One of the real problems with improving education systems is that there tends not to be much agreement about what education is actually for. I’ve written about this issue before and have made clear my view, education should exist to make children cleverer. Clearly this in part depends on a belief that it is actually possible to make children cleverer , no matter their starting point.
So, what evidence is there that we can become more intelligent? Everyone knows about Carol Dweck’s immensely popular theory of the growth mindset; that we can become cleverer by believing we can become cleverer. This is certainly encouraging, but unfortunately I think it’s a bit more complicated than that. If wishes were fishes we’d all have salmon for supper. In this post I pointed out that Dweck is in danger of making her theory unfalsifiable and therefore unscientific.
It’s probably worth looking at the concept of intelligence in a little more detail. In 1971, the psychologist Raymond B Cattell broke intelligence into two separate components: fluid intelligence (Gf) and crystallised intelligence (Gc). Fluid intelligence is usually defined as the ability to reason and solve problems, whereas crystallised intelligence is the ability to access and utilise information stored in long-term memory.
It turns out that while they’re not the same thing, fluid intelligence correlates surprisingly well with working memory capacity. One of the most important things to understand about working memory is that no mater how clever you are, your capacity to pay attention to different ideas and facts at the same time is strictly limited. But, although everyone’s working memory is fragile, there’s no doubt that some people have greater capacities than others. This confers a real advantage and, if we’re interested in making children cleverer, it seems sensible to investigate how we can improve their working memories. Sadly, despite the claims of various brain-training gurus, it doesn’t actually appear possible to increase working memory capacity: what you get is what you get.
So, what about crystallised intelligence? This is a much more profitable avenue of enquiry. If part of the measure of general intelligence is the ability to access items stored in long-term memory, then the good news is that for all practical purposes there’s no real limit to the amount of stuff you can cram in to your brain. Of course what we know is subject to forgetting, but with practice we can improve our long-term stores of knowledge quite considerably. Other good news is that the ability to remember doesn’t seem to rely on fluid intelligence. No matter how poor you are at reasoning or problem solving, you can still commit facts to long term memory. And, the more you remember, the easier it becomes to remember additional items of knowledge.
The real benefits become clear when we understand that by improving crystallised intelligence we can ‘hack’ our fluid intelligence. That is to say, we can use what we’ve stored in long-term memory to compensate for deficits in working memory. When we store information in long-term memory it gets organised into schemas – interconnected webs – which mean that when we retrieve one item we also bring with it all the information we’ve stored in the same schema. So, for instance, if I know nothing about chess and try to remember the positions in the diagram below, the task becomes a formidable feat, and I’ll most probably give up.
However, if I know the starting set up of a chess board the task becomes much easier. Now I only have to track which pieces have moved or are missing. And if I were a very experienced chess player I might recognise this configuration as an opening called The Dutch Defence. In that case the entire board becomes just a single item in working memory.
There are two ways we can cheat the limitations of working memory:
- Extended networks of ideas and information (schemas) take up the same amount of space in working memory as single isolated facts so the more we know about a subject the more space we have to pay attention to novel ideas and interesting combinations of ideas.
- Through practice we can automatise various procedural knowledge so that it becomes background knowledge. When a skill or a fact has been automatised, we are no longer consciously aware of it and it takes up very little space in working memory allowing us to concentrate on things we haven’t yet mastered.
Much of teachers’ efforts in the current system is spent trying (and failing) to improve fluid intelligence by drilling students in ‘skills’ like essay writing. Unfortunately, writing essays isn’t really a skill that we ever automatise – in order to write thoughtfully we have to think. Worse, there are still schools and teachers who see themselves as best serving the needs of children and society by concentrating on generic skills like creativity, collaboration and communication. These skills are for the most part dependent on fluid intelligence and if we take this approach we guarantee that those with greater working memory capacities will do well and those who don’t will struggle and often fail.
If instead teachers prioritised encoding and retrieving knowledge then all children would see an increase in crystallised intelligence. Instead of practising skills that don’t really automatise we could spend time automatising the component parts and on factual recall. In this system, the entire bell curve is more likely to move to the right. Admittedly those with higher fluid intelligence would still do better but there wouldn’t the long tail of underachievement we currently have. Everyone would see themselves get cleverer as they passed through the system.
