Teaching to make children cleverer – Part 2

In my last post I reviewed those aspects on intelligence which are likely to be most malleable by teachers. Briefly, research into individual differences suggests that intelligence is fairly stable and that environmental factors – parenting and teaching – seem to wear off over time. At the same time, research into social attitudes (the rise in IQ scores over that last century) clearly demonstrates that something really is changing and that these changes have real world significance. This present us with a paradox which perhaps can be explained by saying that g (the tendency of cognitive abilities in individuals to correlate with each other) is real, but that individual cognitive factors can be disproportionately affected by social attitudes and so increase with corresponding increases in other cognitive abilities.

By examining the different components of intelligence, my conclusion is that our best bet is likely to be increasing the quantity and quality of what students know. It’s an observable fact that we can only think about things we know, and that in the real world, all creativity, problem solving and critical thinking is sharply increased by knowing more. As teachers this should give us some confidence that increasing intelligence is both likely to work (it’s easy to see that if you teach something to students you can then check whether they know it) and likely to be effective (once they know something you can then see the effects of applying this knowledge).

This suggests we should think carefully about what to teach – clearly some types of knowledge is likely to be more beneficial than others – but does it also suggest anything about how we should teach?

If the goal of teaching is learning, then we need to have a workable description of learning. Kirschner et al have famously told us that, “If nothing has changed in long-term memory, then nothing has been learned.” From this we could argue that whatever else it is, learning is synonymous with changes in long-term memory. These changes in long-term memory are organised into schema. A schema is an interconnected ‘chunk’ of knowledge that can be drawn into consciousness and thought about. Therefore, the goal of teaching is to create these changes and facilitate the acquisition of ‘chunkier’ knowledge.

Broadly speaking, teaching tends to follow two approaches:

  1. Activities designed to get students to remember information.
  2. Activities designed to get students to solve problems.

Although they might prioritise one or the other, most teachers will do a bit of both. There’s nothing wrong with this per se, but the order in which you engage in these approaches might be very important.

It’s well understood that all human being have a limited capacity for paying attention to information and that we can only think about four ‘chunks’ of information at any given time. Although we are not conscious of organising new information into schemas, we only tend to remember what we spend time thinking about. From this perspective it seems reasonable to suggest that either of our two approaches could result in these schematic changes to long-term memory.

Sadly, this seems not to be the case. Working memory limitations restrict how much of an experience reaches our long-term memory and the capacity we need to handle information may leave little space for schema acquisition, even if a problem is solved:

Solving a problem requires problem-solving search and search must occur using our limited working memory 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. [my emphasis]

Kirschner, Sweller & Clark (2006) p. 80

What this tells us is that students can concentrate on solving problems, and they can concentrate on tasks which contribute to developing their schema, but if the task is challenging they are unlikely to manage both. (I wrote about an example of this phenomenon here.)

So, while problem solving activities certainly have their place in strengthening schematic connections once a schema has been acquired, they are a poor way of helping students remember what they need to know in order to solve problems.

Ignoring this tendency is likely to result in a widening of the gap between advantaged and disadvantaged students. Those children who come to school with either an innate advantage (greater mental acuity, faster speed of processing) or those who come from a background where they have been exposed to more useful knowledge of the world already have a serious advantage over their less fortunate peers. If we give children problems to solve without having first spent time on activities designed to help everyone remember the information needed to solve the problems we will unwittingly be privileging the privileged.

To this end, I advocate an approach to teaching best characterised as ‘success followed by struggle‘. This is a social justice issue. I’m sure everyone involved in education has good intentions, but we all know what the road to hell is paved with. Ignoring these findings perpetuates injustice and condemns the least advantaged in society to lives of continued disadvantage.

In my next post I will review what we know about the types of knowledge that we could focus on to ensure that our efforts to make children cleverer result in something with real world significance.

29 Responses to Teaching to make children cleverer – Part 2

  1. James says:

    I enjoyed this David, it seems to me to be very linked to the idea of expert reversal – where collaborative, discovery approaches are excellent for experts but poor for novices – would you make that link? Could be useful in reconciling progressive and traditional approaches.

