.

“If reading is a biological property of the brain, transmitted genetically, then this must have occurred by Lamarckian evolution.”

Why debatable? Because complex human traits are not necessarily ‘talents’; clinicians tend to be more aware of normal variation than most people; reading must be a ‘property of the brain’ if we need a brain to read; and the research McGuinness refers to didn’t claim that ‘reading’ was transmitted genetically.

I can understand why McGuinness might be trying to move away from the idea that reading difficulties are caused by a biological impairment that we can’t fix. After all, the research suggests SP can improve the poor phonological awareness that’s strongly associated with reading difficulties. I get the distinct impression, however, that she’s uneasy with the whole idea of reading difficulties having biological causes. She concedes that phonological processing might be inherited (p.140) but then denies that a weakness in discriminating phonemes could be due to organic brain damage. She’s right that brain scans had revealed no structural brain differences between dyslexics and good readers. And in scans that show functional variations, the ability to read might be a cause, rather than an effect.

But as McGuinness herself points out reading is a complex skill involving many brain areas, and biological mechanisms tend to vary between individuals. In a complex biological process there’s a lot of scope for variation. Poor phonological awareness might be a significant factor, but it might not be the only factor. A child with poor phonological awareness plus visual processing impairments plus limited working memory capacity plus slow processing speed – all factors known to be associated with reading difficulties – would be unlikely to find those difficulties eliminated by SP alone. The risk in conceding that reading difficulties might have biological origins is that using teaching methods to remediate them might then called into question – just what McGuinness doesn’t want to happen, and for good reason.

Natural and unnatural abilities

McGuinness’s view of the role of biology in reading seems to be derived from her ideas about the origin of skills. She says;

It is the natural abilities of people that are transmitted genetically, not unnatural abilities that depend upon instruction and involve the integration of many subskills”. (p.140, emphasis McGuinness)

This is a distinction often made by SP proponents. I’ve been told that children don’t need to be taught to walk or talk because these abilities are natural and so develop instinctively and effortlessly. Written language, in contrast, is a recent man-made invention; there hasn’t been time to evolve a natural mechanism for reading, so we need to be taught how to do it and have to work hard to master it. Steven Pinker, who wrote the foreword to Why Children Can’t Read seems to agree. He says “More than a century ago, Charles Darwin got it right: language is a human instinct, but written language is not” (p.ix).

Although that’s a plausible model, what Pinker and McGuinness fail to mention is that it’s also a controversial one. The part played by nature and nurture in the development of language (and other abilities) has been the subject of heated debate for decades. The reason for the debate is that the relevant research findings can be interpreted in different ways. McGuinness is entitled to her interpretation but it’s disingenuous in a book aimed at a general readership not to tell readers that other researchers would disagree.

Research evidence suggests that the natural/unnatural skills model has got it wrong. The same natural/unnatural distinction was made recently in the case of part of the brain called the fusiform gyrus. In the fusiform gyrus, visual information about objects is categorised. Different types of objects, such as faces, places and small items like tools, have their own dedicated locations. Because those types of objects are naturally occurring, researchers initially thought their dedicated locations might be hard-wired.

But there’s also word recognition area. And in experts, the faces area is also used for cars, chess positions, and specially invented items called greebles. To become an expert in any of those things you require some instruction – you’d need to learn the rules of chess or the names of cars or greebles. But your visual system can still learn to accurately recognise, discriminate between and categorise many thousands of items like faces, places, tools, cars, chess positions and greebles simply through hours and hours of visual exposure.

Practice makes perfect

What claimants for ‘natural’ skills also tend to overlook is how much rehearsal goes into them. Most parents don’t actively teach children to talk, but babies hear and rehearse speech for many months before they can say recognisable words. Most parents don’t teach toddlers to walk, but it takes young children years to become fully stable on their feet despite hours of daily practice.

There’s no evidence that as far as the brain is concerned there’s any difference between ‘natural’ and ‘unnatural’ knowledge and skills. How much instruction and practice knowledge or skills require will depend on their transparency and complexity. Walking and bike-riding are pretty transparent; you can see what’s involved by watching other people. But they take a while to learn because of the complexity of the motor-co-ordination and balance involved. Speech and reading are less transparent and more complex than walking and bike-riding, so take much longer to master. But some children require intensive instruction in order to learn to speak, and many children learn to read with minimal input from adults. The natural/unnatural distinction is a false one and it’s as unhelpful as assuming that reading difficulties are caused by ‘dyslexia’.

Multiple causes

What underpins SP proponents’ reluctance to admit biological factors as causes for reading difficulties is, I suspect, an error often made when assessing cause and effect. It’s an easy one to make, but one that people advocating changes to public policy need to be aware of.

Let’s say for the sake of argument that we know, for sure, that reading difficulties have three major causes, A, B and C. The one that occurs most often is A. We can confidently predict that children showing A will have reading difficulties. What we can’t say, without further investigation, is whether a particular child’s reading difficulties are due to A. Or if A is involved, that it’s the only cause.

We know that poor phonological awareness is frequently associated with reading difficulties. Because SP trains children to be aware of phonological features in speech, and because that training improves word reading and spelling, it’s a safe bet that poor phonological awareness is also a cause of reading difficulties. But because reading is a complex skill, there are many possible causes for reading difficulties. We can’t assume that poor phonological awareness is the only cause, or that it’s a cause in all cases.

The evidence that SP improves children’s decoding ability is persuasive. However, the evidence also suggests that 12% – 15% of children will still struggle to learn to decode using SP. And that around 15% of children will struggle with reading comprehension. Having a method of reading instruction that works for most children is great, but education should benefit all children, and since the minority of children who struggle are the ones people keep complaining about, we need to pay attention to what causes reading difficulties for those children – as individuals. In education, one size might fit most, but it doesn’t fit all.