To me, this seems a worthy aim. I understand that some people may not agree with my analysis but I think it’s hard to dispute that making children cleverer is a good thing. If you think I’m wrong about the benefits of increasing crystallised intelligence then I’d be interested in reading what you would propose we do instead.
It is some time since I read Smart but Scattered by Peg Dawson and Richard Guare but there is something in executive skills development that may be of interest to developing or making the most of working memory.
I’ll take a look, but the scientific consensus is pretty clear that to the best of our current knowledge, working memory capacity can’t be improved across domains.
Having had a brief look (admittedly I haven’t bought the book) this appears to be reheated stuff on character drawing heavily on Walter Mischel’s research. Mischel’s correlational studies look exciting (although they contain several well documented methodological flaws) but even he doesn’t make any claims about increasing fluid intelligence.
David would you do me a favour please? I am trying to follow this post as well as read about Creativity – there appears some overlap in the models of intelligence you describe. Would it be possible for you to send me the composite version of your posts on this topic please – it just would make reading etc much easier and save me missing anything.
I’m not sure what you mean by “composite version”
Did you not do more than one post on this topic – or am I confused (just got back, been on holiday) ? I was just hoping to not have missed anything.
1 Robots, evolution and why schools shouldn’t worry about innate skills
2 Why what you teach matters
3 Making kids cleverer
4 Does ‘brain training’ increase intelligence?
5 What are ‘thinking skills’ and can we teach them?
6 What do we mean by ‘skills’?
Thanks David. I am always impressed with the depth of research you do on topics. I do find them a good starting point but have to admit sometimes I don’t get to the end of each one on the first read.
Are you saying the lack of focus on crystallised means we now need to concentrate to address the imbalance, or that there *should* be an imbalance toward crystallised over fluid?
I’m saying that as fluid intelligence cannot be increased, all efforts should be put into increasing crystallised intelligence, which can.
At present schools spend a portion of time doing arts and technology. This might go on with anyone from the age of 3 to the age of 18. Some schools 16-18 like the Brit School spend virtually their whole time doing the arts and same goes for some courses at degree level. We can list these activities as things like painting, dance, drama, pottery, music-making, working with materials – metal, wood, plastic, textiles,writing stories/poems/plays/film and TV scripts – and so on.
We could design education 3-18 that eliminated all of these activities entirely as they don’t seem to fit into your outline of what intelligence consists of. We could say, for example, that the time and place for them is ‘after school’, weekends and holidays. This would immediately raise questions of access, cost and with a consequence regarding who would end up doing them.
I wonder how you see these kinds of activities fitting in your ideal curriculum – or, as I suggest is possible – not at all.
Why do you assume that the activities you outline don’t fit my outline of what intelligence consists? In case it’s possible to learn more about the world and thereby increase crystallised intelligence. The more students’ Gc was increased in these areas, the better they’d get at them. I’m all for developing students’ knowledge of the arts so they’d fit very happily into my ideal curriculum.
Where did you see that I’ve written that ‘the activities’ I ‘outline’ ‘don’t fit’ your ‘outline’? I asked you ‘how’ (not if) you see these kinds of activities fitting your ideal curriculum. You’ve answered it in part by saying ‘knowledge of the arts’.
Two things occur to me here. For whatever reasons, one course which was specifically tuned into treating the arts as ‘knowledge’ – the History of Art A-level is being phased out. However, we can ask, does the word ‘knowledge’ really handle what it is we do when, say, I make a coil pot or dance? Even if it’s a necessary condition (debatable) is it a sufficient condition (even more debatable)?
As I say, it was an open-ended question. How do you see those ‘activities’ fitting into your ideal curriculum? What percentage of time, do you think, say for 4 year olds/ 11 year olds/ 15 year olds/ 17 year olds?
Yes, the word knowledge does “handle what it is we do when, say, I make a coil pot or dance”. This is procedural knowledge (or ‘know how’) and is precisely the sort of thing we can automate in order to cheat the limits of working memory.
Percentages? I’ve not thought that much about it – for the sake of argument let’s keep the percentages similar to those operating in a more traditional curriculum.
Anyhow, let’s get back to my question: if you object to my suggestions, what do you offer instead?
Where does it say I ‘objected to your suggestions’?
Oh, so you agree that a knowledge-rich curriculum is a good idea? Glad we got that sorted.