  2. Matt says:

    Thanks, David, always an interesting read!

    As someone who researches how children use analogies to form schemas and analogical reasoning to problem solve, there are few points you’ve made that raise questions in my mind. I’d love to discuss them with you in more detail if you have the time.

    First, your argument that problem-solving overloads working memory stands true if all of the information needed is only being represented in working memory, particularly if this is new information as James mentions. However, if some/all of the information needed is ‘offloaded’ into images, text, diagrams and other resources then this reduces the load on working memory. The argument that Kirschner et. al. make when stating “learners can engage in problem-solving activities for extended periods and learn almost nothing” seems more the case of developmentally inappropriate problem-solving tasks overloading working memory, rather than problem-solving tasks intrinsically overloading working memory.

    The second point is to do with schemas involved in problem-solving. Are you assuming that the only schemas needed for and created through problem-solving are ‘knowledge-based’ conceptual schemas? I think I’d argue that this may not be the case. The concept of ‘schema’ is a very useful but still a completely theoretical construct. There is no hard and fast consensus regarding their composition, different types, functions and mechanisms of growth. Are they formed from abstract symbols and syntax? Sensorimotor representations? Both? Do we have procedural schemas for thought as well as action? Are these different from ‘knowledge-based’ conceptual schemas? These are all as yet to be empirically answered questions, with the outcome of these questions having implications for the arguments you are presenting.

    For example, how children solve problems through analogical reasoning and how they develop this process is not well understood. It is far from clear what knowledge schemas are needed, if procedural schemas are necessary, what cognitive mechanisms are involved, how all this works with working memory and attention. Part of the reason why there is still no consensus is that the mechanisms involved are likely to rest on schemas and there is no consensus on how schemas are formed/represented! It is likely that this is also the case for other forms of reasoning as well.

    I would argue that working through problem-solving tasks develops procedural schemas for manipulating ‘knowledge-based’ schemas. I.e. just as we learn procedural schemas for the sequenced manipulation of objects and information in the external world to achieve a task (e.g. riding a bike or writing an essay), we learn procedural schemas for the sequenced manipulation of thought to achieve a cognitive task (e.g. problem-solving and reasoning), and these are learnt through problem-solving tasks that lay down procedural schemas, not just through the accretion of ‘knowledge-based’ conceptual schemas. As such, working through problem-solving tasks generates procedural knowledge schemas that relate to the sequence of thought that are potentially distinct from conceptual knowledge-based schemas, if that makes sense?

    Like I say, would love to discuss in more detail with you at some point if you have the time!

    • manyanaed says:

      Matt. Interesting comments. What is your evidence for us creating “procedural schemas for manipulating ‘knowledge-based’ schemas.”? That seems to be getting close to a generic skill which some call critical thinking? We can link via Twitter. @manyanaed

      • Matt says:

        Untested hypothesis at the moment but it stands up theoretically (I can explain in a bit more detail later if you’re interested). I’m hoping to test it as part of my PhD.

    • David Didau says:

      Hi Matt

      Let me see if I’ve got this straight: you say
      1) We can design problem solving tasks that don’t overload working memory by adding lots of additional details such as ” images, text, diagrams and other resources”.
      2) Schema might not be simply ‘knowledge-based’ but also contain other things such as “abstract symbols and syntax” and “Sensorimotor representations”.
      3) Contrary to my arguments, you think problem solving actually help us acquire schema.

      If I’m correct that this is what you mean, then allow to deal with each point in turn:

      1) If we design problem solving task with “some/all of the information needed is ‘offloaded’ into images, text, diagrams and other resources” how would this reduce cognitive load? This would require a student to work o the problem whilst simultaneously trying to refer to all the offloaded information. This seems a strategy more or less guaranteed to overload working memory.
      2) Why would you conclude that “abstract symbols and syntax” and “Sensorimotor representations” are not knowledge? You have to know these things to either think with or about them. I think your conception of knowledge may be too rooted in propositional knowledge. I think it is more than that: http://www.learningspy.co.uk/featured/if-not-knowledge-what/
      3) This claims seems contrary to all the evidence I’ve seen – can you point me in the direction of anything that supports this idea?

