Concrete Operations Stage

Inductive logic involves going from a specific experience to a general principle. On the other hand, children at this age have difficulty using deductive logic, which involves using a general principle to determine the outcome of a specific event. This stage is also characterized by a loss of egocentric thinking. Egocentrism is Piaget’s term for inability to consider another person’s point of view; a characteristic of young children’s thought (Papalia p. G-3). During this stage, the child has the ability to master most types of conservation experiments, and begins to understand reversibility.

Conservation is the realization that quantity or amount does not change when nothing has been added or taken away from an object or a collection of objects, despite changes in form or spatial arrangement. The concrete operational stage is also characterized by the child’s ability to coordinate two dimensions of an object simultaneously, arrange structures in sequence, and transpose differences between items in a series. The child is capable of concrete problem-solving. Categorical labels such as "number" or "animal" are now available to the child.

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The first, and most discussed, of these limitations is egocentrism. The pre-operational child has a “'self-centred' view of the world” (Smith, Cowie and Blades, 2003, p. 399), meaning that she has difficulty understanding that other people may see things differently, and hence hold a differing point of view. Piaget's classic test for egocentrism is the three mountains task (Piaget and Inhelder, 1956), which concrete operational thinkers can complete successfully. A second limitation which is overcome in the concrete operational stage is the perceptual domination of one aspect of a situation.

Before the stage begins, the child's perception of any situation or problem will be dominated by one aspect; this is best illustrated by the failure of pre-operational children to pass Piaget's conservation tasks (Piaget and Inhelder, 1974). Perhaps the most important limitation, yet the most difficult to describe and measure, is that of the turn to logical operators. A pre-operational child will use mostly simple, heuristic strategies in problem solving. Once a child reaches the concrete operational stage, they will be in possession of a completely new set of strategies, allowing problem solving using logical rules.

This new ability manifests itself most clearly in children's justifications for their answers. Concrete operational thinkers will explicitly state their use of logical rules in problem solving (Harris and Butterworth, 2002). This area also indicates the way in which the concrete operational stage can be negatively defined; although children can now use logical strategies, these can only be applied to concrete, immediately present objects. Thinking has become logical, but is not yet abstract.

These shifts in the child's thinking lead to a number of new abilities which are also major, positively defined characteristics of the concrete operational stage. The most frequently cited ability is conservation. Now that children are no longer perceptually dominated by one aspect of a situation, they can track changes much more easily and recognize that some properties of an object will persevere through change. Conservation is always gained in the same order, firstly with respect to number, followed secondly by weight, and thirdly by volume. A second new ability gained in the concrete operational stage is reversibility.

This refers to the ability to mentally trace backwards, and is of enormous help to the child in both their problem solving and the knowledge they have of their own problem solving. For the former this is because they can see that in a conservation task, for example, the change made could be reversed to regain the original properties. With respect to knowledge of their own problem solving, they become able to retrace their mental steps, allowing an entirely new level of reflection. Concrete operational children also gain the ability to structure objects hierarchically, known as classification.

This includes the notion of class inclusion, e. g. understanding an object being part of a subset included within a parent set, and is shown on Piaget's inclusion task, asking children to identify, out of a number of brown and white wooden beads, whether there were more brown beads or wooden beads (Piaget, 1965). Seriation is another new ability gained during this stage, and refers to the child's ability to order objects with respect to a common property. A simple example of this would be placing a number of sticks in order of height.

An important new ability which develops from the interplay of both seriation and classification is that of numeration. Whilst pre-operational children are obviously capable of counting, it is only during the concrete operational stage that they become able to apply mathematical operators, thanks to their abilities to order things in terms of number (seriation) and to split numbers into sets and subsets (classification), enabling more complex multiplication, division and so on. Finally, and also following the development of seriation, is transitive inference.

This is the name given to children's ability to compare two objects via an intermediate object. So for instance, one stick could be deemed to be longer than another by both being individually compared to another (third) stick. Concrete operational stage (Elementary and early adolescence). This stage (characterized by 7 types of conservation: number, length, liquid, mass, weight, area, volume), intelligence is demonstrated through logical and systematic manipulation of symbols related to concrete objects. Operational thinking develops (mental actions that are reversible). Egocentric thought diminishes.