Kieran Egan’s “The educated mind” 2

The second post in a two-part review of Kieran Egan’s book The Educated Mind: How Cognitive Tools Shape our Understanding.

For Egan, a key point in the historical development of understanding was the introduction by the Greeks of a fully alphabetic representation of language – it included symbols for vowels as well as consonants. He points out that being able to represent speech accurately in writing gives people a better understanding of how they use language and therefore of the concepts that language represents. Egan attributes the flowering of Greek reasoning and knowledge to their alphabet “from which all alphabetic systems are derived” (p.75).

This claim would be persuasive if it were accurate. But it isn’t. As far as we know, the Phoenicians – renowned traders – invented the first alphabetic representation of language. It was a consonantal alphabet that reflected the structure of Semitic languages and it spread through the Middle East. The Greeks adapted it, introducing symbols for vowels. This wasn’t a stroke of genius on their part – Semitic writing systems also used symbols for vowels where required for disambiguation – but a necessary addition because Greek is an Indo-European language with a syllabic structure. The script used by the Mycenaean civilisation that preceded the Greeks was a syllabic one.

“a distinctive kind of literate thinking”

Egan argues that this alphabet enabled the Greeks to develop “extended discursive writing” that “is not an external copy of a kind of thinking that goes on in the head; it represents a distinctive kind of literate thinking” (p.76). I agree that extended discursive writing changes thinking, but I’m not convinced that it’s distinctive nor that it results from literacy.

There’s been some discussion amongst teachers recently about the claim that committing facts to long-term memory mitigates the limitations of working memory. Thorough memorisation of information certainly helps – we can recall it quickly and easily when we need it – but we can still only juggle half-a-dozen items at a time in working memory. The pre-literate and semi-literate civilisations that preceded the Greeks relied on long-term memory for the storage and transmission of information because they didn’t have an alternative. But long-term memory has its own limitations in the form of errors, biases and decay. Even people who had memorisation down to a fine art were obliged to develop writing in order to have an accurate record of things that long-term memory isn’t good at handling, such as what’s in sealed sacks and jars and how old it is. Being able to represent spoken language in writing takes things a step further. Written language not only circumvents the weaknesses of long-term memory, it helps with the limitations of working memory too. Extended discursive writing can encompass thousands of facts, ideas and arguments that a speaker and a listener would find it impossible to keep track of in conversation. So extended discursive writing doesn’t represent “a distinctive kind of literate thinking” so much as significantly extending pre-literate thinking.

the Greek miracle

It’s true that the sudden arrival in Greece of “democracy, logic, philosophy, history, drama [and] reflective introspection… were explainable in large part as an implication of the development and spread of alphabetic literacy” (p.76). But although alphabetic literacy might be a necessary condition for the “Greek miracle”, it isn’t a sufficient one.

Like all the civilisations that had preceded it, the economy of the Greek city states was predominantly agricultural, although it also supported thriving industries in mining, metalwork, leatherwork and pottery. Over time agricultural communities had figured out more efficient ways of producing, storing and trading food. Communities learn from each other, so sooner or later, one of them would produce enough surplus food to free up some of its members to focus on thinking and problem-solving, and would have the means to make a permanent record of the thoughts and solutions that emerged. The Greeks used agricultural methods employed across the Middle East, adapted the Phoenician alphabet and slavery fuelled the Greek economy as it had previous civilisations. The literate Greeks were standing on the shoulders of pre-literate Middle Eastern giants.

The ability to make a permanent record of thoughts and solutions gave the next generation of thinkers and problem-solvers a head start and created the virtuous cycle of understanding that’s continued almost unabated to the present day. I say almost unabated, because there have been periods during which it’s been impossible for communities to support thinkers and problem-solvers; earthquakes, volcanic eruptions, drought, flood, disease, war and invasion have all had a devastating and long-term impact on food production and on the infrastructure that relies on it.

language, knowledge and understanding

Egan’s types of understanding – Somatic, Mythic, Romantic, Philosophic and Ironic – have descriptive validity; they do reflect the way understanding has developed historically, and the way it develops in children. But from a causal perspective, although those phases correlate with literacy they also correlate with the complexity of knowledge. As complexity of knowledge increases, so understanding shifts from binary to scalar to systematic to the exceptions to systems; binary classifications, for example, are characteristic of the way people, however literate they are, tend to categorise knowledge in a domain that’s new to them (e.g. Lewandowski et al, 2005).