McGuinness, D. (1998). Why Children Can’t Read and What We Can Do About It. Penguin.

seven myths about education: finally…

When I first heard about Daisy Christodoulou’s myth-busting book in which she adopts an evidence-based approach to education theory, I assumed that she and I would see things pretty much the same way. It was only when I read reviews (including Daisy’s own summary) that I realised we’d come to rather different conclusions from what looked like the same starting point in cognitive psychology. I’ve been asked several times why, if I have reservations about the current educational orthodoxy, think knowledge is important, don’t have a problem with teachers explaining things and support the use of systematic synthetic phonics, I’m critical of those calling for educational reform rather than those responsible for a system that needs reforming. The reason involves the deep structure of the models, rather than their surface features.

concepts from cognitive psychology

Central to Daisy’s argument is the concept of the limited capacity of working memory. It’s certainly a core concept in cognitive psychology. It explains not only why we can think about only a few things at once, but also why we oversimplify and misunderstand, are irrational, are subject to errors and biases and use quick-and-dirty rules of thumb in our thinking. And it explains why an emphasis on understanding at the expense of factual information is likely to result in students not knowing much and, ironically, not understanding much either.

But what students are supposed to learn is only one of the streams of information that working memory deals with; it simultaneously processes information about students’ internal and external environment. And the limited capacity of working memory is only one of many things that impact on learning; a complex array of environmental factors is also involved. So although you can conceptually isolate the material students are supposed to learn and the limited capacity of working memory, in the classroom neither of them can be isolated from all the other factors involved. And you have to take those other factors into account in order to build a coherent, workable theory of learning.

But Daisy doesn’t introduce only the concept of working memory. She also talks about chunking, schemata and expertise. Daisy implies (although she doesn’t say so explicitly) that schemata are to facts what chunking is to low-level data. That just as students automatically chunk low-level data they encounter repeatedly, so they will automatically form schemata for facts they memorise, and the schemata will reduce cognitive load in the same way that chunking does (p.20). That’s a possibility, because the brain appears to use the same underlying mechanism to represent associations between all types of information – but it’s unlikely. We know that schemata vary considerably between individuals, whereas people chunk information in very similar ways. That’s not surprising if the information being chunked is simple and highly consistent, whereas schemata often involve complex, inconsistent information.

Experimental work involving priming suggests that schemata increase the speed and reliability of access to associated ideas and that would reduce cognitive load, but students would need to have the schemata that experts use explained to them in order to avoid forming schemata of their own that were insufficient or misleading. Daisy doesn’t go into detail about deep structure or schemata, which I think is an oversight, because the schemata students use to organise facts are crucial to their understanding of how the facts relate to each other.

migrating models

Daisy and teachers taking a similar perspective frequently refer approvingly to ‘traditional’ approaches to education. It’s been difficult to figure out exactly what they mean. Daisy focuses on direct instruction and memorising facts, Old Andrew’s definition is a bit broader and Robert Peal’s appears to include cultural artefacts like smart uniforms and school songs. What they appear to have in common is a concept of education derived from the behaviourist model of learning that dominated psychology in the inter-war years. In education it focused on what was being learned; there was little consideration of the broader context involving the purpose of education, power structures, socioeconomic factors, the causes of learning difficulties etc.

Daisy and other would-be reformers appear to be trying to update the behaviourist model of education with concepts that, ironically, emerged from cognitive psychology not long after it switched focus from behaviourist model of learning to a computational one; the point at which the field was first described as ‘cognitive’. The concepts the educational reformers focus on fit the behaviourist model well because they are strongly mechanistic and largely context-free. The examples that crop up frequently in the psychology research Daisy cites usually involve maths, physics and chess problems. These types of problems were chosen deliberately by artificial intelligence researchers because they were relatively simple and clearly bounded; the idea was that once the basic mechanism of learning had been figured out, the principles could then be extended to more complex, less well-defined problems.

Researchers later learned a good deal about complex, less well-defined problems, but Daisy doesn’t refer to that research. Nor do any of the other proponents of educational reform. What more recent research has shown is that complex, less well-defined knowledge is organised by the brain in a different way to simple, consistent information. So in cognitive psychology the computational model of cognition has been complemented by a constructivist one, but it’s a different constructivist model to the social constructivism that underpins current education theory. The computational model never quite made it across to education, but early constructivist ideas did – in the form of Piaget’s work. At that point, education theory appears to have grown legs and wandered off in a different direction to cognitive psychology. I agree with Daisy that education theorists need to pay attention to findings from cognitive psychology, but they need to pay attention to what’s been discovered in the last half century not just to the computational research that superseded behaviourism.

why criticise the reformers?

So why am I critical of the reformers, but not of the educational orthodoxy? When my children started school, they, and I, were sometimes perplexed by the approaches to learning they encountered. Conversations with teachers painted a picture of educational theory that consisted of a hotch-potch of valid concepts, recent tradition, consequences of policy decisions and ideas that appeared to have come from nowhere like Brain Gym and Learning Styles. The only unifying feature I could find was a social constructivist approach and even on that opinions seemed to vary. It was difficult to tell what the educational orthodoxy was, or even if there was one at all. It’s difficult to critique a model that might not be a model. So I perked up when I heard about teachers challenging the orthodoxy using the findings from scientific research and calling for an evidence-based approach to education.

My optimism was short-lived. Although the teachers talked about evidence from cognitive psychology and randomised controlled trials, the model of learning they were proposing appeared as patchy, incomplete and incoherent as the model they were criticising – it was just different. So here are my main reservations about the educational reformers’ ideas:

1. If mainstream education theorists aren’t aware of working memory, chunking, schemata and expertise, that suggests there’s a bigger problem than just their ignorance of these particular concepts. It suggests that they might not be paying enough attention to developments in some or all of the knowledge domains their own theory relies on. Knowing about working memory, chunking, schemata and expertise isn’t going to resolve that problem.

