Piaget, Newton and the EU referendum

This week (20 June), former Chancellor and Tory elder statesman Ken Clarke stated that the referendum should never have been called because the issues were ‘too complicated’ to be decided in such a way. Is this a profoundly undemocratic, elitist  statement, or does he have a point? And why am I writing about this on my education website?

I will address both questions by considering the fact that although humans and our hominid ancestors have been hurling rocks at each other and their prey for around three million years it was not until 1589 that anyone (Galileo) tested the universally held assumption that when dropped, heavy rocks fall faster than lighter ones.

We do not have to be taught this to believe it. I was brought up on a South Birmingham council estate, where I had many friends. We all had bikes and in the late 1950s/early 60s we would make long cycle journeys together through the nearby Warwickshire and Worcestershire countryside. A favourite destination was the ‘Lickey incline’ between Bromsgrove and Blackwell, the steepest on any main railway line in the UK. There is a bridge over a lane near the summit of the incline where we could clamber up the bank to trespass on the railway and watch the drama of the steam locomotives making the ascent from close up. And what drama! Heavy Birmingham bound expresses usually hauled by a named Jubilee class locomotive would be banked at the rear by either the massive 2-10-0 locomotive based at Bromsgrove for the purpose, or by up to three small but powerful pannier tank locos.

That part of Worcestershire is both beautiful and hilly. The outward journey involved the descent of ‘Weatheroak Hill’. We freewheeled down a few feet from each other without using our brakes reaching frightening speeds, long before the era of cycle helmets. We were all of different weights and so were our bikes. The Raleigh ‘All Steel’ bicycle was popular and a heavyweight, while some of us had sportier and lighter bikes. We all expected the heaviest child on the heaviest bike to ‘win’ the race to the bottom of the hill. This did not happen. I would like to claim that we all rolled down the hill exactly together, but this didn’t happen either. Some rolled slightly faster than others, but with no clear link with the weights of boys and their bikes. As a physics teacher I understand this now in terms of the different resistances (drag forces) on the bikes related to wind and road friction, but then, the whole thing remained a puzzle to this curious child, but I still believed heavy objects fell faster than light ones even though our bike rides showed this not to be the case.

Fast forward now to my attempts to teach mass, weight and the acceleration of gravity to my secondary school science students. The vast majority of the general public do not have any coherent understanding of these issues. I fear that my 36 years as a science teacher failed to make much impact on this depressing fact. Why is it so difficult to understand?

We start with the idea that the force of gravity attracts all objects to the earth, so they fall when you drop them – easy to understand. Then, heavy objects are pulled by gravity more strongly than lighter ones – also easy to understand. So when you drop them, heavy objects will fall faster – wrong – but why?

Heavy objects are heavier because they are more massive. Heaviness is weight. Massiveness is mass. They are not the same thing, even though in everyday life and in the old Imperial system of units no consistent distinction is made. Weight is a force properly measured in Newtons. Mass is ‘amount of stuff’ measured in kilograms. A 100g apple weighs about 1N (except on the moon or if it is in ‘free fall’). Getting trickier isn’t it? Crucially, masses also have the property of ‘inertia’. This is ‘resistance to being moved’. The greater the mass/weight, the greater the inertia.

Now stop thinking about dropping masses/weights and think about racing cars. They need high acceleration. To achieve this requires a strong engine (high force) and low mass/weight (less inertia).

The force of gravity on a massive object is large (it is therefore heavy). But the massive object also has greater inertia (resistance to being moved). These effects cancel each other out. When you hold a heavy object in your hand you can feel the large force of gravity on it (it is heavy). However, you cannot feel its large inertia because you are not trying to move it. So in a dropping weights context, in your direct experience, weight trumps inertia. Gravity tries to accelerate the heavy mass but the effort of gravity is resisted by the inertia of the mass exactly enough to ensure that all masses experience the same acceleration when they fall regardless of their weight. The mathematics of this involves very simple algebra and is quite beautiful.

Piaget classifies one dimensional variation (eg bigger masses are heavier) as a ‘concrete’ operational cognitive challenge. Bigger masses have more inertia (and hence lighter racing cars are needed to win races). This is also a one dimensional ‘concrete’ cognitive challenge.