Egan doesn’t just see literacy as an important factor in the development of understanding, he frames understanding in terms of literacy. What this means is that in Egan’s framework, knowledge (notably pre-verbal and non-verbal knowledge) has to get in line behind literacy when it comes to the development of understanding. It also means that Egan overlooks the key role of agriculture and trade in the development of writing systems and of the cultures that invented them. And that apprenticeship, for millennia widely used as a means of passing on knowledge, is considered only in relation to ‘aboriginal’ cultures (p.49). And that Somatic understanding is relegated to a few pages at the end of the chapter on the Ironic.

non-verbal knowledge

These are significant oversights. Non-verbal knowledge is a sine qua non for designers, artisans, architects, builders, farmers, engineers, mariners, surgeons, physiotherapists, artists, chefs, parfumiers, musicians – the list goes on and on. It’s true that much of the knowledge associated with these occupations is transmitted verbally, but much of it can’t be transmitted through language, but acquired only by looking, listening or doing. Jenny Uglow in The Lunar Men attributes the speed at which the industrial revolution took place not to literacy, but to the development of a way to reproduce technical drawings accurately.

Egan appears sceptical about practical people and practical things because when

those who see themselves as practical people engaging in practical things [who] tend not to place any value on acquiring the abstract languages framed to deal with an order than underlies surface diversity” are “powerful in government, education departments and legislatures, pressures mount for an increasingly down-to-earth, real-world curriculum. Abstractions and theories are seen as idle, ivory-tower indulgences removed from the gritty reality of sensible life.” (p.228)

We’re all familiar with the type of people Egan refers to, and I’d agree that the purpose of education isn’t simply to produce a workforce for industry. But there are other practical people engaging in practical things who are noticeable by their absence from this book; farmers, craftspeople, traders and engineers who are very interested in abstractions, theories and the order that underlies surface diversity. The importance of knowledge that’s difficult to verbalise has significant implications for the curriculum and for the traditional academic/vocational divide. Although there is clearly a difference between ‘abstractions and theories’ and their application, theory and application are interdependent; neither is more important than the other, something that policy-makers often find difficult to grasp.

Egan acknowledges that there’s a problem with emphasising the importance of non-verbal knowledge in circles that assume that language underpins understanding. As he points out “Much modernist and postmodernist theory is built on the assumption that human understanding is essentially languaged understanding” (p.166). Egan’s framework elbows aside language to make room for non-verbal knowledge, but it’s a vague, incoherent “ineffable” sort of non-verbal knowledge that’s best expressed linguistically through irony (p.170). It doesn’t appear to include the very coherent, concrete kind of non-verbal knowledge that enables us to grow food, build bridges or carry out heart-transplants.

the internal coherence of what’s out there

Clearly, bodies of knowledge transmitted from person to person via language will be shaped by language and by the thought-processes that produce it, so the knowledge transmitted won’t be 100% complete, objective or error-free. But a vast amount of knowledge refers to what’s out there, and what’s out there has an existence independent of our thought-processes and language. What’s out there also has an internally coherent structure that becomes clearer the more we learn about it, so over time our collective bodies of knowledge more accurately reflect what’s out there and become more internally coherent despite their incompleteness, subjectivity and errors.

The implication is that in education, the internal coherence of knowledge itself should play at least some part in shaping the curriculum. But because the driving force behind Egan’s framework is literacy rather than knowledge, the internal coherence of knowledge can’t get a word in edgeways. During the Romantic phase of children’s thinking, for example, Egan recommends introducing topics randomly to induce ‘wonder and awe’ (p.218), rather than introducing them systematically to help children make sense of the world. To me this doesn’t look very different from the “gradual extension from what is already familiar” (p.86) approach of which Egan is pretty critical. I thought the chapter on Philosophic understanding might have something to say about this but it’s about how people think about knowledge rather than the internal coherence of knowledge itself – not quite the same thing.

the cherries on the straw hat of society

The sociologist Jacques Ellul once described hippies as the cherries on the straw hat of society* meaning that they were in a position to be critical of society only because of the nature of the society of which they were critical. I think this also serves as an analogy for Egan’s educational framework. He’s free to construct an educational theory framed solely in terms of literacy only because of the non-literate knowledge of practical people like farmers, craftspeople, traders and engineers. That brings me back to my original agricultural analogy; wonder and awe, like apple blossom and the aroma of hops, might make might make our experience of education and of agriculture transcendent, but if it wasn’t for coherent bodies of non-verbal knowledge and potatoes, swedes and Brussels sprouts, we wouldn’t be in a position to appreciate transcendence at all.