2. If teachers don’t know about working memory, chunking, schemata and expertise, that suggests there’s a bigger problem than just their ignorance of these particular concepts. It suggests that teacher training isn’t providing teachers with the knowledge they need. To some extent this would be an outcome of weaknesses in educational theory, but I get the impression that trainee teachers aren’t expected or encouraged to challenge what they’re taught. Several teachers who’ve recently discovered cognitive psychology have appeared rather miffed that they hadn’t been told about it. They were all Teach First graduates; I don’t know if that’s significant.

3. A handful of concepts from cognitive psychology doesn’t constitute a robust enough foundation for developing a pedagogical approach or designing a curriculum. Daisy essentially reiterates what Daniel Willingham has to say about the breadth and depth of the curriculum in Why Don’t Students Like School?. He’s a cognitive psychologist and well-placed to show how models of cognition could inform education theory. But his book isn’t about the deep structure of theory, it’s about applying some principles from cognitive psychology in the classroom in response to specific questions from teachers. He explores ideas about pedagogy and the curriculum, but that’s as far as it goes. Trying to develop a model of pedagogy and design a curriculum based on a handful of principles presented in a format like this is like trying to devise courses of treatment and design a health service based on the information gleaned from a GP’s problem page in a popular magazine. But I might be being too charitable; Willingham is a trustee of the Core Knowledge Foundation, after all.

4. Limited knowledge Rightly, the reforming teachers expect students to acquire extensive factual knowledge and emphasise the differences between experts and novices. But Daisy’s knowledge of cognitive psychology appears to be limited to a handful of principles discovered over thirty years ago. She, Robert Peal and Toby Young all quote Daniel Willingham on research in cognitive psychology during the last thirty years, but none of them, Willingham included, tell us what it is. If they did, it would show that the principles they refer to don’t scale up when it comes to complex knowledge. Nor do most of the teachers writing about educational reform appear to have much teaching experience. That doesn’t mean they are wrong, but it does call into question the extent of their expertise relating to education.

Some of those supporting Daisy’s view have told me they are aware that they don’t know much about cognitive psychology, but have argued that they have to start somewhere and it’s important that teachers are made aware of concepts like the limits of working memory. That’s fine if that’s all they are doing, but it’s not. Redesigning pedagogy and the curriculum on the basis of a handful of facts makes sense if you think that what’s important is facts and that the brain will automatically organise those facts into a coherent schema. The problem is of course that that rarely happens in the absence of an overview of all the relevant facts and how they fit together. Cognitive psychology, like all other knowledge domains, has incomplete knowledge but it’s not incomplete in the same way as the reforming teachers’ knowledge. This is classic Sorcerer’s Apprentice territory; a little knowledge, misapplied, can do a lot of damage.

5. Evaluating evidence Then there’s the way evidence is handled. Evidence-based knowledge domains have different ways of evaluating evidence, but they all evaluate it. That means weighing up the pros and cons, comparing evidence for and against competing hypotheses and so on. Evaluating evidence does not mean presenting only the evidence that supports whatever view you want to get across. That might be a way of making your case more persuasive, but is of no use to anyone who wants to know about the reliability of your hypothesis or your evidence. There might be a lot of evidence telling you your hypothesis is right – but a lot more telling you it’s wrong. But Daisy, Robert Peal and Toby Young all present supporting evidence only. They make no attempt to test the hypotheses they’re proposing or the evidence cited, and much of the evidence is from secondary sources – with all due respect to Daniel Willingham, just because he says something doesn’t mean that’s all there is to say on the matter.

cargo-cult science

I suggested to a couple of the teachers who supported Daisy’s model that ironically it resembled Feynman’s famous cargo-cult analogy (p. 97). They pointed out that the islanders were using replicas of equipment, whereas the concepts from cognitive psychology were the real deal. I suggest that even the Americans had left their equipment on the airfield and the islanders knew how to use it, that wouldn’t have resulted in planes bringing in cargo – because there were other factors involved.

My initial response to reading Seven Myths about Education was one of frustration that despite making some good points about the educational orthodoxy and cognitive psychology, Daisy appeared to have got hold of the wrong ends of several sticks. This rapidly changed to concern that a handful of misunderstood concepts is being used as ‘evidence’ to support changes in national education policy.

In Michael Gove’s recent speech at the Education Reform Summit, he refers to the “solidly grounded research into how children actually learn of leading academics such as ED Hirsch or Daniel T Willingham”. Daniel Willingham has published peer-reviewed work, mainly on procedural learning, but I could find none by ED Hirsch. It would be interesting to know what the previous Secretary of State for Education’s criteria for ‘solidly grounded research’ and ‘leading academic’ were. To me the educational reform movement doesn’t look like an evidence-based discipline but bears all the hallmarks of an ideological system looking for evidence that affirms its core beliefs. This is no way to develop public policy. Government should know better.

seven myths about education: deep structure

deep structure and understanding

Extracting information from data is crucially important for learning; if we can’t spot patterns that enable us to identify changes and make connections and predictions, no amount of data will enable us to learn anything. Similarly, spotting patterns within and between facts enables us to identify changes and connections and make predictions will help us understand how the world works. Understanding is a concept that crops up a lot in information theory and education. Several of the proposed hierarchies of knowledge have included the concept of understanding – almost invariably at or above the knowledge level of the DIKW pyramid. Understanding is often equated with what’s referred to as the deep structure of knowledge. In this post I want to look at deep structure in two contexts; when it involves a small number of facts, and when it involves a very large number, as in an entire knowledge domain.

When I discussed the DIKW pyramid, I referred to information being extracted from a ‘lower’ level of abstraction to form a ‘higher’ one. Now I’m talking about ‘deep’ structure. What’s the difference, if any? The concept of deep structure comes from the field of linguistics. The idea is that you can say the same thing in different ways; the surface features of what you say might be different, but the deep structure of the statements could still be the same. So the sentences ‘the cat is on the mat’ and ‘the mat is under the cat’ have different surface features but the same deep structure. Similarly, ‘the dog is on the box’ and ‘the box is under the dog’ share the same deep structure. From an information-processing perspective the sentences about the dog and the cat share the same underlying schema.