      Thanks, David

      • Matt says:

        Thanks for the response! Will get back to you shortly : )

        • Michael Pye says:

          Merriam-Websters definition of knowledge

          a (1) : the fact or condition of knowing something with familiarity gained through experience or association (2) : acquaintance with or understanding of a science, art, or technique
          b (1) : the fact or condition of being aware of something (2) : the range of one’s information or understanding answered to the best of my knowledge
          c : the circumstance or condition of apprehending truth or fact through reasoning : cognition
          d : the fact or condition of having information or of being learned a person of unusual knowledge

          In of itself this contains problem-solving and so called factual learning.
          Matt your idea of knowledge and problem solving (schema) may be very different to Davids or mine.

          David would you mind telling me which of these you consider more accurate.

          Problem solving and thinking skills exist, but they have poor transfer to other domains. Focusing on key ideas/procedures or facts within domains will develop these skills more effectively both within each domain and even across domains, though transfer will still be poor.

          Problem solving and thinking skills do not really exist. They are an illusion created by mastery of context specific skills which is were we should focus.
          Problem solving is really just familiarity with lots of specific examples as well as cross-bridging of ideas within a domain.

          Feel free to write your own. Tried to disguise my own preference.

          • Matt says:

            Thanks, Michael, that’s interesting.

            I think I would agree with aspects of all of those views. See if the below makes sense. What’s your view? (I suspect you’re right re our differences in views of knowledge/schema : )

            I think my view would be that my view would be that problem solving skills do exist and can be developed but they develop within a specific domain (as procedural knowledge) and their use is initially limited to that domain.

            These initially domain-specific problem-solving procedures become more transferable as factual knowledge develops across domains. Once analogous links are formed between the factual knowledge in different domains, the factual knowledge from one domain can be ‘plugged into’ the problem-solving procedures developed in a different domain. I’d say they probably never become ‘fully’ domain-general in the truest sense of the term, but their utility as transferable procedures increases as factual knowledge across domains increases, and can potentially stretch quite far (giving the illusion of domain-general skills?).

            As a side note, I do think children can develop these procedures to some degree without instruction, just as they can develop factual knowledge to some degree without instruction, just neither will develop to the level of sophistication and flexibility that can be achieved through teaching.

          • David Didau says:

            I pretty much agree with all of this. But to respond to your side note: some children can develop some procedures to some degree without explicit instruction. But, explicit or, fully guided instruction makes it more likely that more children will more develop more of these procedures to a greater degree. Or at least, that’s what the evidence points towards.

        • Matt says:

          And thanks for the link, David, looks interesting, will have a read.

          • Michael Pye says:

            Sorry to be a pain David I was trying to ask if you believe problem solving skills exist or if you think it is simply an inefficient way of approaching teaching.

            Greg Ashman seems to believe the first and I was wondering if you agreed as I find it a hard idea to swallow. Despite this I agree with the argument that knowledge teaching is more powerful. (It seems obvious to me that they exist as we can discuss the shared concept, the fact they are nebulous does not discount this as it would also invalidate nearly every abstract concept I have) If I tried arguing problem solving skills are not real my colleagues would act as If I had told them the sky is pink with pokadots. I usually argue relative efficiency and focus instead.

            I remember your post on knowledge and found it very interesting, unfortunately it was really your position on problem solving skills I was looking for. My fault for being to obtuse, I should not post when I am sleep deprived. The question has just been bugging me for a while and I would appreciate your insight.

          • Matt says:

            @David. Yes, agree with your amendments, and that explicit instruction is the best way when learning new procedures. Great discussion, thanks : )

      • Matt says:

        Thanks for taking the time over your detailed response, David, very interesting discussing this with you : ) I’ll respond over a few posts.

        1) If we design problem solving task with “some/all of the information needed is ‘offloaded’ into images, text, diagrams and other resources” how would this reduce cognitive load? This would require a student to work o the problem whilst simultaneously trying to refer to all the offloaded information. This seems a strategy more or less guaranteed to overload working memory.

