Formal operational stage (Adolescence and adulthood)

In this stage, intelligence is demonstrated through the logical use of symbols related to abstract concepts. Early in the period there is a return to egocentric thought. Only 35% of high school graduates in industrialized countries obtain formal operations; many people do not think formally during adulthood.

Many pre-school and primary programs are modeled on Piaget's theory, which, as stated previously, provides part of the foundation for constructivist learning. Discovery learning and supporting the developing interests of the child are two primary instructional techniques. It is recommended that parents and teachers challenge the child's abilities, but NOT present material or information that is too far beyond the child's level. It is also recommended that teachers use a wide variety of concrete experiences to help the child learn (e.g., use of manipulatives, working in groups to get experience seeing from another's perspective, field trips, etc).

Piaget's research methods were based primarily on case studies (they were descriptive). While some of his ideas have been supported through more correlational and experimental methodologies, others have not. For example, Piaget believed that biological development drives the movement from one cognitive stage to the next. Data from cross-sectional studies of children in a variety of western cultures seem to support this assertion for the stages of sensorimotor, preoperational, and concrete operations (Renner, Stafford, Lawson, McKinnon, Friot & Kellogg, 1976).

The stage of formal operations is quite different from concrete operations. While both are logical and systematic thought functions, people in the formal operations stage can apply these processes to more abstract problems and hypotheses. This is Piaget’s last stage of cognitive development, after this he proposed “no further structural imrpovements in the quality of reasoning” (Wadsworth, 1989. pg.115). Unfortunately, it is believed that not all adults arrive at formal operations although most have reached their full potential by about 14 - 15 years of age.

There are several structures that are developed in this stage, hypothetico-deductive reasoning, scientific-inductive reasoning and reflective abstraction. Piaget (1981) described the capacity for hypothetico-deductive reasoning as the ability to be able to deal with not only objects and experiences but with hypotheses as well, with "the possible as well as the real". Conclusions can now be deduced from hypotheses rather than just physical facts. This highlights the persons ability to make conclusions by going from general to specific (deductive reasoning).

Scientific-inductive reasoning is the ability to think like a scientist, to make conclusions by going from specific observations to generalisations. When people in this stage have been confronted by a problem they can think about it abstractly, and can think over each of the different variables and how they, or combinations of them would affect the situation while sytematically testing for these. A common problem used to study this type of reasoning is the pendulum problem in which young people are given strings of different lengths that can be attached to a pole, they are also given objects of various weights to hang from the string and make pendulums. The underlying problem is to find out what it is that makes the pendulum swing faster, the length of string, the weight of the pendulum, the height from which the weight is dropped or the force exerted on the weight when it is dropped (Bjorklund, 1995). It is not till children reach the formal operational stage that they can systematically go about solving this problem and arrive at the correct and logical conclusion.

Another structure that has developed over this period is reflective abstraction, a mechanism by which knowledge (such as logical-mathematical) can be gained. According to Wadsworth (1989) “reflective abstraction is internal thought or reflection based on available knowledge”. Analogies provide a good example in which to study reflective abstraction. Analogies are about constructing relationships between objects, and these relationships can only come about through reflective abstraction.

But the concrete operations child has a hard time applying his new-found logical abilities to non-concrete -- i.e. abstract -- events. If mom says to junior “You shouldn’t make fun of that boy’s nose. How would you feel if someone did that to you?” he is likely to respond “I don’t have a big nose!” Even this simple lesson may well be too abstract, too hypothetical, for his kind of thinking.

Don’t judge the concrete operations child too harshly, though. Even adults are often taken-aback when we present them with something hypothetical: “If Edith has a lighter complexion than Susan, and Edith is darker than Lily, who is the darkest?” Most people need a moment or two.
From around 12 on, we enter the formal operations stage. Here we become increasingly competent at adult-style thinking. This involves using logical operations, and using them in the abstract, rather than the concrete. We often call this hypothetical thinking.

It is the formal operations stage that allows one to investigate a problem in a careful and systematic fashion. Ask a 16 year old to tell you the rules for making pendulums swing quickly or slowly, and he may proceed like this:
A long string with a light weight -- let’s see how fast that swings. A long string with a heavy weight -- let’s try that. Now take a short string with a light weight. And finally, a short string with a heavy weight.

His experiment -- and it is an experiment -- would tell him that a short string leads to a fast swing, and a long string to a slow swing, and that the weight of the pendulum means nothing at all!

The teenager has learned to group possibilities in four different ways:

By conjunction: “Both A and B make a difference” (e.g. both the string’s length and the pendulum’s weight).

By disjunction: “It’s either this or that” (e.g. it’s either the length or the weight).

By implication: “If it’s this, then that will happen” (the formation of a hypothesis).

By incompatibility: “When this happens, that doesn’t” (the elimination of a hypothesis).

On top of that, he can operate on the operations -- a higher level of grouping. If you have a proposition, such as “it could be the string or the weight,” you can do four things with it:

Identity: Leave it alone. “It could be the string or the weight.”

Negation: Negate the components and replace or’s with and’s (and vice versa). “It might not be the string and not the weight, either.”

Reciprocity: Negate the components but keep the and’s and or’s as they are. “Either it is not the weight or it is not the string.”

Correlativity: Keep the components as they are, but replace or’s with and’s, etc. “It’s the weight and the string.

Someone who has developed his or her formal operations will understand that the correlate of a reciprocal is a negation, that a reciprocal of a negation is a correlate, that the negation of a correlate is a reciprocal, and that the negation of a reciprocal of a correlate is an identity (phew!!!).
Maybe it has already occured to you: It doesn’t seem that the formal operations stage is something everyone actually gets to. Even those of us who do don’t operate in it at all times. Even some cultures, it seems, don’t develop it or value it like ours does. Abstract reasoning is simply not universal.

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