In the DIKW knowledge hierarchy, extracted information is at a ‘higher’ level, not a ‘deeper’ one. The two different terminologies are used because the concepts of ‘higher’ level extraction of information and ‘deep’ structure have different origins, but essentially they are the same thing. All you need to remember is that in terms of information-processing ‘high’ and ‘deep’ both refer to the same vertical dimension – which term you use depends on your perspective. Higher-level abstractions, deep structure and schemata refer broadly to the same thing.

deep structure and small numbers of facts

Daniel Willingham devotes an entire chapter of his book Why don’t students like school? to the deep structure of knowledge when addressing students’ difficulty in understanding abstract ideas. Willingham describes mathematical problems presented in verbal form that have different surface features but the same deep structure – in his opening example they involve the calculation of the area of a table top and of a soccer pitch (Willingham, p.87). What he is referring to is clearly the concept of a schema, though he doesn’t call it that.

Willingham recognises that students often struggle with deep structure concepts and recommends providing them with many examples and using analogies they’re are familiar with. These strategies would certainly help, but as we’ve seen previously, because the surface features of facts aren’t consistent in terms of sensory data, students’ brains are not going to spot patterns automatically and pre-consciously in the way they do with consistent low-level data and information. To the human brain, a cat on a mat is not the same as a dog on a box. And a couple trying to figure out whether a dining table would be big enough involves very different sensory data to that involved in a groundsman working out how much turf will be needed for a new football pitch.

Willingham’s problems involve several levels of abstraction. Note that the levels of abstraction only provide an overall framework, they’re not set in stone; I’ve had to split the information level into two to illustrate how information needs to be extracted at several successive levels before students can even begin to calculate the area of the table or the football pitch. The levels of abstraction are;

• data – the squiggles that make up letters and the sounds that make up speech
• first-order information – letters and words (chunked)
• second-order information – what the couple is trying to do and what the groundsman is trying to do (not chunked)
• knowledge – the deep structure/schema underlying each problem.

To anyone familiar with calculating area, the problems are simple ones; to anyone unfamiliar with the schema involved, they impose a high cognitive load because the brain is trying to juggle information about couples, tables, groundsmen and football pitches and can’t see the forest for the trees. Most brains would require quite a few examples before they had enough information to be able to spot the two patterns, so it’s not surprising that students who haven’t had much practical experience of buying tables, fitting carpets, painting walls or laying turf take a while to cotton on.

visual vs verbal representations

What might help students further is making explicit the deep structure of groups of facts with the help of visual representations. Visual representations have one huge advantage over verbal representations. Verbal representations, by definition, are processed sequentially – you can only say, hear or read one word at a time. Most people can process verbal information at the same rate at which they hear it or read it, so most students will be able to follow what a teacher is saying or what they are reading, even if it takes a while to figure out what the teacher or the book are getting at. However, if you can’t process verbal information quickly enough, can’t recall earlier sentences whilst processing the current one, miss a word, or don’t understand a crucial word or concept, it will be impossible to make sense of the whole thing. In visual representations, you can see all the key units of information at a glance, most of the information can be processed in parallel and the underlying schema is more obvious.

The concept of calculating area lends itself very well to visual representation; it is a geometry problem after all. Getting the students to draw a diagram of each problem would not only focus their attention on the deep structure rather than its surface features, it would also demonstrate clearly that problems with different surface features can have the same underlying deep structure.

It might not be so easy to make visual representations of the deep structure of other groups of facts, but it’s an approach worth trying because it makes explicit the deep structure of the relationship between the facts. In Seven Myths about Education, one of Daisy’s examples of a fact is the date of the battle of Waterloo. Battles are an excellent example of deep structure/schemata in action. There is a large but limited number of ways two opposing forces can position themselves in battle, whoever they are and whenever and wherever they are fighting, which is why ancient battles are studied by modern military strategists. The configurations of forces and what subsequent configurations are available to them are very similar to the configurations of pieces and next possible moves in chess. Of course chess began as a game of military strategy – as a visual representation of the deep structure of battles.

Deep structure/underlying schemata are a key factor in other domains too. Different atoms and different molecules can share the same deep structure in their bonding and reactions and chemists have developed formal notations for representing that visually; the deep structure of anatomy and physiology can be the same for many different animals – biologists rely heavily on diagrams to convey deep structure information. Historical events and the plots of plays can follow similar patterns even if the events occurred or the plays were written thousands of years apart. I don’t know how often history or English teachers use visual representations to illustrate the deep structure of concepts or groups of facts, but it might help students’ understanding.

deep structure of knowledge domains

It’s not just single facts or small groups of facts that have a deep structure or underlying schema. Entire knowledge domains have a deep structure too, although not necessarily in the form of a single schema; many connected schemata might be involved. How they are connected will depend on how experts arrange their knowledge or how much is known about a particular field.

Making students aware of the overall structure of a knowledge domain – especially if that’s via a visual representation so they can see the whole thing at once – could go a long way to improving their understanding of whatever they happen to be studying at any given time. It’s like the difference between Google Street View and Google Maps. Google Street View is invaluable if you’re going somewhere you’ve never been before and you want to see what it looks like. But Google Maps tells you where you are in relation to where you want to be – essential if you want to know how to get there. Having a mental map of an entire knowledge domain shows you how a particular fact or group of facts fits in to the big picture, and also tells you how much or how little you know.

Daisy’s model of cognition

Daisy doesn’t go into detail about deep structure or schemata. She touches on these concepts only a few times; once in reference to forming a chronological schema of historical events, then when referring to Joe Kirby’s double-helix metaphor for knowledge and skills and again when discussing curriculum design.

