Piaget, Newton and the EU Referendum

Roger Titcombe's picture

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 posts. 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 GERMwill 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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Roger Titcombe's picture
Thu, 23/06/2016 - 14:28

"And why am I writing about this on my education website?"  I do apologise - I am a mere grateful guest on LSN. This line crept in because I first posted this article on my 'Learning Matters' website then copied it onto LSN, without editing it properly. 




agov's picture
Thu, 23/06/2016 - 15:50

Obviously far too complex, and indeed long, for the ill-educated likes of me to even begin to understand but fortunately sages on twitter have found ways to make things easier for ordinary people to understand -

with even the prime minister doing his bit to improve the careful thought we all treasure and aspire too -

Happily though, if only #Remain can manage to squeak through to a win having had to struggle, as it did, with nothing to assist its campaign but big business money, the government machine, and the full propaganda resources of Channel 4 and Al-Beeb, there may be little need ever again for uneducated people to be much troubled by voting on anything at all, which was after all a founding purpose of the EU. I gather the dreadful Selina Scott said something of the sort on last night's show trial on Channel 4. Some of these horrible people struggling with things too complicated for them to understand may, outrageous as it sounds, have even been thinking of their own economic self-interest rather than more worthwhile things like holding down the cost of nannies. The next thing will be them refusing to ever again vote for the Labour Party that has so safeguarded them by wisely campaigning to protect the incomes of bankers and indeed the entirely justified huge expenses, salaries, and jollies that the enlightened bureaucrats in Brussels provide to deserving supporters in the European political classes.

Roger Titcombe's picture
Thu, 23/06/2016 - 16:24

Yes agov it is easy for a Brexiter to twist my argument into one of despising the 'working class'.

Barely a week goes by without a press story about the working class 'attainment gap'. There is no attainment gap, but there really is a cognitive ability gap. This is well known by all the schools, mainly Academies, that have CATs-driven banded admissions systems as in the London Borough of Hackney. The CATs data show that school students overwhelmingly perform according to their cognitive ability. Rather than generating red herrings about discrimination against class, ethnic and religious groups, educationalists and schools should be concentrating on remedying the fact of the cognitive ability deficits. You can read about this in Part 4 of my book.

There is no doubt that this can be done.

To quote my article:

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.

I am not going to argue with you about Brexit, but Ken Clarke really is right that the issues are too complex to be decided in a referendum.

agov's picture
Sun, 26/06/2016 - 08:11

Yes, they had it right in Athens. Voting isn't for the likes of slaves and women.

And now it's time for champagne.

Roger Titcombe's picture
Sun, 26/06/2016 - 09:31

agov - I look forward to the new Brexit-led government having referenda on the judicial punishment for murder (hanging) and paedophilia (chop their bollocks off). Should the world's Islamic Republics decide to go in for referenda too, then they will be stoning to death females guilty of adultery. Blasphemers and gays will be subject to legally sanctioned murder by vigilantes.

Voting does have its limitations. Take the very simple problem given by Kahneman.

A bat and ball costs £1.10 in total.

The bat costs one pound more than the ball.

How much does the ball cost?

This was indeed put to the vote on Radio 4 after Kahneman was interviewed and listeners were aked to phone in the answer.

Virtually no-one voted for the correct answer which is 5p, not 10p. The correct solution requires the conscious slow thinking of the cerebral cortex that Kahneman refers to as System 2 (Piaget's formal thinking). Everybody has their System 1 (Piaget's concrete thinking), primed for action.

Referenda would not have helped the civil war in Rwanda or the fictional child victims in 'Lord of the Flies'.

The questions raised here are not about the principle of democracy so much as the nature of it. The UK, the US and many successful democracies do not have referenda. They have 'representative' democracies. In our system MPs are not 'delegates' who can be mandated by mini referenda, but individuals 'trusted' by the elecorate to to take the right decisions paticularly on complex matters.

Referenda can work in countries like Switzerland, where the majority of the population are educated to a high level. In Part 2 of 'Learning Matters', I argue that our debased and degraded education system, where behaviourism is the default pedagogy resuting from the perverse incentives of marketisation, risks creating a 'lumpen proletariat' (to quote Marx), which can easily be manipulated by demagogues (political leaders who seek support by appealing to popular desires and prejudices rather than by using rational argument.)

The only democratic defence against demoguery (my word) is an education system based on slow learning  for deep understanding. What we are seeing is the consequence of the planned destruction of such a sysyem for ideological reasons.

It is especially sad that Maurice Holt, an educational giant and advocate of 'slow learning' has recently died.


agov's picture
Mon, 27/06/2016 - 10:39

"referenda on the judicial punishment"

So you again assume fellow citizens are too stupid to agree with you.

"Islamic Republics decide to go in for referenda too, then they will be stoning to death females guilty of adultery."

They already do that without benefit of referenda. Even the propaganda channels of Channel 4 and Al-Beeb occasionally report such things - though you do have to listen carefully as they quickly sweep on to tell us how terrible we are and how it's probably all our fault anyway.

"A bat and ball costs £1.10 in total"

Seriously? Anna Soubry? Diane Abbott? David Lammy? Nicky Morgan?

"Referenda would not have helped the civil war in Rwanda"

Nor did not having one.

"or the fictional child victims in 'Lord of the Flies'."

Perhaps they should have had a secret ballot.

