Question

Describe at least three ways in which students in Piaget’s formal operations stage are likely to think differently from those in the concrete operations stage. Illustrate each characteristic with a concrete example of how students in each of the two stages might think or behave.

Answer 1

The three ways in which students in Piaget’s formal operations stage differ from those in the concrete operations stage in terms of thinking, are as follows:

1. Students in the concrete operations stage rely upon the presence of an actual object or data in order to process any information regarding it. Thinking for such individuals is based upon the concrete object or data which they can directly manipulate if necessary. On the other hand, students in the formal operations stage can think in an abstract manner, which means that they do not rely upon the actual presence of the object or data, but rather their information processing is based upon the mental image that they create of the data. Thinking for them is through symbolic processing in which they use symbolic representations of the object or data, and manipulate them mentally. For example, the use of ABACUS, blocks, balls, sticks, cut-outs of fruits or vegetables, picture books, candies, etc. are effective ways of teaching mathematics to younger kids (concrete operations stage) because they can manually add on to or subtract from the items or objects available in order to come to a solution to the given mathematical problems. But for students in the formal operations stage such efforts are not required, since it is not difficult for them to mentally visualize the symbols and solve them accordingly. They thus indulge in higher level operations.
2. The concrete operations stage and formal operations stage also differ on the basis of ‘reasoning’. Concrete operations stage marks the beginning of logic-based information processing. Students in the concrete operations stage use inductive reasoning, which involves the movement from specific bits of information towards a general rule. The principle used is that of generalization. For example, a student might feel that since he has not performed well in the last two examinations, he will never perform well in the future. Although sometimes it is subject to errors, inductive reasoning is an easier way of arriving at conclusions, especially for the younger children. Students in the formal operations stage on the other hand, use deductive reasoning, which involves moving down from general principles or theories to specific solutions, using logic. It follows a premise and a conclusion. For example, Premise: Persons L and M are always together. M is at the cafeteria. Conclusion: L is also at the cafeteria. Deductive reasoning is a more complex task of arriving at solutions because it uses a general principle and a subsequent deduction of conclusions.
3. ‘Problem solving’ is another aspect based on which the two stages differ. In the concrete operations stage, the basic approach of the student is a rudimentary trial and error process. This stage marks the beginning of new learning experiences and a sense of independence in areas of problem solving. A child belonging to this stage makes several attempts while trying to reach a solution, whether in solving simple mathematical problems or solving puzzles. For example, a child may make multiple attempts to solve a maze (on paper) by trying to move along the different paths or routes, until the correct one is arrived at. On the other hand, in formal operations stage, the approach towards problem solving is more complex, systematic and target-oriented. For example, in solving the maze, the child will now observe the paths carefully, and use mental tracing in order to connect the starting point to the destination, and then go forward with his actions.