References

Lewandowski G, Gutschow A, McCartney R, Sanders K, Shinners-Kennedy D (2005). What novice programmers don’t know. Proceedings of the first international workshop on computing education research, 1-12. ACM New York, NY.

Uglow, J (2003). The Lunar Men: The Friends who made the Future. Faber & Faber.

Note
*I can’t remember which of Ellul’s books this reference is from and can’t find it quoted anywhere. If anyone knows, I’d be grateful for the source.

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Kieran Egan’s “The educated mind” 1

I grew up in a small hamlet on the edge of the English Fens. The clay soil it was built on retains nutrients and moisture, so, well-drained, it provides an ideal medium for arable farming. Arable crops aren’t very romantic. The backdrop to my childhood wasn’t acres of lacy apple blossom in spring or aromatic hops in summer, although there were a few fields of waving golden wheat. I grew up amongst potatoes, swedes and Brussels sprouts. Not romantic at all, but the produce of East Anglia has long contributed to the UK population getting through the winter.

A few weeks ago on Twitter Tim Taylor (@imagineinquiry) asked me what I thought about Kieran Egan’s book The Educated Mind: How Cognitive Tools Shape our Understanding. This book is widely cited by teachers, so I read it. It reminded me of the sticky clay and root vegetables of my childhood – because sticky clay, root vegetables and other mundane essentials are noticeable by their absence from Egan’s educational and cultural framework. For Egan, minds aren’t grounded in the earth, but in language. To me the educational model he proposes is the equivalent of clouds of apple blossom and heady hops; breathtakingly beautiful and dizzying, but only if you’ve managed to get through the winter living on swedes and potatoes. My agricultural allusion isn’t just a simile.

recapitulation

Egan begins by claiming there’s a crisis in mass education systems in the West due to their being shaped by three fundamentally incompatible ideas; socialisation, Plato’s concept of reason and knowledge, and Rousseau’s focus on the fulfilment of individual potential. To resolve this inherent conflict, Egan proposes an alternative educational framework based on the concept of recapitulation. Recapitulation was a popular idea in the 19th century, fuelled by the theory of evolution and the discovery that during gestation human embryos go through phases that look remarkably like transformations from simple life forms to more complex ones. As Ernst Haeckel put it ‘ontogeny recapitulates phylogeny’.

The theory of recapitulation has been largely abandoned by biologists, but is still influential in other domains. Egan applies it to the intellectual tools – the sign systems that children first encounter in others and then internalise – that Vygotsky claimed shape our understanding of the world. Egan maps the historical ‘culturally accumulated complexity in language’ onto the ways that children’s understanding changes as they get older and proposes that what children are taught and the way they are taught should be shaped by five distinct, though not always separate, phases of understanding:

Somatic; pre-linguistic understanding
Mythic; binary opposites – good/bad, strong/weak, right/wrong
Romantic; transcendent qualities – heroism, bravery, wickedness
Philosophic; the principles underlying patterns in information
Ironic; being able to challenge philosophic principles – seeing alternatives.

At first glance Egan’s arguments appear persuasive but I think they have several fundamental weaknesses, all originating in flawed implicit assumptions. First, the crisis in education.

crisis? what crisis?

I can see why a fundamentally incoherent education system might run into difficulties, but Egan observes:

“…today we are puzzled by the schools’ difficulty in providing even the most rudimentary education to students”… “the costs of…social alienation, psychological rootlessness and ignorance of the world and possibilities of human experience within it, are incalculable and heartbreaking.” (p.1)

Wait a minute. There’s no doubt that Western education systems fail to provide even the most rudimentary education for some students, but those form a tiny minority. And although some school pupils could be described as socially alienated, psychologically rootless or ignorant of the world and possibilities of human experience within it, that description wouldn’t apply to many others. So what exactly is the crisis Egan refers to? The only clue I could find was on page 2 where he describes ‘the educational ineffectiveness of our schools’ as a ‘modern social puzzle’ and defines ‘modern’ as beginning with the ‘late nineteenth century development of mass schooling’.

