Because learning is invisible, we can only hope to measure whether students are making progress by observing proxies. Most people now seem to agree that certain activities which routinely take place in lessons are, in the words of Robert Coe, ‘poor proxies for learning’. Rob has suggested that a better proxy might be ‘thinking hard’. This seemed sensible and, like many others, I’ve embraced the idea, but the harder I think about this the less sure I am. In this post I began considering of the limitations of think hard as a good proxy for learning but was still wedded to the idea that although learning can certainly occur without students having to ‘think hard’, thinking hard would still be likely to result in learning.
I started reading Daisy Christodoulou’s new book, Making Good Progress? today, and, as I’ve come to expect, she’s got me reconsidering things I had thought were almost certainly true. She cites this extract from Kirschner, Sweller and Clark’s paper, Why Minimal Guidance During Instruction Does Not Work:
Solving a problem requires problem-solving search and search must occur using our limited working memory. Problem-solving search is an inefficient way of altering long-term memory because its function is to find a problem solution, not alter long-term memory. Indeed, problem-solving search can function perfectly with no learning whatsoever (Sweller, 1988). Thus, problem-solving search overburdens limited working memory and requires working memory resources to be used for activities that are unrelated to learning. As a consequence, learners can engage in problem-solving activities for extended periods and learn almost nothing (Sweller et al., 1982). p. 80
This is something I’d read before but failed to realise its significance. As Daisy points out, “…it is possible for a pupil to be thinking hard and struggling but still not learning.” (p.42) If this is the case – and I think it must be – then ‘thinking hard’ may need to be consigned to the list of poor proxies for learning.
Previously, I’ve suggested that there might be other ‘good proxies for learning’ and that learning probably happens when students have to:
- concentrate on relevant examples and non-examples
- retrieve content they have previously been taught
- apply concepts to new examples
- engage in practice drills (which may involve repetition or formulas and procedures)
- answer questions without cues or prompts.
None of these things require much in the way of thinking especially hard. This matters because, our understanding of how learning occurs affects the approaches we use to teach and design a curriculum. This means we need to be really clear about the differences between learning and performance; just because students seem to be making progress in our lessons does not mean that they will retain what they’ve learned or that they will be able to effectively transfer it to other contexts. Whilst we want students to perform well in exams – and in life – this depends on creating effective ‘mental models’. Counter-intuitively, the kind of practice which seems to best build these models is not the same as expert performance. I still think struggle has a place in our efforts to design effective teaching sequences, but this must be undertaken with a lot of thought and a fair bit of caution. I’ve outlined these ideas in my post Struggle and success.
I’ve never bought the ‘struggle’ argument. When teaching any remedial reading and spelling, you may be almost certain that the pupil has struggled endlessly. When I assessed new pupils I always used to reassure them that if my teaching confused them, I wasn’t a very good teacher. Yes, I know we shouldn’t diss other teachers, but if you’ve ever been personally involved with a child who spent the first few years in school thinking that they were a dummy, I think you can forgive this. It certainly worked a treat, if for no other reason that it reminded me to plan lessons so that my pupils were almost always getting it right. Even when the pupil’s confidence is not in question, a wrong answer is counter-productive if our goal of achieving automaticity of response.
Of course, this is working at the bottom of Bloom’s Pyramid, and I’ll admit that things might just be a bit different if you are teaching material that is more challenging cognitively. But I’m not so sure. There’s something exhilarating about teaching that takes us through a cognitive jungle swiftly and surely, leaving us with insights, skills and understanding that seemed almost unsurmountable at first inspection. Building knowledge from the bottom up is relatively easy; once all the pitons are in place, it’s amazing how fast you can climb. Doing things the hard way just doesn’t make sense–I’d go so far as to argue that the ‘struggle’ concept is constructivist: it’s just a very poor way to implant the schemata we need to become effective thinkers and problem-solvers.
Yes, as Tom has suggested above, there is a huge amount of ground which can be gained by direct/explicit instruction at the lowest levels of Bloom’s taxonomy which really should be utilised.
However… isn’t there a Goldilocks Zone/ ZPD here where just the right amount of struggling/thinking hard transforms the relationship with what is being learned, and also changes the attitudes & resourcefulness of the person doing it in the process…?
I don’t think there’s any empirical support for the idea that having to struggle in one area makes you more persistent or resourceful in another.
Also, it may be right that some struggle might be helpful, but that would be towards the end of the process when you are already pretty competent.
I will play into all kinds of issues here with a personal anecdote, but I have no other way to raise the question, and I am posing a question rather than suggesting an educational approach.
When I was at school, I was very good at maths. I read a lot, was taught well, and learned a lot of Maths. I also sought out the most difficult maths problems I could find, and sat in front of them for hours until I had cracked them. I could sit in front of a problem for three hours and make no visible progress and come back to it the next day for another shot. What was I learning? Well, I was learning to solve difficult maths problems – I wasn’t learning a huge amount of maths, because I pretty much knew all the things I needed to know. I was also learning to be a mathematician – a person who had some mastery of the subject. I represented the UK at the International Mathematical Olympiad in my last year at school.
