One of my concerns about the model of knowledge promoted by the Tiger Teachers is that it hasn’t been subjected to sufficient scrutiny. A couple of days ago on Twitter I said as much. Jonathan Porter, a teacher at the Michaela Community School, thought my criticism unfair because the school has invited critique by publishing a book and hosting two debating days. Another teacher recommended watching the debate between Guy Claxton and Daisy Christodoulou Sir Ken is right: traditional education kills creativity. She said it may not address my concerns about theory. She was right, it didn’t. But it did suggest a constructive way to extend the Tiger Teachers’ model of knowledge.
the debate
Guy, speaking for the motion and defending Sir Ken Robinson’s views, highlights the importance of schools developing students’ creativity, and answers the question ‘what is creativity?’ by referring to the findings of an OECD study; that creativity emerges from six factors – curiosity, determination, imagination, discipline, craftsmanship and collaboration. Daisy, opposing the motion, says that although she and Guy agree on the importance of creativity and its definition, they differ over the methods used in schools to develop it.
Daisy says Guy’s model involves students learning to be creative by practising being creative, which doesn’t make sense. It’s a valid point. Guy says knowledge is a necessary but not sufficient condition for developing creativity; other factors are involved. Another valid point. Both Daisy and Guy debate the motion but they approach it from very different perspectives, so they don’t actually rigorously test each other’s arguments.
Daisy’s model of creativity is a bottom-up one. Her starting point is how people form their knowledge and how that develops into creativity. Guy’s model, in contrast, is a top-down one; he points out that creativity isn’t a single thing, but emerges from several factors. In this post, I propose that Daisy and Guy are using the same model of creativity, but because Daisy’s focus is on one part and Guy’s on another, their arguments shoot straight past each other, and that in isolation, both perspectives are problematic.
Creativity is a complex construct, as Guy points out. A problem with his perspective is that the factors he found to be associated with creativity are themselves complex constructs. How does ‘curiosity’ manifest itself? Is it the same in everyone or does it vary from person to person? Are there multiple component factors associated with curiosity too? Can we ask the same questions about ‘imagination’? Daisy, in contrast, claims a central role for knowledge and deliberate practice. A problem with Daisy’s perspective is, as I’ve pointed out elsewhere, that her model of knowledge peters out when it comes to the complex cognition Guy refers to. With bit more information, Daisy and Guy could have done some joined-up thinking. To me, the two models look like the representation below, the grey words and arrows indicating concepts and connections referred to but not explained in detail.
cognition and expertise
If I’ve understood it correctly, Daisy’s model of creativity is essentially this: If knowledge is firmly embedded in long-term memory (LTM) via lots of deliberate practice and organised into schemas, it results in expertise. Experts can retrieve their knowledge from LTM instantly and can apply it flexibly. In short, creativity is a feature of expertise.
Daisy makes frequent references to research; what scientists think, half a century of research, what all the research has shown. She names names; Herb Simon, Anders Ericsson, Robert Bjork. She reports research showing that expert chess players, football players or musicians don’t practise whole games or entire musical works – they practise short sequences repeatedly until they’ve overlearned them. That’s what enables experts to be creative.
Daisy’s model of expertise is firmly rooted in an understanding of cognition that emerged from artificial intelligence (AI) research in the 1950s and 1960s. At the time, researchers were aware that human cognition was highly complex and often seemed illogical. Computer science offered an opportunity to find out more; by manipulating the data and rules fed into a computer, researchers could test different models of cognition that might explain how experts thought.
It was no good researchers starting with the most complex illogical thinking – because it was complex and illogical. It made more sense to begin with some simpler examples, which is why the AI researchers chose chess, sport and music as domains to explore. Expertise in these domains looks pretty complex, but the complexity has obvious limits because chess, sport and music have clear, explicit rules. There are thousands of ways you can configure chess pieces or football players and a ball during a game, but you can’t configure them any-old-how because chess and football have rules. Similarly, a musician can play a piece of music in many different ways, but they can’t play it any-old-how because then it wouldn’t be the same piece of music.
In chess, sport and music, experts have almost complete knowledge, clear explicit rules, and comparatively low levels of uncertainty. Expert geneticists, doctors, sociologists, politicians and historians, in contrast, often work with incomplete knowledge, many of the domain ‘rules’ are unknown, and uncertainty can be very high. In those circumstances, expertise involves more than simply overlearning a great many facts and applying them flexibly.