To claim an educational system is in crisis, you have to compare it to something. Critics often make comparisons with other nations, with the best schools (depending on how you define ‘best’) or with what they think the education system should be like. Egan appears to fall into the last category, but to overlook the fact that prior to mass schooling children did well if they manage to learn to read and write at all, and that girls and children with disabilities often didn’t get any education at all.

Critics often miss a crucial point. Mass education systems, unlike specific schools, cater for entire populations, with all their genetic variation, socio-economic fluctuations, dysfunctional families, unexpected illnesses and disruptive life events. In a recent radio interview, Tony Little headmaster of Eton College was asked if he thought the very successful Eton model could be rolled out elsewhere. He pointed out, dryly, that Eton is a highly selective school, which might just be a factor in its academic success. One obvious reason for the perceived success of schools outside state systems is that those schools are not obliged to teach whichever children happen to live nearby. Even the best education system won’t be problem-free because life is complex and problems are inextricably woven into the fabric of life itself. I’m not suggesting that we tolerate bad schools or have low aspirations. What I am suggesting is that our expectations for mass education systems need to be realistic, not based on idealised speculation.

incompatible ideas

Speculation also comes into play with regard to the incompatibility of the three ideas Egan claims shape mass education in the West. They have certainly shaped education historically and you could see them as in tension. But the ideas are incompatible only if you believe that one idea should predominate or that the aims inherent in each idea can be perfectly met. There’s no reason why schools shouldn’t inculcate social values, teach reason and knowledge and develop individual potential. Indeed, it would be difficult for any school that taught reasoning and knowledge to avoid socialisation because of the nature of schools, and in developing reasoning and knowledge children would move towards realising their potential anyway.

If, as Egan argues, Western mass education systems have been ineffective since they started, his complaint appears to be rooted in assumptions about what the system should be like rather than in evidence about its actual potential. And as long as different constituencies have different opinions about the aims of the education system, someone somewhere will be calling ‘Crisis!’. That doesn’t mean there is one. But Egan believes there is, hence his new framework. The framework is based on the development of written language and its impact on thinking and understanding. For Egan, written language marked a crucial turning point in human history.

why write?

There’s no doubt that written language is an important factor in knowledge and understanding. Spoken language enables us to communicate ideas about things that aren’t right here right now. Written language enables us to communicate with people who aren’t right here right now. The increasing sophistication of written language as it developed from pictograms to syllabaries to alphabets enabled increasingly sophisticated ideas to be communicated. But the widely held belief that language is the determining factor when it comes to knowledge and understanding is open to question.

The earliest known examples of writing were not representations of language as such but records of agricultural products; noting whether it was wheat or barley in the sacks, wine or oil in the jars, when the produce was harvested and how many sacks and jars were stored where. Early writing consisted of pictograms (images of what the symbols represent) and ideograms (symbols for ideas). It was centuries before these were to develop into the alphabetic representations of language we’re familiar with today. To understand why it took so long, we need to put ourselves in the shoes (or sandals) of the early adopters of agriculture.

food is wealth

Farming provides a more reliable food supply than hunting and gathering. Farming allows food that’s surplus to requirements to be stored in case the next harvest is a bad one, or to be traded. Surplus food enables a community to support people who aren’t directly involved in food production; rulers, administrators, artisans, traders, scribes, teachers, a militia to defend its territory. The militia has other uses too. Conquering and enslaving neighbouring peoples has for millennia been a popular way of increasing food production in order to support a complex infrastructure.

But for surplus food to be turned into wealth, storage and trade are required. Storage and trade require written records and writing is labour-intensive. While scribes are being trained and are maintaining records they can’t do much farming; writing is costly. So communities that can’t predict when a series of bad harvests will next result in them living hand-to-mouth, will focus on writing about things that are difficult to remember – what’s in a sealed container, when it was harvested etc. They won’t need to keep records of how to grow food, look after animals, histories, myths, poems or general knowledge if that information can be transmitted reliably from person to person orally. It’s only when oral transmission stops being reliable that written language as distinct from record-keeping, starts to look like a good idea. And the more you trade, the more oral transmission gets to be a problem. Travellers might need detailed written descriptions of people, places and things. Builders and engineers using imported designs or materials might need precise instructions.