"the US not have referenda"

Completely wrong. They have loads. And lots of judges are elected not appointed. Plus they have elections at more levels of government.

"In our system MPs are not 'delegates"

The electors of Bristol rewarded Burke for telling them that by kicking him out at the next election.

"the majority of the population are educated to a high level"

Because only educated people can see what is being done to their lives by the self-entitled and self-enriching misgoverning class.

"appealing to popular desires and prejudices rather than by using rational argument"

Have you ever actually listened to the Commons?

"The only democratic defence against demoguery"

It was the ghastly uneducated working class that supported Churchill when the entire educated establishment would have preferred to surrender.

Roger Titcombe's picture
Mon, 27/06/2016 - 12:46

"It was the ghastly uneducated working class that supported Churchill when the entire educated establishment would have preferred to surrender."

Not true. It was a significant part of the Conservative Party  and major elements of the aristocracy including the Royal Family that wanted to 'do a deal with Hitler'. The 'working class' were never asked. The 'left wing establishment' was always rock solid in its opposition to fascism. Many volunteered to fight in the Spanish Civil War. The British government during the war was a coalition in which Labour played a prominent part. This was presumably in the mind of working class voters in 1945 when Labour, not Churchill, was swept to power with a huge majority.

The point I am making is that if you want referenda on complex matters then you need an education system focussed on building capability to understand the issues. Our education system is moving in the opposite direction.

I am not going to get involved in a BREXIT argument on this educational website, beyond stating  which way I voted.


agov's picture
Tue, 28/06/2016 - 12:33

"The 'left wing establishment' was always rock solid in its opposition to fascism."

The Labour Party in Parliament was possibly the strongest supporter of Chamberlain's appeasement. Until it no longer could be. Don't be conflating the left wing establishment with people like Orwell.

"you need an education system focussed on building capability to understand the issues"

Don't remember anyone having a problem with that.

"I am not going to get involved in a BREXIT argument "

And yet it seemed to be you who raised it.

Roger Titcombe's picture
Tue, 28/06/2016 - 12:40

Yes, but with regard to the complexity of the arguments and the educational issues in relation to the appropriateness of a referedum.

Your knowledge of the parliamentary history of WW2 is probably better than mine, but Labour played a full part in the coalition government.

James Coombs's picture
Fri, 24/06/2016 - 14:43

I'm more interested in the pedagogy than the politics so appreciate the Kahneman tip.  Whoever came up with 'slow thinking' didn't work in marketing  but this strikes a chord with me as I've always considered myself to be a very slow thinker whilst never attributing anything positive to this.  Instead I've tried a positive spin by describing my thinking as 'deep' rather than 'quick' but never considered there could be two distinct types.  Are these really distinct or in any given situation there is an unmeasurable amount of each and how would you evaluate an individual's  (or a nation's) tendency to think one or the other way?  I can't see the "Kahneman Scale" for determining the proportion of System 1 thinking in a person or a class catching on as well as, say the Richter Scale.  

I'm currently on target for a third class degree in Mathematics and its Learning with the OU so I'm obliged to trot out Bruner's enactive-iconic-symbolic view of learning on a regular basis even though it's clear that Piaget got there decades earlier.  If I were to mention Piaget instead of Bruner in my assignments I'd lose (even more!) marks because I'm not "addressing the marking scheme".  If that's happening at degree level, where one would hope the universities are trying to foster independent thinking, then what hope at secondary schools where final GCSE results (regardless of attainment on entry) are the one and only mark of success?

Roger Titcombe's picture
Fri, 24/06/2016 - 16:00

Hello James - Thank you for your comment. The following is the start of Section 5.6 in my book.

5.6 Thinking, Fast and Slow

This is the title of the 2011 book by the Nobel Laureate Daniel Kahneman, who is a cognitive psychologist at Princeton University and Emeritus Professor of Public Affairs at Woodrow Wilson School of Public and International Affairs. He was awarded the Nobel Prize in Economics in 2002. He appears to have no background in learning theory or pedagogy and his book makes no direct reference to school age education or curriculum, so what is the relevance to the failures of the English education system?

It is because all his work is based on his assertion that humans have two discrete modes of thinking that he refers to as System 1 and System 2. System 1 is a result of human evolution and to a major extent is written into the human genome. It is the ‘fast thinking’ that is linked to survival in evolutionary terms. It is very good at solving certain kinds of problems very rapidly but frequently fails spectacularly with complex problems associated with scientific and mathematical concepts that millions of years of evolution have not prepared us for, other than giving us large brains with a highly flexible cerebral cortex. Kahneman describes System 1 as “a machine for jumping to conclusions”, which is the title of Chapter 7 in his book.

If you go the Amazon website page for my book, you can the 'turn the page' feature to read all of it for free! You will find the Daniel Kahneman section on p121 However his book is very cheap and a good investment.

Professors Philip Adey and Michael Shayer both helped me a lot with my book. Philip sadly died last year. I have had many on-line discussions with Michael Shayer about the relevance of Daniel Kahneman. There is no indication that Kahneman drew on Piaget at all, but there is no doubt that his System 1 and System 2 thinking correspond directly with Piaget's concrete and formal operations.

I wish you well with your studies and you are right about the 'marking scheme' - shallowness of much teaching in our secondary schools. It is disappointing if even higher education is now also so infected. 

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