PIAGET'S COGNITIVE CONSTRUCTIVIST THEORY
concept
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Jean Piaget
Jean Piaget's (1952) theory states that people are internally motivated to learn about the world around them. He believed that individuals go through four stages of development. Piaget states that in order for adolescents to make sense of our world they organize their experiences. This allows adolescents to separate important from unimportant information, and connect ideas to one another (Miller, 2011). Piaget also states that while constructing a healthy life adolescents use schemas, which is a useful way of organizing and interpreting information. The first of the two processes of a schema is assimilation. Assimilation is the way in which adolescents incorporate new information into their knowledge. The second process of a schema is accommodation. Accommodation is how the adolescent adjusts their schema based on the new information. These ideas are important to healthy adolescent development.
Piaget's theory states that individuals develop through four cognitive stages. The first stage, sensorimotor, is where infants gain knowledge by their physical actions. The second stage, preoperational, is where the child begins to use mental representations to understand the world around them. The third stage, concrete operational, is where the child can use logical thinking. The fourth and final stage of cognitive development is the formal operational stage. The formal operational stage is where the adolescent reasons in a more hypothetical-deductive way (Piaget 1954).
The fourth stage of Piaget's (1954) cognitive stage development, formal operational, is the stage at which the adolescents will be taught a higher level of math. Piaget concluded that this stage takes place at eleven to fifteen years of age. At this stage adolescents develop a way to problem solve and test solutions systematically, which gave it the name hypothetical-deductive reasoning (2.6). Hypothetical-deductive reasoning is the ability to use best guesses in order to solve problems, such as algebraic equations.
Another aspect of Piaget's cognitive development theory is idealism (Harter, 2006). Adolescents at this stage begin to think in more abstract and idealistic ways. For example, if an adolescent was asked to describe themself they would be most likely to use abstract and idealistic terms. So if an adolescent was asked to describe themself in an abstract way they would describe themself from a broader, more obvious perspective. If an adolescent was asked to describe themself in an idealistic way they would describe themselves in a narrowed, more ideal way. With time the way adolescents view themselves change, which is all part of a healthy
development.
Piaget's theory states that individuals develop through four cognitive stages. The first stage, sensorimotor, is where infants gain knowledge by their physical actions. The second stage, preoperational, is where the child begins to use mental representations to understand the world around them. The third stage, concrete operational, is where the child can use logical thinking. The fourth and final stage of cognitive development is the formal operational stage. The formal operational stage is where the adolescent reasons in a more hypothetical-deductive way (Piaget 1954).
The fourth stage of Piaget's (1954) cognitive stage development, formal operational, is the stage at which the adolescents will be taught a higher level of math. Piaget concluded that this stage takes place at eleven to fifteen years of age. At this stage adolescents develop a way to problem solve and test solutions systematically, which gave it the name hypothetical-deductive reasoning (2.6). Hypothetical-deductive reasoning is the ability to use best guesses in order to solve problems, such as algebraic equations.
Another aspect of Piaget's cognitive development theory is idealism (Harter, 2006). Adolescents at this stage begin to think in more abstract and idealistic ways. For example, if an adolescent was asked to describe themself they would be most likely to use abstract and idealistic terms. So if an adolescent was asked to describe themself in an abstract way they would describe themself from a broader, more obvious perspective. If an adolescent was asked to describe themself in an idealistic way they would describe themselves in a narrowed, more ideal way. With time the way adolescents view themselves change, which is all part of a healthy
development.
classroom
Piaget's cognitive constructivist theory can be applied in a math classroom through hypothetical-deductive reasoning. Hypothetical-deductive reasoning is the ability to use best guesses in order to solve problems. Numerous algebraic equations can be solved more than one way, but there are certain rules that have to be followed. For example, if a person wants to solve a+b/b they have to realize that the 'b's cannot cancel out because it is addition. But if the problem was ab/b, then the 'b's could cancel out because 'a' and 'b' are being multiplied. These are rules that have to be followed when solving equations, but there are different ways of getting the same answer.
If an adolescent was trying to solve an expression, based on hypothetical-deductive reasoning, the adolescent would have to choose the most logical formula to fit the problem. The adolescent can then test their hypothesis through trial and error, by plugging in the formulas to see if they would fit the specific expression. One way to apply this in the classroom is by having a problem of the day. Every day the students come into class there would be a different expression on the board. The students could be asked to use different formulas they have learned over the past week or so, given in their notes, to try and solve the equation. The problem will not necessarily have to count against them if they get it wrong, but it would be a good way to get their minds set on math before class begins.
If an adolescent was trying to solve an expression, based on hypothetical-deductive reasoning, the adolescent would have to choose the most logical formula to fit the problem. The adolescent can then test their hypothesis through trial and error, by plugging in the formulas to see if they would fit the specific expression. One way to apply this in the classroom is by having a problem of the day. Every day the students come into class there would be a different expression on the board. The students could be asked to use different formulas they have learned over the past week or so, given in their notes, to try and solve the equation. The problem will not necessarily have to count against them if they get it wrong, but it would be a good way to get their minds set on math before class begins.