Daisy is right that expertise and creativity emerge from deliberate practice of short sequences – for those who play chess, sport or music. Chess, soccer and Beethoven’s piano concerto No. 5 haven’t changed much since the current rules were agreed and are unlikely to change much in future. But domains like medicine, economics and history still periodically undergo seismic shifts in the way whole areas of the domains are structured, as new knowledge comes to light.
This is the point at which Daisy’s and Guy’s models of creativity could be joined up. I’m not suggesting some woolly compromise between the two. What I am suggesting is that research that followed the early AI work offers the missing link.
I think the missing link is the schema. Daisy mentions schemata (or schemas if you prefer) but only in terms of arranging historical events chronologically. Joe Kirby in Battle Hymn of the Tiger Teachers also recognises that there can be an underlying schema in the way students are taught. But the Tiger Teachers don’t explore the idea of the schema in any detail.
schemas, schemata
A schema is the way people mentally organise their knowledge. Some schemata are standardised and widely used – such as the periodic table or multiplication tables. Others are shared by many people, but are a bit variable – such as the Linnaean taxonomy of living organisms or the right/left political divide. But because schemata are constructed from the knowledge and experience of the individual, some are quite idiosyncratic. Many teachers will be familiar with students all taught the same material in the same way, but developing rather different understandings of it.
There’s been a fair amount of research into schemata. The schema was first proposed as a psychological concept by Jean Piaget*. Frederic Bartlett carried out a series of experiments in the 1930s demonstrating that people use schemata, and in the heyday of AI the concept was explored further by, for example, David Rumelhart, Marvin Minsky and Robert Axelrod. It later extended into script theory (Roger Schank and Robert Abelson), and how people form prototypes and categories (e.g. Eleanor Rosch, George Lakoff). The schema might be the missing link between Daisy’s and Guy’s models of creativity, but both models stop before they get there. Here’s how the cognitive science research allows them to be joined up.
Last week I finally got round to reading Jerry Fodor’s book The Modularity of Mind, published in 1983. By that time, cognitive scientists had built up a substantial body of evidence related to cognitive architecture. Although the evidence itself was generally robust, what it was saying about the architecture was ambiguous. It appeared to indicate that cognitive processes were modular, with specific modules processing specific types of information e.g. visual or linguistic. It also indicated that some cognitive processes operated across the board, e.g. problem-solving or intelligence. The debate had tended to be rather polarised. What Fodor proposed was that cognition isn’t a case of either-or, but of both-and; that perceptual and linguistic processing is modular, but higher-level, more complex cognition that draws on modular information, is global. His prediction turned out to be pretty accurate, which is why Daisy’s and Guy’s models can be joined up.
Fodor was familiar enough with the evidence to know that he was very likely to be on the right track, but his model of cognition is a complex one, and he knew he could have been wrong about some bits of it. So he deliberately exposes his model to the criticism of cognitive scientists, philosophers and anyone else who cared to comment, because that’s how the scientific method works. A hypothesis is tested. People try to falsify it. If they can’t, then the hypothesis signposts a route worth exploring further. If they can, then researchers don’t need to waste any more time exploring a dead end.
joined-up thinking
Daisy’s model of creativity has emerged from a small sub-field of cognitive science – what AI researchers discovered about expertise in domains with clear, explicit rules. She doesn’t appear to see the need to explore schemata in detail because the schemata used in chess, sport and music are by definition highly codified and widely shared. That’s why the AI researchers chose them. The situation is different in the sciences, humanities and arts where schemata are of utmost importance, and differences between them can be the cause of significant conflict. Guy’s model originates in a very different sub-field of cognitive science – the application of high-level cognitive processes to education. Schemata are a crucial component; although Guy doesn’t explore them in this debate, his previous work indicates he’s very familiar with the concept.
Since the 1950s, cognitive science has exploded into a vast research field, encompassing everything from the dyes used to stain brain tissue, through the statistical analysis of brain scans, to the errors and biases that affect judgement and decision-making by experts. Obviously it isn’t necessary to know everything about cognitive science before you can apply it to teaching, but if you’re proposing a particular model of cognition, having an overview of the field and inviting critique of the model would help avoid unnecessary errors and disagreements. In this debate, I suggest schemata are noticeable by their absence.
*First use of schema as a psychological concept is widely attributed to Piaget, but I haven’t yet been able to find a reference.
logicalincrementalism 