I don’t know if Daisy emphasises facts but downplays deep structure and schemata to highlight the point that the educational orthodoxy does essentially the opposite, or whether she doesn’t appreciate the importance of deep structure and schemata compared to surface features. I suspect it’s the latter. Daisy doesn’t provide any evidence to support her suggestion that simply memorising facts reduces cognitive load when she says;

“So when we commit facts to long-term memory, they actually become part of our thinking apparatus and have the ability to expand one of the biggest limitations of human cognition”(p.20).

The examples she refers to immediately prior to this assertion are multiplication facts that meet the criteria for chunking – they are simple and highly consistent and if they are chunked they’d be treated as one item by working memory. Whether facts like the dates of historical events meet the criteria for chunking or whether they occupy less space in working memory when memorised is debatable.

What’s more likely is that if more complex and less consistent facts are committed to memory, they are accessed more quickly and reliably than those that haven’t been memorised. Research evidence suggests that neural connections that are activated frequently become stronger and are accessed faster. Because information is carried in networks of neural connections, the more frequently we access facts or groups of facts, the faster and more reliably we will be able to access them. That’s a good thing. It doesn’t follow that those facts will occupy less space in working memory.

It certainly isn’t the case that simply committing to memory hundreds or thousands of facts will enable students to form a schema, or if they do, that it will be the schema their teacher would like them to form. Teachers might need to be explicit about the schemata that link facts. Since hundreds or thousands of facts tend to be linked by several different schemata – you can arrange the same facts in different ways – being explicit about the different ways they can be linked might be crucial to students’ understanding.

Essentially, deep structure schemata play an important role in three ways;

Students’ pre-existing schemata will affect their understanding of new information – they will interpret it in the light of the way they currently organise their knowledge. Teachers need to know about common misunderstandings as well as what they want students to understand.

Secondly, being able to identify the schema underlying one fact or small group of facts is the starting point for spotting similarities and differences between several groups of facts.

Thirdly, having a bird’s-eye view of the schemata involved in an entire knowledge domain increases students’ chances of understanding where a particular fact fits in to the grand scheme of things – and their awareness of what they don’t know.

Having a bird’s-eye view of the curriculum can help too, because it can show how different subject areas are linked. Subject areas and the curriculum are the subjects of the next post.

seven myths about education: facts and schemata

Knowledge occupies the bottom level of Bloom’s taxonomy of educational objectives. In the 1950s, Bloom and his colleagues would have known a good deal about the strategies teachers use to help students to acquire knowledge. What they couldn’t have known is how students formed their knowledge; how they extracted information from data and knowledge from information. At the time cognitive psychologists knew a fair amount about learning but had only a hazy idea about how it all fitted together. The DIKW pyramid I referred to in the previous post explains how the bottom layer of Bloom’s taxonomy works – how students extract information and knowledge during learning. Anderson’s simple theory of cognition explains how people extract low-level information. More recent research at the knowledge and wisdom levels is beginning to shed light on Bloom’s higher-level skills, why people organise the same body of knowledge in different ways and why they misunderstand and make mistakes.

Seven Myths about Education addresses the knowledge level of Bloom’s taxonomy. Daisy Christodoulou presents a model of cognition that she feels puts the higher-level skills in Bloom’s taxonomy firmly into context. Her model also forms the basis for a pedagogical approach and a structure for a curriculum, which I’ll discuss in another post. Facts are a core feature of Daisy’s model. I’ve mentioned previously that many disciplines find facts problematic because facts, by definition, have to be valid (true), and it’s often difficult to determine their validity. In this post I want to focus instead on the information processing entailed in learning facts.

a simple theory of cognition

Having explained the concept of chunking and the relationship between working and long-term memory, Daisy introduces Anderson’s paper;

So when we commit facts to long-term memory, they actually become part of our thinking apparatus and have the ability to expand one of the biggest limitations of human cognition. Anderson puts it thus:

‘All that there is to intelligence is the simple accrual and tuning of many small units of knowledge that in total produce complex cognition. The whole is no more than the sum of its parts, but it has a lot of parts.’”

She then says “a lot is no exaggeration. Long-term memory is capable of storing thousands of facts, and when we have memorised thousands of facts on a specific topic, these facts together form what is known as a schema” (p. 20).


This was one of the points where I began to lose track of Daisy’s argument. I think she’s saying this:

Anderson shows that low-level data can be chunked into a ‘unit of knowledge’ that is then treated as one item by WM – in effect increasing the capacity of WM. In the same way, thousands of memorised facts can be chunked into a more complex unit (a schema) that is then treated as one item by WM – this essentially bypasses the limitations of WM.

I think Daisy assumes that the principle Anderson found pertaining to low-level ‘units of knowledge’ applies to all units of knowledge at whatever level of abstraction. It doesn’t. Before considering why it doesn’t, it’s worth noting a problem with the use of the word ‘facts’ when describing data. Some researchers have equated data with ‘raw facts’. The difficulty with defining data as ‘facts’ is that by definition a fact has to be valid (true) and not all data is valid, as the GIGO (garbage-in-garbage-out) principle that bedevils computer data processing and the human brain’s often flaky perception of sensory input demonstrate. In addition, ‘facts’ are more complex than raw (unprocessed) data or raw (unprocessed) sensory input.