I was concerned as to whether the knowledge-rich curriculum included the arts. You have clarified that you think doing the arts is ‘knowledge-rich’. Sorted.
However, on your previous thread, I’ve raised the question of what environment is this knowledge-rich curriculum being enacted. In abstract, a knowledge-free curriculum sounds great. The question as always is; In what environment is it being (or to be) enacted? At present, and in the immediate future it’s in a selecting, segregating one which step by step excludes the knowledge from more and more pupils. That seems to me to be problematic. I hasten to say – not problematic for the wish, the desire, the intention in abstract of knowledge-richness, but in its actual enactment in the her and now and apparent immediate future.
I think I understand your concern, but all I can say is that I see this as the best alternative in an imperfect world. Do you think there’s a better alternative?
Thank you for your blog and for the invitation to react. I subscribe to your notion that schools should make pupils cleverer and share your belief that crystallized intelligence is ‘malleable’ given the right stimulation of intellect (on the basis of a rich curriculum/rich sources). There is much supporting evidence for this. The evidence I currently like most comes from Belgian researchers (Brysbaert et al., 2013) who found that vocabulary varies positively with age. People above 80 typically have much larger vocabularies than 20-year olds. Aging (having more experience with the world) tends to improve crystallized intelligence. As to the subject of IQ I am heavily influenced by the critical appraisal of the subject in Kaufman, 2013: Ungifted, chapter 2. In the end his criticism boils down to the question whether intelligence can and should be measured at all. Maybe ‘intelligence’ is just not the threshold concept that we have for a long time considered it to be, unless we regard it in a much more flexible and malleable way.
Where my opinions deviate from the ones expressed by you here, is regarding to your advice to stick to the practice of encoding and retrieving knowledge in order to automate factual recall. This seems to me to be at odds with your statement about the advantages of schemas. Simple encoding and retrieval practice does not lead to the creation of schemas. Therefore it seems important to think about the question how schema’s can be effectively created in education. My advice for educational practice would currently closely allign with the work of Carole L. Hamilton (2016). Identify threshold concepts, confront students with rich sources that exemplify these concepts and have them draw up and present their own theories, schemes and analogies. Guide them through quality questioning.
My understanding of the way schemas are developed is that they are enhanced and strengthened by multiple attempts to encode and retrieve in a variety of contexts. Your assertion that, “Simple encoding and retrieval practice does not lead to the creation of schemas” could do with some empirical support. Maybe the confusion comes from the word ‘simple’? I’m not sure what you think I mean, but I don’t think I’m suggesting anything simple. These blogs I’ve written might make my meaning clearer:
Liminality: https://www.learningspy.co.uk/learning/learning-is-liminal-2/
Threshold concepts: https://www.learningspy.co.uk/planning/using-threshold-concepts-to-think-about-curriculum-design/
Struggle: https://www.learningspy.co.uk/featured/what-might-be-a-good-proxy-for-learning/
Not come across Hamilton before. A quick trawl on google scholar hasn’t turned anything up. Do you have a link to her work? Thanks
To be clear, are you saying that we can make increase pupils’ academic ability by focusing on creating schemas which will be retained within crystallised intelligence, and when recalled will help pupils to tackle increasingly complex problems?
Yes, that’s exactly what I’m saying.
Makes sense to me. When we talk about teaching kids ‘thinking skills’, though’ I understand thinking skills to be schemas in which pupils learn the right questions to ask in order to critically analyse a text (for example).
However, in your next post, about brain training, you talk about thinking skills as a product of fluid intelligence, rather than crystallised (unless I’ve misunderstood?). Here’s the bit:
“That might be that except that some people want to argue there’s more to intelligence than working memory capacity and that teaching ‘thinking skills’ would be a productive way forward.”
I’d guess that my definition of ‘thinking skills’ is possibly just different from Jaeggi, so maybe I’m just getting muddled up about semantics here.
But I would be interested to know what you think about defining thinking skills as schemas, and whether you believe it’s worthwhile trying to teach such schemas and try to help pupils transfer them across the curriculum (particularly given the issues with transfer you’ve identified in one of your previous posts).
All interesting stuff!