Spoken language wasn’t the only driving force behind the development of written language – economic and technical factors played a significant role. I don’t think Egan gives these factors sufficient weight in his account of the development of human understanding nor in his model for education, as I explain in the next post.

seven myths about education – what’s missing?

Old Andrew has raised a number of objections to my critique of Seven Myths about Education. In his most recent comment on my previous (and I had hoped, last) post about it, he says I should be able to easily identify evidence that shows ‘what in the cognitive psychology Daisy references won’t scale up’.

One response would be to provide a list of references showing step-by-step the problems that artificial intelligence researchers ran into. That would take me hours, if not days, because I would have to trawl through references I haven’t looked at for over 20 years. Most of them are not online anyway because of their age, which means Old Andrew would be unlikely to be able to access them.

What is more readily accessible is information about concepts that have emerged from those problems, for example; personal construct theory, schema theory, heuristics and biases, bounded rationality and indexing, connectionist models of cognition and neuroconstructivism. Unfortunately, none of the researchers says “incidentally, this means that students might not develop the right schemata when they commit facts to long-term memory” or “the implications for a curriculum derived from cultural references are obvious”, because they are researching cognition not education, and probably wouldn’t have anticipated anyone suggesting either of these ideas. Whether Old Andrew sees the relevance of these emergent issues or not is secondary, in my view, to how Daisy handles evidence in her book.

concepts and evidence

In the last section of her chapter on Myth 1, Daisy takes us through the concepts of the limited capacity of working memory and chunking. These are well-established, well-tested hypotheses and she cites evidence to support them.

concepts but no evidence

Daisy also appears to introduce two hypotheses of her own. The first is that “we can summon up the information from long-term memory to working memory without imposing a cognitive load” (p.19). The second is that the characteristics of chunking can be extrapolated to all facts, regardless of how complex or inconsistent they might be; “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 evidence she cites to support this extrapolation is Anderson’s paper – the one about simple, consistent information. I couldn’t find any other evidence cited to support either idea.

evidence but no concepts

Daisy does cite Frantz’s paper about Simon’s work on intuition. Two important concepts of Simon’s that Daisy doesn’t mention but Frantz does, are bounded rationality and the idea of indexing.

Bounded rationality refers to the fact that people can only make sense of the information they have. This supports Daisy’s premise that knowledge is necessary for understanding. But it also supports Freire’s complaint about which facts were being presented to Brazilian schoolchildren. Bounded rationality is also relevant to the idea of the breadth of a curriculum being determined by the frequency of cultural references. Simon used it to challenge economic and political theory.

Simon also pointed out that not only do experts have access to more information than novices do, they can access it more quickly because of their mental cross-indexing, ie the schemata that link relevant information. Rapid speed of access reduces cognitive load, but it doesn’t eliminate it. Chess experts can determine the best next move within seconds, but for most other experts, their knowledge is considerably more complex and less well-defined. A surgeon or an engineer is likely to take days rather than seconds to decide on the best procedure or design to resolve a difficult problem. That implies that quite a heavy cognitive load is involved.

Daisy does mention schemata but doesn’t go into detail about how they are formed or how they influence thinking and understanding. She refers to deep learning in passing but doesn’t tackle the issue Willingham raises about students’ problems with deep structure.

burden of proof

Old Andrew appears to be suggesting that I should assume that Daisy’s assertions are valid unless I can produce evidence to refute them. The burden of proof for a theory usually rests with the person making the claims, for obvious reasons. Daisy cites evidence to support some of her claims, but not all of them. She doesn’t evaluate that evidence by considering its reliability or validity or by taking into account contradictory evidence.

If Daisy had written a book about her musings on cognitive psychology and education, or about how findings from cognitive psychology had helped her teaching, I wouldn’t be writing this. But that’s not what she’s done. She’s used theory from one knowledge domain to challenge theory in another. That can be a very fruitful strategy; the application of game theory and ecological systems theory has transformed several fields. But it’s not helpful simply to take a few concepts out of context from one domain and apply them out of context to another domain.