It’s clear from Daisy’s examples of facts that she isn’t referring to raw data or raw sensory input. Her examples include the date of the battle of Waterloo, key facts about numerous historical events and ‘all of the twelve times tables’. She makes it clear in the rest of the book that in order to understand such facts, students need prior knowledge. In terms of the DIKW hierarchy, Daisy’s ‘facts’ are at a higher level to Anderson’s ‘units of knowledge’ and are unlikely to be processed automatically and pre-consciously in the same way as Anderson’s units. To understand why, we need to take another look at Anderson’s units of knowledge and why chunking happens.

chunking revisited

Data that can be chunked easily have two key characteristics; they involve small amounts of information and the patterns within them are highly consistent. As I mentioned in the previous post, one of Anderson’s examples of chunking is the visual features of upper case H. As far as the brain is concerned, the two parallel vertical lines and linking horizontal line that make up the letter H don’t involve much information. Also, although fonts and handwriting vary, the core features of all the Hs the brain perceives are highly consistent. So the brain soon starts perceiving all Hs as the same thing and chunks up the core features into a single unit – the letter H. If H could also be written Ĥ and Ħ in English, it would take a bit longer for the brain to chunk the three different configurations of lines and to learn the association between them, but not much longer, since the three variants involve little information and are still highly consistent.

understanding facts

But the letter H isn’t a fact, it’s a symbol. So are + and the numerals 1 and 2. ‘1+2’ isn’t a fact in the sense that Daisy uses the term, it’s a series of symbols. ‘1+2=3’ could be considered a fact because it consists of symbols representing two entities and the relationship between them. If you know what the symbols refer to, you can understand it. It could probably be chunked because it contains a small amount of information and has consistent visual features. Each multiplication fact in multiplication tables could probably be chunked, too, since they meet the same criteria. But that’s not true for all the facts that Daisy refers to, because they are more complex and less consistent.

‘The cat is on the mat’ is a fact, but in order to understand it, you need some prior knowledge about cats, mats and what ‘on’ means. These would be treated by working memory as different items. Most English-speaking 5 year-olds would understand the ‘cat is on the mat’ fact, but because there are different sorts of cats, different sorts of mats and different ways in which the cat could be on the mat, each child could have a different mental image of the cat on the mat. A particular child might conjure up a different mental image each time he or she encountered the fact, meaning that different sensory data were involved each time, the mental representations of the fact would be low in consistency, and the fact’s component parts couldn’t be chunked into a single unit in the same way as lower-level more consistent representations. Consequently the fact is less likely to be treated as one item in working memory.

Similarly, in order to understand a fact like ‘the battle of Waterloo was in 1815’ you’d need to know what a battle is, where Waterloo is (or at least that it’s a place), what 1815 means and how ‘of’ links a battle and a place name. If you’re learning about the Napoleonic wars, your perception of the battle is likely to keep changing and the components of the facts would have low consistency meaning that it couldn’t be chunked in the way Anderson describes.

The same problem involving inconsistency would prevent two or more facts being chunked into a single unit. But clearly people do mentally link facts and the components of facts. They do it using a schema, but not quite in the way Daisy describes.


Before discussing how people use schemata (schemas), a comment on the biological structures that enable us to form them. I mentioned in an earlier post that the neurons in the brain form complex networks a bit like the veins in a leaf. Physical connections are formed between neighbouring neurons when the neurons are activated simultaneously by incoming data. If the same or very similar data are encountered repeatedly, the same neurons are activated repeatedly, connections between them are strengthened and eventually networks of neurons are formed that can carry a vast amount of information in their patterns of connections. The patterns of connections between the neurons represent the individual’s perception of the patterns in the data.

So if I see a cat on a mat, or read a sentence about a cat on a mat, or imagine a cat on a mat, my networks of neurons carrying information about cats and mats will be activated. Facts and concepts about cats, mats and things related to them will readily spring to mind. But I won’t have access to all of those facts and concepts at once. That would completely overload my working memory. Instead, what I recall is a stream of facts and concepts about cats and mats that takes time to access. It’s only a short time, but it doesn’t happen all at once. Also, some facts and concepts will be activated immediately and strongly and others will take longer and might be a bit hazy. In essence, a schema is a network of related facts and concepts, not a chunked ‘unit of knowledge’.

Daisy says “when we have memorised thousands of facts on a specific topic, these facts together form what is known as a schema” (p. 20). It doesn’t work quite like that, for several reasons.

the structure of a schema A schema is what it sounds like – a schematic plan or framework. It doesn’t consist of facts or concepts, but it’s a representation of how someone mentally arranges facts or concepts. In the same way the floor-plan of a building doesn’t consist of actual walls, doors and windows, but it does show you where those things are in the building in relation to each other. The importance of this apparently pedantic point will become clear when I discuss deep structure.

implicit and explicit schemata Schemata can be implicit – the brain organises facts and concepts in a particular way but we’re not aware of what it is – or explicit – we actively organise facts and concepts in a particular way and we aware of how they are organised.

the size of a schema Schemata can vary in size and complexity. The configuration of the three lines that make up the letter H is a schema, so is the way a doctor organises his or her knowledge about the human circulatory system. A schema doesn’t have to represent all the facts or concepts it links together. If it did, a schema involving thousands of facts would be so complex it wouldn’t be much help in showing how the facts were related. And in order to encompass all the different relationships between thousands of facts, a single schema for them would need to be very simple.

For example, a simple schema for chemistry would be that different chemicals are formed from different configurations of the sub-atomic ‘particles’ that make up atoms and configurations of atoms that form molecules. Thousands of facts can be fitted into that schema. In order to have a good understanding of chemistry, students would need to know about schemata other than just that simple one, and would need to know thousands of facts about chemistry before they would qualify as experts, but the simple schema plus a few examples would give them a basic understanding of what chemistry was about.

experts’ schemata Research into expertise (e.g. Chi et al, 1981) shows that experts don’t usually have one single schema for all the facts they know, but instead use different schemata for different aspects of their body of knowledge. Sometimes those schemata are explicitly linked, but sometimes they’re not. Sometimes they can’t be linked because no one knows how the linkage works yet.

chess experts

Daisy refers to research showing that expert chess players memorise thousands of different configurations of chess pieces (p.78). This is classic chunking; although in different chess sets specific pieces vary in appearance, their core visual features and the moves they can make are highly consistent, so frequently-encountered configurations of pieces are eventually treated by the brain as single units – the brain chunks the positions of the chess pieces in essentially the same way as it chunks letters into words.

De Groot’s work showed that chess experts initially identified the configurations of pieces that were possible as a next move, and then went through a process of eliminating the possibilities. The particular configuration of pieces on the board would activate several associated schemata involving possible next and subsequent moves.

