Piaget, however, ...

He published papers from the age of 10, with his favourite topic for observation and publication during secondary school being molluscs.

The reason we studied his theories was because he charted stages of cognitive development, detailing what children could do, and how they could intellectually operate, at different ages. His theory said that the child had to work through these stages sequentially; sensorimotor before preoperational, before Concrete operations, and that before, finally, formal operations from about the age of 12.

The classic story was of Piaget walking down a path with his own son, on a damp morning. His son saw a snail and commented on it. A few metres further down the path they saw another snail but Piaget’s son understood it to be the same snail – ‘there’s that snail again!’ Piaget’s son was about 4 years old.

I tell of the theory, and the age band, so I can tell a short story from today in school, and consider what we learn from it.

As I do, I was sweeping up a multitude of misplaced balls from in the wood towards the end of the lunch break. (It is one of my things – I had fetched twenty odd items down from the overgrowth on the stable walls before school.) There were hockey balls (Year 5 PE), tennis balls (last term’s cricket or tennis?), volleyballs (Year 6 PE topic), a couple of black, white and purple footballs (Evo Soccer after-school club), a netball (labelled from a Year 4 class) and a bright yellow, shiny new, football (unlabelled).

Two Year 6 pupils instantly claimed it as theirs.

‘That’s our ball?’

How do you know?’

‘Ours is yellow.’

‘It doesn’t have your class name on.’

‘It’s yellow. Our ball is yellow.’

This is ‘transductive’ thinking – using logic, but rather fuzzily. ‘Yellow’ is the feature in the children’s schema of ‘our football’, and so they could mistake any and every yellow football as belonging to their class. They may be correct on this occasion but are likely not to be mistaken (we have a cupboard containing more than a dozen yellow footballs).

Piaget would have it that these two children should have moved past this way of thinking around three to five years ago, aged between 4 and 7.

We challenge the logic, correct the statement (this is a yellow football, one of many. It only might be yours) and ask them to explain, so that they orally practice the logical arguments.

Theories can still resonate, and examples can still illustrate, many years later.

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