This is the second stage of cognitive development according to Piaget. This includes children who are two to seven years old and probably who are in preschool. The notable characteristic of this stage is that children can now make believe or pretend through the use of symbols. This is called "symbolic function". The most dominant symbol used is language, wherein children represent the objects that they experience through names or words. They can also use a certain object to symbolize or represent something else. Just imagine the tv commercial of a popular milk. The girl was singing something like "Mom said, don't eat your WOOOOOORDS!...She said, I have a beautiful VOOOOOOICE!".hahaha... Well, as you have seen, she was singing using a hair brush as her microphone. She pretended that the hair brush was her microphone. Have you seen your little brother or sister play? The boys especially in which they use sticks as their swords. But as they grow and develop, they can pretend only in their mind even without these objects. Again, imagine you as a child or seeing children play "Power power rangers" or " Good Morning Princess".(Do you know these games?hehe). Those explain it.
Aside from symbolic function, children have the tendency to be egocentric. It means that they do not assume that each of us has different perspective. They believe that their point of view is the same as with all the people. This is the reason why for example, children have occasional "mine is better than yours" arguements with their agemates or your nephew or niece will ask you why you didn't call his/her mama or papa "mommy" or "daddy".
Another characteristic of these stage is what we call centration. This can be explained by the experiment done by Piaget himself. In his experiment, he presented a child two identical glasses with the same amount of water. When the child was asked which glass has more water, he answered that both glasses are the same. However, when the water from one of the glasses was transferred to a narrower but taller glass, and was asked again, the child chose that the taller glass has the greater amount of water. This is centration. The child "centered" only on one aspect that is the tallness of the glass without taking into consideration the narrowness of it. This can also be seen when children tend to determine the sex of the people they meet. Boys wear pants while girls wear skirts. Or they will say that a person is already old when they see that that person is wearing glasses, has gray hair or has a mustache, without considering the age or the other details.
Furthermore, children on this stage are very animistic. This is very obvious when they play dolls and stuff toys. And they will say to you not to throw their teddies and handle it with care because teddy might get "hurt". Or seeing a girl telling her agemate not to pick the leaves or the flowers of a plant because the plant will cry.
According to one of our textbooks in college by Corpus, preoperational children has transductive reasoning. For example, if a preschool will be asked why there are no classes, he will probably answer "because it's Saturday." And if you'll ask again, "How did you know that it's Saturday?" He will probably answer "because there are no classes."
Lastly, children on this stage has still the inability to reverse their thinking. In short, they still don't know that 1+2 is still the same with 2+1. This is the reason why I really had a difficult time explaining to my 6-year old tutee the commutative property of multiplication. That is why I wondered how come this topic was included in an Elementary Mathematics textbook for grade 1. Psychologically, this is inappropriate considering the mental stage of children. However, I thought that the author intended to put this topic maybe in order to help children develop reversibility. This might be true especially with the help of an adult, a teacher or a parent, or an older significant other, children will gradually develop the ability of reversibility.
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