So, each of the different configurations of chess pieces that are encountered so frequently they are chunked, has an underlying (simple) schema. Expert chess players then access more complex schemata for next and subsequent possible moves. Even if they have an underlying schema for chess as a whole, it doesn’t follow that they treat chess as a single unit or that they recall all possible configurations at once. Most people can reliably recognise thousands of faces and thousands of words and have schemata for organising them, but when thinking about faces or words, they don’t recall all faces or all words simultaneously. That would rapidly overload working memory.

Compared to most knowledge domains, chess is pretty simple. Chess expertise consists of memorising a large but limited number of configurations and having schemata that predict the likely outcomes from a selection of them. Because of the rules of chess, although lots of moves are possible, the possibilities are clearly defined and limited. Expertise in medicine, say, or history, is considerably more complex and less certain. A doctor might have many schemata for human biology; one for each of the skeletal, nervous, circulatory, respiratory and digestive systems, for cell metabolism, biochemistry and genetics etc. Not only is human biology more complex than chess, there’s also more uncertainty involved. Some of those schemata we’re pretty sure about, some we’re not so sure about and some we know very little about. There’s even more uncertainty involved in history. Evaluating evidence about how the human body works might be difficult, but the evidence itself is readily available in the form of human bodies. Historical evidence is often absent and likely to stay that way, which makes establishing facts and developing schemata more challenging.

To illustrate her point about schemata Daisy claims that learning couple of key facts about 150 historical events from 3000BC to the present, will form “the fundamental chronological schema that is the basis of all historical understanding” (p.20). Chronological sequencing could certainly form a simple schema for history, but you don’t need to know about many events in order to grasp that principle – two or three would suffice. Again, although this simple schema would give students a basic understanding of what history was about, in order to have a good understanding of history, students would need to know not only thousands of facts, but to develop many schemata about how those facts were linked before they would qualify as experts. This brings us on to the deep structure of knowledge, the subject of the next post.

Chi, MTH, Feltovich, PJ & Glaser, R (1981). Categorisation and Representation of Physics Problems by Experts and Novices, Cognitive Science, 5, 121-152
de Groot, AD (1978). Thought in Chess. Mouton.

Edited for clarity 8/1/17.

seven myths about education: a knowledge framework

In Seven Myths about Education Daisy Christodoulou refers to Bloom’s taxonomy of educational objectives as a metaphor that leads to two false conclusions; that skills are separate from knowledge and that knowledge is ‘somehow less worthy and important’ (p.21). Bloom’s taxonomy was developed in the 1950s as a way of systematising what students need to do with their knowledge. At the time, quite a lot was known about what people did with knowledge because they usually process it actively and explicitly. Quite a lot less was known about how people acquire knowledge, because much of that process is implicit; students usually ‘just learned’ – or they didn’t. Daisy’s book focuses on how students acquire knowledge, but her framework is an implicit one; she doesn’t link up the various stages of acquiring knowledge in an explicit formal model like Bloom’s. Although I think Daisy makes some valid points about the educational orthodoxy, some features of her model lead to conclusions that are open to question. In this post, I compare the model of cognition that Daisy describes with an established framework for analysing knowledge with origins outside the education sector.

a framework for knowledge

Researchers from a variety of disciplines have proposed frameworks involving levels of abstraction in relation to how knowledge is acquired and organised. The frameworks are remarkably similar. Although there are differences of opinion about terminology and how knowledge is organised at higher levels, there’s general agreement that knowledge is processed along the lines of the catchily named DIKW pyramid – DIKW stands for data, information, knowledge and wisdom. The Wikipedia entry gives you a feel for the areas of agreement and disagreement involved. In the pyramid, each level except the data level involves the extraction of information from the level below. I’ll start at the bottom.


As far as the brain is concerned, data don’t actually tell us anything except whether something is there or not. For computers, data are a series of 0s and 1s; for the brain data is largely in the form of sensory input – light, dark and colour, sounds, tactile sensations, etc.

It’s only when we spot patterns within data that the data can tell us anything. Information consists of patterns that enable us to identify changes, identify connections and make predictions. For computers, information involves detecting patterns in all the 0s and 1s. For the brain it involves detecting patterns in sensory input.

Knowledge has proved more difficult to define, but involves the organisation of information.

Although several researchers have suggested that knowledge is also organised at a meta-level, this hasn’t been extensively explored.

The processes involved in the lower levels of the hierarchy – data and information – are well-established thanks to both computer modelling and brain research. We know a fair bit about the knowledge level largely due to work on how experts and novices think, but how people organise knowledge at a meta-level isn’t so clear.

The key concept in this framework is information. Used in this context, ‘information’ tells you whether something has changed or not, whether two things are the same or not, and identifies patterns. The DIKW hierarchy is sometimes summarised as; information is information about data, knowledge is information about information, and wisdom is information about knowledge.

a simple theory of complex cognition

Daisy begins her exploration of cognitive psychology with a quote by John Anderson, from his paper ACT: A simple theory of complex cognition (p.20). Anderson’s paper tackles the mystique often attached to human intelligence when compared to that of other species. He demonstrates that it isn’t as sophisticated or as complex as it appears, but is derived from a simple underlying principle. He goes on to explain how people extract information from data, deduce production rules and make predictions about commonly occurring patterns, which suggests that the more examples of particular data the brain perceives, the more quickly and accurately it learns. He demonstrates the principle using examples from visual recognition, mathematical problem solving and prediction of word endings.

natural learning

What Anderson describes is how human beings learn naturally; the way brains automatically process any information that happens to come their way unless something interferes with that process. It’s the principle we use to recognise and categorise faces, places and things. It’s the one we use when we learn to talk, solve problems and associate cause with effect. Scattergrams provide a good example of how we extract information from data in this way.

Scatterplot of longitudinal measurements of total brain volume for males (N=475 scans, shown in dark blue) and females (N=354 scans, shown in red).  From Lenroot et al (2007).

