The development of children’s thinking

Jean Piaget (1896-1980) is well known for his belief that children’s thinking develops through
distinct stages. He also proposed that intellectual development is not simply a matter of
learning more things, but of growing into qualitatively different ways of thinking about the
observed world. Piaget and his co-workers reported hundreds of hours of detailed analysis of
the thinking of children of different ages. This massive corpus of work provides a wonderfully
rich resource for understanding cognitive development.
Piaget used the term ‘concrete operations’ to describe mental operations involving the world
of material things. A concrete operation is a mental operation involving concrete reality and
concrete operations skills are acquired over many years.
In broad terms, the whole phase of primary education, from around five to 11 years of age,
corresponds to the period during which children are developing concrete operations. A concrete
operation is a mental operation on concrete reality: for example, adding five beans to three
beans and getting eight — consistently and reliably. This may seem rather simple, but for a child
of, maybe, four years old who is not yet using concrete operations, the concrete world appears
to be a surprisingly slippery place. For example, she may agree that two rows of beads have
the same number, as one bead has been put in one row and a corresponding bead in the other
row. But when we push the beads in one row close together, and spread those in the other
row further apart, she will now claim that there are more beads in the longer row. This is
preoperational thinking — the child is not yet able to use simple mental operations reliably in
real situations. There is little in the concrete world that is perceived as constant.
A few children even at nine years old will find concrete operations difficult. These are likely to
be children identified as having learning difficulties. At the other end of the scale, a few 10-
year-olds will have started to deal comfortably with abstractions and multi-variable situations.
These are gifted children who are moving into the stage of thinking typical of adolescents:
formal operations. So concrete operations spans a wide age-range and growth through
concrete operations involves becoming increasingly confident in dealing with situations that
need four or five bits of information to be held at once in the active ‘processing’ space of the
mind. There are clear differences between the types of thinking characteristic of early and late
concrete operations. Let’s Think through Science! 8 & 9 is designed specifically to stimulate
intellectual growth through concrete operations.