        I’m not sure I follow your thinking there. I would argue that externalising information that you can refer to during the problem when you need to means you don’t have to hold it in working memory the whole time.

        For example, if you had the problem of scheduling an appointment, holding your day’s/week’s schedule in working memory and searching through it would seem to place significantly more load on working memory than holding your day’s/week’s schedule in a physical resource such as a calendar and searching through that instead. In the later, you only need to hold in working memory the goal of ‘find the an appropriate space’, where as in to former you need hold the same goal in working memory, and all of your appointments. Surely that places more load on working memory?

        The same with if you presented the problem below to a child verbally (e.g. children have all the information in working memory) or by text (e.g. information is held in a physical resource and different aspects of it are referred to as they work through stages of the problem). Which is going to place more load on working memory?

        Penny’s favourite pizza restaurant offers 6 toppings: ham, onions, mushrooms, pineapple, tomato and peppers. Penny orders a pizza with ham and pineapple. Unfortunately the server only writes down that she wants 2 toppings but doesn’t write down what they are. The cook decides to pick two toppings at random. What is the probability that Penny will get the pizza she ordered?

        • Matt says:

          2) Why would you conclude that “abstract symbols and syntax” and “Sensorimotor representations” are not knowledge? You have to know these things to either think with or about them. I think your conception of knowledge may be too rooted in propositional knowledge. I think it is more than that: http://www.learningspy.co.uk/featured/if-not-knowledge-what/

          I don’t conclude that – apologies if it came across that way. They are the extreme ends of two different theories of how schemas are represented in the brain. Abstract symbols and syntax at one end (e.g. Chomsky, Pinker et al) and more contemporary theories at the other – often know as grounded (or embodied) cognition (good review here: http://matt.colorado.edu/teaching/highcog/readings/b8.pdf) with various shades in between.

          These theories propose radically different views of how schema are represented, develop, what functions they do, different types and how they would support/constrain cognitive tasks. There is no agreed upon consensus which is right if any? (Although many would strongly argue one way or the other.)

          Have you heard the quote the great “all models are wrong, some are useful”? The notion that knowledge is organised and represented as schemas is a very powerful and useful model, but it’s use only extends so far given the ambiguity regarding what schemas actually are/do.

          • Matt says:

            3) This claims seems contrary to all the evidence I’ve seen – can you point me in the direction of anything that supports this idea?

            So this all fits within a cognitive development theory called ‘neuroconstructivism’. It argues against a view of cognitive development where children are born with lots of innate capacities (e.g. Chomsky, Pinker etc.) and that representations (what we have been calling schema) are created for cognitive processing, the nature of which depended on the environment the child develops in. There is a precis to the theory that also includes lots of peer commentary here (http://www.bbk.ac.uk/psychology/dnl/personalpages/BBSprecis.pdf). Dependent on knowledge of psychology in may/may not be a little technical, but happy to further discuss the ideas further. A thing to bear in mind is what we have been referring to as schema, the authors refer to as representations.

            I’ll try and pull it all together with a couple of examples:

            My own work looks the development of problem solving through analogical reasoning. A test commonly used to measure children’s analogical reasoning ability are classical a:b::c:d problems such as ‘cat is to kitten and dog is to ???’.

            If you presented 6 year old children with such a problem verbally (in more age appropriate language obviously) they would struggle even though they have all the necessary knowledge of [cat] [kitten] [kitten is the offspring of a cat] [dog] [puppy] [puppy is the offspring of a dog]. Why do they struggle when they have the required conceptual knowledge?

            If you presented the same problem to 6yo children as illustrations and also gave them multiple choice answers, thus reducing reducing the demand on working memory by, their performance improves. However, they still struggle and successfully complete similar problems around 50% / 60% of the time. Children don’t achieve adult like competence on this type of problem until into adolescence.