In the terms of the post, I was perhaps learning to deploy my working memory effectively in the face of an apparently intractable challenge.
To teach mathematics through enquiry and problem-solving seems to me to be misguided. That is how very clever and capable people in previous generations made the breakthroughs which provide us with everyday mathematical tools today. Mathematics represents centuries of intellectual progress of the highest order, and it is foolish to imagine that relatively unguided students will replicate that development over a few years. Teaching the results, and giving some insight into the development is more effective teaching of mathematics.
But in training mathematicians, people we need to make breakthroughs on problems as yet unsolved, we do need to develop skills and resilience and imagination appropriate to the task.
This is not, I would note, a plea for a skills-based curriculum, but it poses a question as to whether our curriculum should have, as part of its aim, the formation of new mathematicians as well as the teaching of mathematics. It would be a mistake to imagine every pupil will be a mathematician, but it also seems to me to be a mistake to run a school system on the implicit assumption that none will, or that it can all be done after they leave school.
And the point about learning to use working memory effectively may be important? If we feed pupils information in chunks they can digest, what happens when they encounter situations where information is out of control?
Good questions. Here’s what I reckon:
1. Should we aim to create mathematicians (or other experts)? Yes. But as KSC say, the practice of a profession is not the same as learning to practice the profession’. That’s not to say we’ve got the curriculum right – I’m pretty sure we haven’t! – but it does suggest that the best way to create mathematicians is to build domain knowledge by practising discrete skills.
2. Can we learn a generic skill of ‘using working memory effectively’? I think not. I’m fairly sure that using WM to think about problem solving in maths won’t transfer to using WM to solve problems in other domains.
3. What happens when students experience ‘real life’ complexity? Once sufficient expertise has developed we encounter the ‘expertise reversal effect’ in which people learn more from problem solving & enquiry then they do from practising discrete skills and worked examples. I’d suggest the best way to prepare students for life is to build up expertise through explicit instruction and purposeful practice.
Does that help?
“I think not. I’m fairly sure that using WM to think about problem solving in maths won’t transfer to using WM to solve problems in other domains.”
Why are you fairly sure. What empirical evidence is there that working memory is not working memory is not working memory?
I feel that you tend to reduce some of the most complex processes and biological interactions we know of to a few rules of thumb.
If one considers “learning” to be a problem, then surely problem solving is just the tool for effective learning. Dan Willingham told me once that he thought that higher order thinking was and excellent way to learn.
The problem I am coming up against with academics is that they often nail their colours to a particular mast, after which they will defend their position to the death.
One other thought. It is fairly obvious to most teachers with anything about them that minimally guided instruction ALA Kirschner is often (but not always) unlikely to be the most efficient way to acquire knowledge and understanding. Empirical evidence is vastly over rated most of the time methinks.
One question I have is what do you mean “proxy for learning”. Do you mean a proxy for the process or a proxy for the outcome or some other proxy. Just interested.
Thank you Mark – I think this very thoughtfully expands on what my previous comment was scratching at. I particularly like that your own personal experience of how certain things have worked can give you tacit personal evidence (which of course COULD be illusory) in the absence of large-scale empirical studies.
Whilst many advances remain restricted to the domain they are acquired in, I think that there are always other levels of us which are changed through the endeavour to make these advances come about, and which are then applicable in other areas (call it ‘character’). I’ve seen it in my own life particularly as I’ve developed my own ‘growth mindset’ from a teenage ‘fixed mindset’ about myself and what I’m capable of. That personal discovery had nothing to do with being persuaded by research, and has produced empirically measurable results as I’ve gone from mediocre O and A level grades to much better undergraduate and postgraduate degree results.
I’ve never been terribly impressed with the ‘growth mindset’ concept–after all, it does come from California. There are all sorts of reasons why children and adults become more motivated to learn. Two of the major elements which are largely neglected in most schools are competition and breaking learning down into manageable and well-defined components so that pupils understand exactly what they have to achieve.
But for most of us, it’s simply a matter of getting older: as you kick around the world, you learn a lot more, so it’s far more likely that new information will relate to your existing knowledge. You also become more aware of how much you don’t know. At the undergraduate level, the contrast between the motivation of mature students and those straight out of A-level is striking. In my experience, most of the former regard education mainly as a progression to a comfortable salary.
The point that I’m making though Tom is that I know exactly what scripts were going through my own head at certain points in my own personal education and life. I know full well that there were large academic areas as a child in which I simply wouldn’t try to do anything more than simply ‘get by without embarrassment’, because I was convinced that that was my natural position. I would openly describe myself as someone who couldn’t do languages for example, and – funnily enough – I couldn’t do them.
