More on common sense. 'Thinking fast and slow'

Roger Titcombe's picture
This is the title of the 2011 book by the Nobel Laureate Daniel Kahneman. Kahneman 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.

This is precisely the theme of Lewis Wolpert’s ‘The Unnatural Nature of Science’ (1992). Kahneman would surely agree with the former 1997 Economics Laureate James Meade about the limitations and dangers of common sense.

I first came across Daniel Kahneman by accident on listening to BBC Radio 4 in June 2012, when he was being interviewed about his new book. He repeated the following puzzle and the programme presenter asked the audience to phone in their solutions.

A bat and ball costs £1.10 in total.
The bat costs one pound more than the ball.
How much does the ball cost?

System 1 provides the almost instant answer of 10p, which is, of course, wrong. The correct solution requires the conscious slow thinking of the cerebral cortex that Kahneman refers to as System 2.

Everybody has a System 1, primed for action. System 2 is a product of developmental education. Although Kahneman does not consider the educational implications of the ‘bat and ball’ problem they are profound. System 1 can also be developed by teaching and learning designed to produce ‘fast thinking’. For example we can all respond instantly to, ‘What is two add two?’, and even, ‘What is two times two?’, because familiarity and repetition have burned these responses onto our genetically inherited and incredibly efficient System 1.

The educational theory of behaviourism was based on the principle that all learning was about extending System 1 through repetition, punishment and reward. Most modern mainstream theories of learning are based on the developmental models of Piaget, Vygotsky and many others. The following quotation from Vygotsky is so important it is worth repeating.

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.

Not only are such concepts a feature requiring Kahneman’s System 2, but so also is the process of building the sophistication and power of the internalised individual concept structure that allows access to the higher Bloom levels of thinking.

Marketisation of the education system has driven English classroom practice back towards System 1 behaviourism and away from the System 2 approaches that can make children more intelligent as they progress through a cognitively aware education system.

So what is the answer to the ‘bat and ball’ problem and why do even the best System 2 educated mathematicians and others often get it wrong?

Kahneman states that even if you possess sufficient System 2 capability, you still get it wrong because System 2 is lazy. Firing up System 2 takes effort and if System 1 jumps to a convincing conclusion quickly enough, as it nearly always does, then System 2 is not even deployed even by the brightest and most expert.

Effective education is therefore not just about developing System 2 so it is able to cope with complex problems but also making us sufficiently mentally resilient that we routinely make the conscious effort of actually ‘using our brains’.

Johnston-Wilder and Lee’s term, ‘Developing Mathematical Resilience’ is therefore well chosen and highly applicable to engaging our brain's System 2 capability.

Johnston-Wilder S & Lee C (2010), Developing mathematical resilience, in: BERA Annual Conference 2010, 1-4 Sep 2010, University of Warwick
Have you worked out the correct solution to the ‘bat and ball’ problem yet? No mathematical expertise is needed, just the resilience to test your System 1 answer.

If the ball costs 10p and the bat costs £1.00 more than the ball, then the bat and the ball together must cost £1.20, not £1.10. Not difficult is it? So how do you get the answer? Try trial and error. The ball must cost less than 10p so try 5p. The bat now costs £1.05 giving a total of £1.10. So you have it: the ball costs 5p.

Before the GCSE C grade in maths became so grossly degraded, every holder of this qualification, and many with lower grades, should have been able to apply the following simple algebraic solution to the problem rather than resort to trial and error.

Let the price of the ball be x pence
Then the price of the bat must be x + 100
If the total price of bat and ball is 110 pence then:

x + (x +100) = 110
2x + 100 = 110
2x = 10
Therefore x = 5

Slow thinking wins, and our education system needs much more of it.
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