The reason is that theoretical concepts aren’t free-standing; they are embedded in a conceptual framework. If you’re challenging theory with theory, you need to take a long hard look at both knowledge domains first to get an idea of where particular concepts fit in. You can’t just say “I’m going to apply the concepts of chunking and the limited capacity of working memory to education, but I shan’t bother with schema theory or bounded rationality or heuristics and biases because I don’t think they’re relevant.” Well, you can say that, but it’s not a helpful way to approach problems with learning, because all of these concepts are integral to human cognition. Students don’t leave some of them in the cloakroom when they come into class.

On top of that, the model for pedagogy and the curriculum that Daisy supports is currently influencing international educational policy. If the DfE considers the way evidence has been presented by Hirsch, Willingham and presumably Daisy, as ‘rigorous’, as Michael Gove clearly did, then we’re in trouble.

For Old Andrew’s benefit, I’ve listed some references. Most of them are about things that Daisy doesn’t mention. That’s the point.

references

Axelrod, R (1973). Schema Theory: An Information Processing Model of Perception and Cognition, The American Political Science Review, 67, 1248-1266.
Elman, J et al (1998). Rethinking Innateness: Connectionist Perspective on Development. MIT Press.
Frantz, R (2003). Herbert Simon. Artificial intelligence as a framework for understanding intuition, Journal of Economic Psychology, 24, 265–277.
Kahneman, D., Slovic, P & Tversky A (1982). Judgement under Uncertainty: Heuristics and Biases. Cambridge University Press.
Karmiloff-Smith, A (2009). Nativism Versus Neuroconstructivism: Rethinking the Study of
Developmental Disorders. Developmental Psychology, 45, 56–63.
Kelly, GA (1955). The Psychology of Personal Constructs. New York: Norton.

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).

facts

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.

schemata

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.

references
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: cognitive psychology & levels of abstraction

In her book Seven Myths about Education, Daisy Christodoulou claims that a certain set of ideas dominant in English education are misguided and presents evidence to support her claim. She says “Essentially, the evidence here is fairly straightforward and derives mostly from cognitive psychology”.

Whilst reading Daisy’s book, there were several points where I found it difficult to follow her argument despite the clarity of her writing style and the validity of the findings from cognitive psychology to which she appeals. It then occurred to me that Daisy and some of the writers she cites were using the same terminology to refer to different things, and different terminology to refer to the same thing. This is almost inevitable if you are drawing together ideas from different knowledge domains, but obviously definitions need be clarified or you end up with people misunderstanding each other.

In the next few posts, I want to compare the model of cognition that Daisy outlines with a framework for analysing knowledge that’s been proposed by researchers in several different fields. I’ve gone into some detail because of the need to clarify terms.

why cognitive psychology?

Cognitive psychology addresses the way people think, so has obvious implications for education. In Daisy’s view its findings challenge the assumptions implicit in her seven myths. In the final section of her chapter on myth 1, having recapped on what Rousseau, Dewey and Freire have to say, Daisy provides a brief introduction to cognitive psychology. Or at least to the interface between information theory and cognitive psychology in the 1960s and 70s that produced some important theoretical models of human cognition. Typically, researchers would look at how people perceived or remembered things or solved problems, infer a model that explained how the brain must have processed the information involved and would then test it by running computer simulations. Not only did this approach give some insights into how the brain worked, it also meant that software might be developed that could do some of the perceiving, remembering or problem-solving for us. At the time, there was a good deal of interest in expert systems – software that could mimic the way experts thought.

Much of the earlier work in cognitive psychology had involved the biology of the brain. Researchers knew that different parts of the brain specialised in processing different types of information, that the parts were connected by nerve fibres (neurons) activated by tiny electrical impulses. A major breakthrough came when they realised the brain wasn’t constructed like a railway network, with the nerve fibres connecting parts of the brain as a track connects stations, but in complex networks that were more like the veins in a leaf. Another breakthrough came when they realised information isn’t stored and retrieved in the form of millions of separate representations, like books in a vast library, but in the patterns of connections between the neurons. It’s like the way the same pixels on a computer monitor can display an infinite number of images, depending on which pixels are activated. A third breakthrough occurred when it was found that the brain doesn’t start off with all its neurons already connected – it creates and dissolves connections as it learns. So connections between facts and concepts aren’t just metaphorical, they are biological too.