            So… Question:

            If you further scaffolded the problem by providing a diagram of a procedure that they need work through whilst they are completing the problems (something like (a) workout the relationship between cat and kitten, (b) systematically go through check ‘dog’ with each of the multiple choice options to see if the relationship is the same, (c) some kind of evaluation), do you think they would improve further? I would be very surprised if they didn’t.

            If they do improve, what is that scaffolding providing? I’d argue that it is scaffolding their still relatively impoverished procedural schemas for problem solving by analogical reasoning.

            One last example:

            If you have the problem of planning the tasks involved in a project, one way to do it is to organising the tasks hierarchically into main tasks, sub-tasks, sub-sub-tasks etc. Where does that knowledge come from to do that? The procedures involved in such a tasks have to be learnt and represented in schema.

          • David Didau says:

            OK. If this is what you mean by problem solving that we’ve been talking past each other. This is what I would call “fully guided instruction” and would agree that it is the best way to acquire and develop schema.

          • David Didau says:

            Yes, *of course* schemas are just a model but they seem to adequately described something we cannot introspect about: long term memory. There for, useful. My view is that a schema is made up of propositional knowledge, procedural knowledge and tacit knowledge. They are spun of facts, experiences, feelings, visual impressions, sounds, any pretty much anything that it is possible to know. Knowledge is not just the declarative knowledge that you think about it is also the much vaster realm of non-declarative knowledge: that which you think *with*.

        • David Didau says:

          I think you’re mistaken here. Anything external you have to refer to when trying to solve a problem occupies working memory, leaving less space to work on the problem. The only real way around this is to have internalised the information by storing it in longterm memory. You’re correct to say that giving a student an external scaffold as well as verbal instruction will place *less* cognitive load on them, but this should be a mere stepping stone. Over time all such external scaffolds should be withdrawn and internalised to prevent dependency. So, what you might refer to as “guided discovery” I would call worked examples and carefully sequenced modelling & scaffolding.

          • manyanaed says:

            At some point, the information that has been committed to paper has to be brought back into working memory so the positive impact is this ‘external storage’ is temporary until the information stored on paper becomes part of LTM.

          • Matt says:

            Ah… ok… very interesting. I’m not sure I fully understand the distinction between fully guided instruction and other type of problem solving? Any examples of problems that would not involve a procedure?

            Gotya, so are you of the view that children are born with an innate propositional syntax al la Chomsky/Pinker that guides thinking? I think this may be the crux in the difference of our views. I’m more inclined to believe that this is learnt, inline with the theories I linked to above, and that the ‘syntax’ of thought develops in what I would say is a procedural schema for thinking.

            I think we’re reaching some agreement with the scaffolding : )

          • David Didau says:

            I don’t believe children are “born with an innate propositional syntax” (and I’m fairly sure from reading The Blank Slate that Pinker doesn’t think this either) But I do think we’ve evolved capacities to very quickly acquire certain sorts of species-wide adaptive modules very quickly from our environment, whereas other forms of cultural learning are much less easy for us to learn. here’s an explanation: http://www.learningspy.co.uk/psychology/can-learn-evolutionary-psychology/

  3. manyanaed says:

    The individual steps may themselves be a reduced cognitive load but is there an increase when one needs to put the parts together.

    • David Didau says:

      Is that a question for me?

      Putting them together is – or should – internalising them. It’s the difference between following a recipe and being able to look in fridge and work out what you can cook from memory. The latter definitely has the least cognitive load.

    • Matt says:

      I’m not sure you need to put it all back together in the end, you just need to have the answer. Perhaps we’re talking cross purposes, but if you take the maths example I gave above, as you work through it you only need to represent the procedure, parts of the information contained within the problem when necessary and your ‘work in progress answer’ as you sequentially work through it. By the end of it you have your answer. I’m not sure you have to represent in working memory all of the information at once to complete the problem.

      • Matt says:

        The above was a response to manyanaed, the one above that was to David… : ) I think my forum chat schemas need a little practice ; )

  4. […] cognitive capacities is to increase the quantity and the quality of what they know. In Part 2 I discussed ways we might increase the quantity of what of what children know about the world and […]

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