Dropping objects and thinking about their rate of fall requires both weight and inertia to be considered at the same time. Piaget classifies this as a ‘formal’ operational cognitive challenge because it involves multiple interacting factors.

Philip Adey and Michael Shayer were both science teachers concerned with the issue of ‘difficulty’ (why some students can understand hard stuff while others can’t). This remains controversial. Some argue that it is to do with ‘working memory’, which is presumably a physical property of the brain related to neural networks and connections. Piagetians like Adey and Shayer are clear that it has nothing to do with memory at all. The progression from ‘concrete’ to ‘formal’ thinking is developmental in the sense of the sophistication of personal cognitive software, not neurons. It is determined by both age-related and experience-driven development of individual cognitive software. At any given moment a mixed ability secondary class will contain ‘concrete’ and ‘formal’ thinkers. The latter will be able to understand the distinction between mass and weight and why Galileo was right, provided they have a competent teacher. The ‘concrete’ thinkers will not, however hard they try and regardless of how much they memorise Newton’s Laws of Motion, the size of the bribe offered or the ability of the teacher. Professor Brian Cox would do no better than me.

We are now back in the more familiar subject territory of my website. Secondary school pedagogy should be focussed onto getting the maximum proportion of students through the concrete/formal barrier, because then they will not only be able to understand Newton’s Laws of Motion, but other hard stuff in other subjects too. And this includes Economics, which is full of trade-offs like weight/inertia and which also makes cognitive demands at the formal operation level.

So at last we come to the EU referendum. There are two main ‘dimensions’ in the EU leave/remain debate.

The first is ‘immigration’ – less immigration good – more immigration bad. This is not only easy to understand it resonates with very deep evolutionary fears. For all but the most recent hominid history the greatest threat to your survival and that of your children was from the ‘tribe over the hill’ that has a tendency to attack your tribe, kill the men and boy children, carry off the women and girl children into sexual slavery and plunder your assets. Racists have always played on such primitive fears, often with great success.

The contrary argument, more immigration good – less immigration bad can also be made, but it is much more complex. It involves formal operational thinking, which can also be characterised as the dominance of the rational (Kahneman System 2 mind) over the instinctive/reactive (Kahneman System 1) mind.

Then there is the second dimension – trade with Europe good – trade barriers with Europe bad. This involves complex economics and is clearly in the formal operational thinking category.

This second economic dimension can be exploited through fear of less individual wealth.

However, even if this is effective, it has to be balanced in the mind against the immigration dimension. Immigration is like the weight of the object in your hand. It can be directly sensed. It is ‘concrete’. The economic argument is like the inertia of the object in your hand. It cannot be sensed – its existence must be reasoned. It is ‘formal’.

If I am right, for concrete operational thinkers ‘immigration’ will trump ‘economics’, while for formal operational thinkers the economic arguments may prevail.

The result is therefore likely to depend on the relative voting proportions of concrete and formal operational thinkers in the UK population.

Ken Clarke is right and therefore as a ‘remainer’ I am pessimistic about the outcome.

There can be no clearer example of why the English education system must be reformed so as to produce over time a cleverer, wiser and healthier population. The dismal behaviourist pedagogy of marketisation and GERM will produce the opposite effect. It must be replaced by developmentalism or else our democracy will end up degrading our society rather than enriching and uplifting it.

This is the subject of my book, ‘Learning Matters‘.

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6 Responses to Piaget, Newton and the EU referendum

  1. Chris Ormell says:

    . Roger, you start with a very good intro about the counter-intuitive nature of physics. But Piaget’s notion that there is a great barrier between concrete thinking and what he calls formal doesn’t stand careful scrutiny. There were early scientists like Oliver Heaviside who managed to bridge the gap without any “formal” help, i.e. maths. Piaget had a 19th century view of maths which was deeply wedded to the idea that it was on a higher plane than concrete. A line of thinkers including Wittgenstein, Lakatos, Davis, Hersh have shown us that mathematic experience is basically similar to concrete experience. The link between the two is imagination. Chris Ormell


  2. Chris – I do not regard Piaget as an infallible guru. He can be wrong about some things, but still be right about the main things. A good example is Isaac Newton himself, who maintained a lifelong interest and belief in alchemy and the occult.