Because it’s difficult to investigate functioning brains, computers offered a way of figuring out how information was being processed by the brain. Although this was a fruitful area of research in the 1960s and 70s, researchers kept running into difficulties. Problems arose because the human brain isn’t built like a computer; it’s more like a Heath Robinson contraption cobbled together from spare parts. It works after a fashion, and some parts of it are extremely efficient, but if you want understand how it works, you have get acquainted with its idiosyncrasies. The idiosyncrasies exist because the brain is a biological organ with all the quirky features that biological organs tend to have. Trying to figure out how it works from the way people use it has limitations; information about the biological structure and function of the brain is needed to explain why brains work in some rather odd ways.

Since the development of scanning techniques in the 1980s, the attention of cognitive science has shifted back towards the biological mechanisms involved. This doesn’t mean that the information theory approach is defunct – far from it – there’s been considerable interest in computational models of cognition and in cognitive errors and biases, for example. But the information theory and biological approaches are complementary; each approach makes more sense in the light of the other.

more than artificial intelligence

Daisy points out that “much of the modern research into intelligence was inspired and informed by research into artificial intelligence” (p.18). Yes, it was, but work on biological mechanisms, perception, attention and memory was going on simultaneously. Then “in the 1960s and 1970s researchers agreed on a basic mental model of cognition that has been refined and honed since then.” That’s one way of describing the sea change in cognitive science that’s happened since the introduction of scanning techniques, but it’s something of an understatement. Daisy then quotes Kirschner, Sweller and Clark; “ ‘working memory can be equated with consciousness’”. In a way it can, but facts and rules and digits are only a tiny fraction of what consciousness involves, though you wouldn’t know that to read Daisy’s account. Then there’s the nature of long-term memory. According to Daisy “when we try to solve any problem, we draw on all the knowledge that we have committed to long-term memory” (p.63). Yes, we do in a sense, but long-term memory is notoriously unreliable.

What Daisy didn’t say about cognitive psychology is as important as what she did say. Aside from all the cognitive research that wasn’t about artificial intelligence, Daisy fails to mention a model of working memory that’s dominated cognitive psychology for 40 years – the one proposed by Baddeley and Hitch in 1974. Recent research has shown that it’s an accurate representation of what happens in the brain. But despite being a leading authority on working memory, Baddeley gets only one mention in an endnote in Daisy’s book (the same ‘more technical’ reference that Willingham cites – also in an endnote) and isn’t mentioned at all in the Kirschner, Sweller and Clark paper. At the ResearchED conference in Birmingham in April this year, one teacher who’d given a presentation on memory told me he’d never heard of Baddeley. I’m drawing attention to this is not because have a special interest in Baddeley’s model, but because omitting his work from a body of evidence about working memory is a bit like discussing the structure of DNA without mentioning Crick and Watson’s double helix, or 19th century literature omitting Dickens. Also noticeable by her absence is Susan Gathercole, a professor of cognitive psychology at York, who researches working memory problems in children. Her work couldn’t be more relevant to education if it tried, but it’s not mentioned. Another missing name is Antonio Damasio, a neurologist who’s tackled the knotty problem of consciousness – highly relevant to working memory. Because of his background in biology, Damasio takes a strongly embodied view of consciousness; what we are aware of is affected by our physiology and emotions as well as our perceptions and memory. Daisy can’t write about everything, obviously, but it seemed odd to me that her model of cognition is drawn only from concepts central to one strand of one discipline at one period of time, not from an overview of the whole field. It was also odd that she cited secondary sources when work by people who have actually done the relevant research is readily accessible.

does this matter?

On her blog, Daisy sums up the evidence from cognitive psychology in three principles: “working memory is limited; long-term memory is powerful; and we remember what we think about”. When I’ve raised the issue of memory and cognition being more complex than Willingham’s explicitly ‘very simple’ model, teachers who support Daisy’s thesis have asked me if that makes any difference.

Other findings from cognitive psychology don’t make any difference to the three principles as they stand. Nor do they make it inappropriate for teachers to apply those principles, as they stand, to their teaching. But they do make a difference to the conclusions Daisy draws about facts, schemata and the curriculum. Whether they refute the myths or not depends on those conclusions.

a model of cognition

If I’ve understood correctly, Daisy is saying that working memory (WM) has limited capacity and limited duration, but long-term memory (LTM) has a much greater capacity and duration. If we pay attention to the information in WM, it’s stored permanently in LTM. The brain ‘chunks’ associated information in LTM, so that several smaller items can be retrieved into WM as one larger item, in effect increasing the capacity of WM. Daisy illustrates this by comparing the difficulty of recalling a string of 16 numerals

4871947503858604

with a string of 16 letters

the cat is on the mat

The numerals are difficult to recall, but the letters are easily recalled because our brains have already chunked those frequently encountered letter patterns into words, the capacity of WM is large enough to hold six words, and once the words are retrieved we can quickly decompose them into their component letters. So in Daisy’s model, memorising information increases the amount of information WM can handle.

