The developing mind
A 10-year-old generally thinks better than a 5-year-old. This is more than just knowing more things, or thinking faster. The older child thinks in important ways more powerfully than the younger child, is able to hold more ideas in mind at once and is able mentally to handle more difficult ideas and concepts. This process of the development of the thinking mechanism or ‘cognitive development’ has been well known for over a century. But it was Jean Piaget and his co-workers at the University of Geneva who really did the work over many decades of probing the thinking of children from infancy to late adolescence and establishing a comprehensive theory of cognitive development. The theory is based on an enormous body of empirical evidence but, as usual, in the process of building theory from observations there is a process of interpretation and certainly some interpretations of Piaget’s theory have been quite controversial. This should not blind us to the fundamental validity of the Piagetian model of cognitive development which you can easily verify for yourself.
More, less, or the same amount?
Go into your Reception class with a tall thin glass, a short fat glass, a jug of orange juice and a small measuring container such as a plastic scoop. Sitting with one child, pour juice into the measuring container to the brim, explaining what you are doing, then pour this into one of the glasses. Do this twice more and check that the child agrees that you have poured three measures into the glass. Now do the same with the other glass. Recall what you have done:
‘I poured three measures into this glass and three measures into this glass’. Now ask the child to look at the juice in the two glasses and say: ‘Which one do you think has more juice, or are they both the same?’.
Figure 1.2: The conservation of liquid amount
Just three small measures, brimful, are poured into each of the glasses — one tall and thin, the other
short and fat.
Do they both now contain the same amount of
Quite a few (but by no means all) 4-year-olds will think that there is more juice in the thin vessel because the level is higher. They do not have the idea that an amount of liquid is conserved even when it is poured from one shape vessel to another. You can push them quite hard with questions such as ‘But I poured the same amount into each?’ or ‘Another child told me it must be the same amount’, but non-conserving children will remain firm in their conviction. This is because they can attend to only one dimension at a time, so they look at the level without taking account of the width. By contrast, most (but not all) 6-year olds will be amazed by the conservation question: ‘Of course it’s the same, you poured the same amount into each’. They might wonder why you are asking such a daft question! And this is a characteristic of cognitive development: once one has developed to a higher stage, one cannot imagine how anyone could think in any other way. This is a problem that student teachers sometimes have also — because they are fully intellectually developed, they have great difficulty in understanding the cognitive difficulties that children encounter.
As far as primary-aged children and this handbook are concerned, we only really need to pay attention to these stages of cognitive development:
• Early Concrete Operational
• Late Concrete Operational.
Preoperational thought is characterised by the non-conservation illustrated above, while ‘Concrete Operations’ means mental operations on concrete reality. Just a very few of your most able Year 6 children may have started to use a higher level of thinking, Formal Operations — although that is more typical of 15-year-olds. ‘Formal Operations’ means being able to use mental operations on abstractions, such as understanding the density of a material as the mass of a given volume, regardless of shape or size. This kind of thinking need not concern us further here.
Have a look at Appendix 1 which, for some major topics in maths, science and literacy, details the types of thinking that are available to children at different stages of cognitive development. In particular it shows the types of thinking characteristic of Concrete Operations, the development of which is the big mental event throughout the primary years. We have added some notes on Preoperational thought and Formal Operations in order to frame the development of Concrete Operations. We call these tables ‘Curriculum Analysis Taxonomies’ because they can classify everything that appears in the school curriculum in terms of the type of thinking that is required. You do not really need the detail of this unless you want to do a deep analysis of your school curriculum, but the principle that the curriculum can be analysed in terms of the thinking required is important.