    What Piaget gives us is ‘developmentalism’ rather than ‘behaviourism’. The latter results in a pedagogy driven by the rote learning of facts. Dickens’ Gradgrind comes to mind. If cognition ‘develops’ in both children and adults then it reasonable to identify the stages and the pedagogy that best promotes the development. If you reject Piaget then you also have to reject Vygotsky, Bruner and current theorists like Mortimer and Scott (Section 5.3 in Learning Matters), and the Mathematics Resilience movement (Section 5.4 in Learning Matters), not to mention all the work on ‘Cognitive Acceleration’ by Shayer and Adey and the current ‘Growth Mindset’ movement led by Carol Dweck. The ‘Utopian Socialists’ like Ruskin and the ultra-progressives of the 1970s were also developmentalists. Their error was in seeing cognitive development as ‘natural unfolding’ that has to be protected from the stunting contamination of the ‘evil’ real world. The truth is the opposite. Cognitive development requires the stimulation and mental challenge arising from the ‘cognitive conflict’ that results in the mind of the learner from exposure to real world issues and experiences. Science education is an especially rich resource in this regard.

    When it comes to Piaget I am with Shayer and Adey rather than his critics. They have experimentally tested the robustness of concrete and formal operations as reported in a large amount of published work.

    I note the line you take in ‘Prospero’. Your recognition and alarm at the growth of ‘behaviourism’ in our schools is spot on, but you label it as ‘managerialism’ mistaking the fact of behaviourism’s key role in vocational training, as its prime driving force. This is in reality the neo-liberal ideology of the Global Education Reform Movement.

    Returning to your main point, many critics of Piaget point to the apparent ability of ‘concrete’ thinkers to understand ‘formal’ concepts. The confusion here is with the depth, generality and transferability of understanding that underpins the ‘formal’ stage. An good example is found in ‘the green mammoth’ lesson described in Chapter 3 of ‘Learning Intelligence’ edited by Shayer & Adey. This was a sorting and classification task in an infant class that involved sorting plastic models of dinosaurs and mammoths between two wooden hoops placed on the desk. The dinosaurs were all green. The mammoths were different colours, but one was also green. Into which hoop did the green mammoth belong? After much rich classroom discussion the problem was eventually solved by overlapping the hoops to provide a ‘home’ for the green mammoth. The children produced a Venn diagram. Understanding Venn diagrams requires ‘formal thinking’. Infants are not formal thinkers so does this invalidate Piaget? Not at all because the children did not understand ‘Venn diagrams’ as a general concept, but as a single example. However it was still a richly developmental activity in Piagetian (and Vygotskian) terms.

    Valid tests of Piagetian stages have to based not on what students may appear to able to do in defined circumstances, but on what, in general, they cannot do in all circumstances.

    For me the clearest Piagetian statement actually comes from Vygotsky.

    ” As we know from investigations of concept formation, a concept is more than the sum of certain associative bonds formed by memory, more than a mere mental habit; it is a genuine and complex act of thought that cannot be taught by drilling, but can only be accomplished when the child’s mental development has itself reached the requisite level.”


  3. Chris Ormell says:

    Roger, Yes, I agree that behaviourism is a dreadful mistake. It treats the developing psyche as a machine. In my view we need to understand maths better. I have spent about fifty years developing a greater awareness of the maths-imagination link. We can field imagination to prompt children’s imagination into harnessing emotive acceptance of simple features of maths in problems. This is a ramp which can take the child into what Piaget calls Formal Operations, but without the formality.
    I see the current maths establishment, with their aesthetic elitism and triumphalism about multiple infinities, as being at the root of the problem.


    • What is the difference between your ‘imagination’ and the ‘metacognition’ that is common to Piagetian/Vygotsyian approaches? Personal ‘thought experiments’, requiring imagination and creative thinking have always been involved in science and maths.


  4. Pingback: Bringing back grammar schools would lower the national IQ | Roger Titcombe's Learning Matters

  5. Pingback: Piaget, Kahneman, Flynn and Donald Trump | Roger Titcombe's Learning Matters

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