I was with her so far. It was the conclusions that Daisy then goes on to draw about facts, schemata and the curriculum that puzzled me. The aha! moment came when I re-read her comments on Bloom’s taxonomy of educational objectives. Bloom adopts a concept that’s important in many fields, including information theory and cognitive psychology. It’s the concept of levels of abstraction, sometimes referred to as levels of granularity.

levels of abstraction

Levels of abstraction form an integral part of some knowledge domains. Chemists are familiar with thinking about their subject at the subatomic, atomic and molecular levels; biologists with thinking about a single organism at the molecular, cellular, organ, system or whole body level; geographers and sociologists with thinking about a population at the household, city or national level. It’s important to note three things about levels of abstraction:

First, the same fundamental entities are involved at different levels of abstraction. The subatomic ‘particles’ in a bowl of common salt are the same particles whether you’re observing their behaviour as subatomic particles, as atoms of sodium and chlorine or as molecules of sodium chloride. Cells are particular arrangements of chemicals, organs are particular arrangements of cells, and the circulatory or respiratory systems are particular arrangements of organs. The same people live in households, cities or nations.

Secondly, entities behave differently at different levels of abstraction. Molecules behave differently to their component atoms (think of the differences between sodium, chlorine and sodium chloride), the organs of the body behave differently to the cells they are built from, and nations behave differently to the populations of cities and households.

Thirdly, what happens at one level of abstraction determines what happens at the next level up. Sodium chloride has its properties because it’s formed from sodium and chlorine – if you replaced the sodium with potassium you’d get a chemical compound that tastes very different to salt. And if you replaced the cells in the heart with liver cells you wouldn’t have a heart, you’d have a liver. The behaviour of nations depends on how the population is made up.

Bloom’s taxonomy

The levels of abstraction Bloom uses in his taxonomy are (starting from the bottom) knowledge, comprehension, application, analysis, synthesis and evaluation. In her model of cognition Daisy refers to several levels of abstraction, although she doesn’t call them that and doesn’t clearly differentiate between them. That might be intentional. She describes Bloom’s taxonomy as a ‘metaphor’ and says it’s a misleading one because it implies that ‘the skills are somehow separate from knowledge’ and that ‘knowledge is somehow less worthy and important’ (p.21). Whether Bloom’s taxonomy is accurate or not, it looks as if Daisy’s perception of it as a ‘metaphor’, and her focus on the current popular emphasis on higher-level skills mean that she overlooks the core principle implicit in Bloom’s taxonomy that you can’t evaluate without synthesis, or synthesise without analysis or analyse without application or apply without comprehension. And you can’t do any of those things without knowledge. The various processes are described as ‘lower’ and ‘higher’ not because a value judgement is being made about their importance or because they involve different things entirely, but because the higher ones are derived from the lower ones in the taxonomy.

It’s possible, of course, that educational theorists have also got hold of the wrong end of the stick and have seen Bloom’s six levels of abstraction not as dependent on one another but as independent from each other. Daisy’s comments on Bloom explained why I’ve had some confusing conversations with teachers about ‘skills’. I’ve been using the term in a generic sense to denote facility in handling knowledge; the teachers have been using it in the narrow sense of specific higher-level skills required by the national curriculum.

Daisy appears to be saying that the relationship between knowledge and skills isn’t hierarchical. She provides two alternative ‘metaphors’; ED Hirsch’s scrambled egg and Joe Kirby’s double helix representing the dynamic, interactive relationship between knowledge and skills (p.21). I think Joe’s metaphor is infinitely better than Hirsch’s but it doesn’t take into account the different levels of abstraction of knowledge.

Bloom’s taxonomy is a framework for analysing educational objectives that are dependent on knowledge. In the next post, I look at a framework for analysing knowledge itself.