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Option 2 : Formal operation period
Jean Piaget, a Swiss psychologist, belongs to the cognitive school of psychology, is famous for his work on child development. He strongly believed that children are little scientist and they actively construct their understanding of the world.
He made a systematic study of cognitive development in his theory that is categorised in four stages as explained below:
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Stage |
Characteristics of a child |
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Sensorimotor (0-2 yrs): |
Egocentric (has no view of others, self-view matters) |
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Learning by taste, smell |
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Able to crawl and walk |
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Object permanence (ability to remember objects) |
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Pre-operational (2-7 yrs) |
Learns language and pretending |
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Animism (belief that toys have emotions) |
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Learn symbolic representation |
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Egocentric initially, but at the end of the stage it began to vanish |
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Centration: Focus on only one aspect |
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Conservation: The idea which states the quantity of a substance remains the same even if transferred from one object to another |
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Concrete operational (7-11) |
Conservation |
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Seriation: Ability to understand that even if objects are placed at distant positions, their number remains the same. |
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Reversibility: Ability to understand that a process can be reversed. |
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Decentring: ability to think on another aspect. |
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| Transitivity: If A = B and B = C, then A = C | |
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Formal operational (11 yrs onwards) |
Abstract thinking (ability to be imaginative) |
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Learns complex calculations |
Hence, we conclude that in the Formal Operational Period of Cognitive development in a child, his abstract mathematical concepts are likely to develop.