Scatterplot of longitudinal measurements of total brain volume for
males (N=475 scans, shown in dark blue) and females (N=354 scans,
shown in red). From Lenroot et al (2007).

Although the image consists of a mass of dots and lines in two colours, we can see at a glance that the different coloured dots and lines form two clusters.

Note that I’m not making the same distinction that Daisy makes between ‘natural’ and ‘not natural’ learning (p.36). Anderson is describing the way the brain learns, by default, when it encounters data. Daisy, in contrast, claims that we learn things like spoken language without visible effort because language is ‘natural’ whereas we need to be taught ‘formally and explicitly’, inventions like the alphabet and numbers. That distinction, although frequently made, isn’t necessarily a valid one. It’s based on an assumption that the brain has evolved mechanisms to process some types of data e.g. to recognise faces and understand speech, but can’t have had time to evolve mechanisms to process recent inventions like writing and mathematics. This assumption about brain hardwiring is a contentious one, and the evidence about how brains learn (including the work that’s developed from Anderson’s theory) makes it look increasingly likely that it’s wrong. If formal and explicit instruction are necessary in order to learn man-made skills like writing and mathematics, it begs the question of how these skills were invented in the first place, and Anderson would not have been able to use mathematical problem-solving and word prediction as his examples of the underlying mechanism of human learning. The theory that the brain is hardwired to process some types of information but not others, and the theory that the same mechanism processes all information, both explain how people appear to learn some things automatically and ‘naturally’. Which theory is right (or whether both are right) is still the subject of intense debate. I’ll return to the second theory later when I discuss schemata.

data, information and chunking

Chunking is a core concept in Daisy’s model of cognition. Chunking occurs when the brain links together several bits of data it encounters frequently and treats them as a single item – groups of letters that frequently co-occur are chunked into words. Anderson’s paper is about the information processing involved in chunking. One of his examples is how the brain chunks the three lines that make up an upper case H. Although Anderson doesn’t make an explicit distinction between data and information, in his examples the three lines would be categorised as data in the DIKW framework, as would be the curves and lines that make up numerals. When the brain figures out the production rule for the configuration of the lines in the letter H, it’s extracting information from the data – spotting a pattern. Because the pattern is highly consistent – H is almost always written using this configuration of lines – the brain can chunk the configuration of lines into the single unit we call the letter H. The letters A and Z also consist of three lines, but have different production rules for their configurations. Anderson shows that chunking can also occur at a slightly higher level; letters (already chunked) can be chunked again into words that are processed as single units, and numerals (already chunked) can be chunked into numbers to which production rules can be applied to solve problems. Again, chunking can take place because the patterns of letters in the words, and the patterns of numerals in Anderson’s mathematical problems are highly consistent. Anderson calls these chunked units and production rules ‘units of knowledge’. He doesn’t use the same nomenclature as the DIKW model, but it’s clear from his model that initial chunking occurs at the data level and further chunking can occur at the information level.

The brain chunks data and low-level units of information automatically; evidence for this comes from research showing that babies begin to identify and categorise objects using visual features and categorise speech sounds using auditory features by about the age of 9 months (Younger, 2003). Chunking also occurs pre-consciously (e.g. Lamme 2003); we know that people are often aware of changes to a chunked unit like a face, a landscape or a piece of music, but don’t know what has changed – someone has shaved off their moustache, a tree has been felled, the song is a cover version with different instrumentation. In addition, research into visual and auditory processing shows that sensory information initially feeds forward in the brain; a lot of processing occurs before the information reaches the location of working memory in the frontal lobes. So at this level, what we are talking about is an automatic, usually pre-conscious process that we use by default.

knowledge – the organisation of information

Anderson’s paper was written in 1995 – twenty years ago – at about the time the DIKW framework was first proposed, which explains why he doesn’t used the same terminology. He calls the chunked units and production rules ‘units of knowledge’ rather than ‘units of information’ because they are the fundamental low-level units from which higher-level knowledge is formed.

Although Anderson’s model of information processing for low-level units still holds true, what has puzzled researchers in the intervening couple of decades is why that process doesn’t scale up. The way people process low-level ‘units of knowledge’ is logical and rational enough to be accurately modelled using computer software, but when handling large amounts of information, such as the concepts involved in day-to-day life, or trying to comprehend, apply, analyse, synthesise or evaluate it, the human brain goes a bit haywire. People (including experts) exhibit a number of errors and biases in their thinking. These aren’t just occasional idiosyncrasies – everybody shows the same errors and biases to varying extents. Since complex information isn’t inherently different to simple information – there’s just more of it – researchers suspected that the errors and biases were due to the wiring of the brain. Work on judgement and decision-making and on the biological mechanisms involved in processing information at higher levels has demonstrated that brains are indeed wired up differently to computers. The reason is that what has shaped the evolution of the human brain isn’t the need to produce logical, rational solutions to problems, but the need to survive, and overall quick-and-dirty information processing tends to result in higher survival rates than slow, precise processing.

What this means is that Anderson’s information processing principle can be applied directly to low-level units of information, but might not be directly applicable to the way people process information at a higher-level, the way they process facts, for example. Facts are the subject of the next post.

Anderson, J (1996) ACT: A simple theory of complex cognition, American Psychologist, 51, 355-365.
Lamme, VAF (2003) Why visual attention and awareness are different, TRENDS in Cognitive Sciences, 7, 12-18.
Lenroot,RK, Gogtay, N, Greenstein, DK, Molloy, E, Wallace, GL, Clasen, LS, Blumenthal JD, Lerch,J, Zijdenbos, AP, Evans, AC, Thompson, PM & Giedd, JN (2007). Sexual dimorphism of brain developmental trajectories during childhood and adolescence. NeuroImage, 36, 1065–1073.
Younger, B (2003). Parsing objects into categories: Infants’ perception and use of correlated attributes. In Rakison & Oakes (eds.) Early Category and Concept development: Making sense of the blooming, buzzing confusion, Oxford University Press.