For a long time now I have understood the process of learning much better, and believed that I could learn to do anything better with focus and the right kind of practice, and – funnily enough – I have had far more success in far wider areas. Indeed, I’m almost appalled to think back to who I was at the age of 13, and the way I wasted significant school years after a promising Primary School start.
The labels and bandwagon might have come from California in the past 10 years, but the reality of the concept has been obvious to me for longer than that, and I’m not really interested in maintaining scepticism about this one until there have been sufficient randomised double-blind studies.
However… how the bandwagon gets implemented in schools is a whole different kettle of fish, and there might well have been nothing much that would have changed my outlook at that time!
We have very different concepts of what schooling is all about. Being rather old-fashioned, I think of it in terms of the teacher being entirely responsible for learning. Pupils may occasionally have the volition to go beyond the syllabus, but this only accounts for a tiny percentage of the academic knowledge that they learn. A good teacher not only teaches everything demanded by the syllabus, but constantly quizzes and tests to ensure that all pupils learn and retain what they’ve been taught. This kind of school, which is all too rare these days, does not rely upon Californian self-improvement gurus–it has no need to.
This attitude to teaching was reinforced when I was trained as an instructor in the TA. No one was daft enough to use discovery learning with grenades, General Purpose Machine Guns or the Light Anti-Tank weapon; rather, we understood that as instructors, the entire responsibility for learning rested upon our shoulders. In theory we could put a soldier on a charge if they refused to pay attention in class, but this was never remotely necessary. Soldiers, like pupils in school, respond eagerly to someone who has something worthwhile to teach and knows how to teach it–someone who will take the trouble to ensure that even the slowest student ‘gets it’.
As David suggests, as we acquire knowledge, we develop the capacity, ability and motivation to direct our own learning. However, in our knowledge-lite schools where even primary school pupils are expected to provide much of motivation for learning, pupils often fail to acquire that ‘critical mass’ of knowledge in academic subjects even at undergraduate level.
Tom – this is fascinating. You’ve mapped out a highly compelling version of what I’m now going to start calling a ‘partial reality’ approach. I’ve hesitated as to whether to respond to this with a blog, rather than mucking-up David’s comments section, but I’ll give it one go here anyway, and we can move-on to my own site if necessary.
At first I was surprised at the opening to your previous comment, as I myself am a fan of a knowledge intensive curriculum dominated by explicit instruction and with the teacher centre stage as ‘The Sage’.
However, it’s clear that there is a genuine chasm between us, as it seems that you believe that the what people themselves believe about their own capabilities, along with the environmentally and culturally sculpted incessant internal monologue which goes through their heads either doesn’t have any impact at all on what they will ACTUALLY learn from a situation, or that it can be so controlled by the person walking into the room as to be readily dismissed.
Basically, the kind of schooling which you describe will be very successful for certain teachers, teaching certain students certain things, in certain situations, and your Territorial Army example perfectly exemplifies this. Perhaps your definition of the purpose of ‘schooling’ is so confined as to ensure that this does work – but then one has to ask whether some of the term time allocated to schools should also be spent on ‘wider education’ (whatever that might involve – and wherever that might alternatively happen).
Reflecting on your T.A. example, I myself was an officer in the regular RAF straight from school, having been taught at a ‘traditional’ Grammar School, and having decided that academia wasn’t my thing. [I’d got a 6th Form Scholarship to train as a pilot, which was wonderfully beguiling – and I had been psychologically hammered by a very intensive cadet unit prior to that!]. In my time I have instructed both voluntary Air Cadets, AND conscripted ones (in a compulsory CCF unit), and I know full well that there is a massive difference in what it is possible to get out of the two kinds of cadets, because it turns out that something being ‘worthwhile’ is an entirely subjective point of view – no matter the skill of the instructor – and this translates to the vast majority of educational situations (as I’ve also discovered in almost two decades now as a teacher).
Things such as “Teach Like a Champion” (which seemingly you would ‘champion’, works with the extreme cases in as much as it convinces them that “You HAVE to get to College or your life is screwed!” Your T.A. tutees (volunteers) had already decided that what you were teaching was relatively worthwhile, which created huge psychological buy-in. Isn’t this obvious?
I’m sorry, but your comment overall smacks of an idealism which just doesn’t map onto the real breadth of the human world which I’ve experienced I’m afraid. People THINK, people predict, people interfere with what it is which is actually intended to be being learned within their heads – despite the most seemingly logical curriculum, being delivered in the most efficacious means (according to ONLY those principles which have been PROPERLY proven at the time – basically according to the best current Cognitive Psychology research.]
If you’ve ever had a tutee who said “Sorry I don’t want to do that because I know that I can’t”, and you’ve said “Just give it a go anyway”, or they’ve failed at something and you’ve said “tell you what, try it again this way” instead of “bad luck – you need to move onto something else”, then you’ve actually been doing the “Californian self-help guru” nonsense.
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