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In Piaget's theory, concrete operational reasoning is characterized by patterns of serial ordering, simple classification, conservation reasoning, and other operations applied to objects that a person is able to observe or manipulate directly. Formal reasoning patterns include these operations but go beyond them to utilize other processes in situations where one does not deal with tangible objects. Formal patterns often involve proportional reasoning, separation of variables, and combinatorial reasoning.
The film "Formal Reasoning Patterns" Davidson Films, 1976) will enable you to watch two interviews (Dr. Karplus and Dr. Peterson) working with several secondary school students who exhibit concrete or formal operational reasoning patterns while responding to four Piagetian tasks. The young people appearing in this film were enrolled in Berkeley's High Potential program for secondary school students. They were above average in showing talent in some areas of accomplishment, not necessarily in academic achievement.
The students' performances were completely unrehearsed - none of them had prepared for the interview or knew in advance what would be required. The scenes in the film were selected to illustrate the concrete and formal operational reasoning patterns described in Module 2. Though not representative of a random sample of secondary school students, the film demonstrates that a diverse group of such students - a typical high school class, for instance, is likely to reveal both types of reasoning patterns.