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. Concrete operations skills are acquired over many years. Those who are able to perform concrete operations successfully will confidently handle situations that require four or five pieces 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. In broad terms, the whole phase of primary education, from around five to eleven 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 5 beans to 3 beans and getting 8 — 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 on reality. There is little in the concrete world which is perceived as constant.
A few children even at eight years old will find concrete operations difficult. These are likely to be pupils identified as having learning difficulties. At the other end of the scale, a few 10year-olds will have started to deal comfortably with abstractions and multi-variable situations. These are gifted pupils who are moving into the stage of thinking typical of adolescents, formal operations. So concrete operations spans a wide age range and the growth through concrete operations involves becoming increasingly confident in dealing with situations which need 4 or 5 bits of information held at once in the active processing space of the mind. There are clear differences between the types of thinking characteristic of early concrete and of late concrete operations. Let’s Think through Science! is designed specifically to stimulate intellectual growth through concrete operations.