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In Piaget' s theory, concrete operational thought is characterized by serial ordering , simple classification, and conservation logic applied directly to objects. A concrete thinker doing a Piagetian task must be able to observe objects and/or manipulate them. Formal operational thought involves proportional reasoning , separation of variables, elimination of contradictions, and class inclusion or exclusion operations. A formal thinker is able to work in situations where he does nor deal with tangible objects. The formal thinker can apply the operations used by a concrete thinker, but goes beyond these operations when solving problems.