Sorry Chris – that was probably confusing. In my next post I will specifically deal with ‘thinking skills’ and show them to be entirely different from fluid intelligence. Basically, my argument is that such ‘skills’ are in fact a body of knowledge – which form and are connected to other schemas – that increases crystallised intelligence.
Thanks, that clears that up. I agree – this is the way I’ve always seen thinking skills.
Michael, David, what do you think about the Michaela school, where (according to their blog) they don’t set, they claim not to differentiate, they apparently try to give everyone a knowledge-based curriculum, they do appear to teach music and art….
Love it. I wrote about my visit here: https://www.learningspy.co.uk/featured/michaela-school-route-one-schooling/
I prefer mackerel
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“If instead teachers prioritised encoding and retrieving knowledge then all children would see an increase in crystallised intelligence.”
That’s a bold claim. Has anyone tested this? Your analysis seems plausible, but it would seem foolish to act on your hypothesis without evidence that it actually makes a positive difference in a school environment.
Crystallised intelligence is the application of stored knowledge. It increases the more you know. This is a well established and relatively uncontroversial consensus position. That being the cse it would highly unlikely that teaching children more stuff wouldn’t help raise the crystalised intelligence which would, in turn,. raise their intelligence.
Sorry David – of course it’s not your job to test in practice the ideas you expound on your blog. I commented more for readers of your blog who might be tempted to act on your ideas without due reflection and diligence, and only because you are so highly influential. And of course my comments would apply to any proposed change in education.
The history of schooling is littered with things which ought to work in theory but which, in practice, end up either having unintended negative consequences or failing to deliver the intended improvements.
For example, it might turn out that “teaching children more stuff” actually resulted in their learning less stuff, because the way this “teaching children more stuff” was implemented led to lower pupil engagement. I’m not in any way suggesting that would happen, but it *might*, as might lots of other unintended negative consequences, or unintended positive consequences even!
So in answer to your question “what would you do instead?” – nothing, unless I had established that the change I was making had been shown to have the desired effect, either in school-based research by someone else or in a small-scale improvement project of my own.
I’m probably just stating the bleedin’ obvious!
Robert – I’m not proposing anything new or weird. Teaching stuff ought to be the essence of what happens in school and any proposal to the contrary should be considered weird. I really can’t see how teaching would lead to learning less unless you do it really badly but then, it’s possible to screw anything up. The burden of proof, I believe, is with anyone disagreeing with my contention,
I guess it depends on whether you wish to remain in the world of ideas about education or are actually interested in practical school improvement. To be interested in the former is entirely honourable – you present us with fascinating, illuminating facts about the nature or learning and intelligence and leave it up to others to do what they will with that knowledge.
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[…] can be broken into fluid intelligence and crystallised intelligence. Fluid intelligence is our raw reasoning power, and is, as far as we can tell, fixed; nothing […]
Hi David. This is a fascinating piece. Is there a difference between how quickly knowledge fades, between people. I’m assuming there is, but can it be measured? So that we know which children will need more retrieval practise than others. And is this an inherited difference, as with Fluid Intelligence, and is it something that we can address? I’m planning phonics interventions for next half term. Some children have received an intervention and are back up with everyone else, but I’m wondering how quickly they might slip back down without that additional input. I’d be interested in what has been written around this area. Thanks.
Current theories in memory suggest that knowledge doesn’t fade as such. Everything we know has both a storage strength – how well embedded an item in l0ng-term memory – and a retrieval strength – how easily we can recall it when desired. If we want to improve both of these indices, spaced retrieval practice seems to be the way to go.
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[…] But, much as I’m enjoying Caplan’s arguments, I’m pretty sure he’s wrong. What he misses is the effect of education on our minds. To be fair, he does address the finding that education seems to add to our intelligence. There’s good evidence that we get a boost of 3 IQ points for each year we spend in school. Caplan’s doesn’t dispute this, but he does point out that most of the evidence seems to show that these gains tend to fade out with time. He notes, with some triumphalism, that, “education raises ‘crystallised intelligence’ but not ‘fluid intelligence.” As regular readers will know, crystallised intelligence refers to our ability to apply what we know, whereas fluid intelligence is our ability to reason without prior knowledge. It should therefore be fairly unsurprising that education is only likely to improve our knowledge, and not our ability to do without it. I’ve argued previously that increasing crystallised intelligence is a sensible, pragmatic goal for education. […]
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