Piaget's Theory
One theory that is useful in the classroom is Jean Piaget’s theory of cognitive development. Piaget believed that there were four stages, which the majority of children experience during cognitive development. They are: sensorimotor, preoperational, cognitive operational, and formal operational (Piaget, 1954). Because I plan to teach at the high school level, I would assume that most of my students would be in the formal operational stage, and thus I would base my teaching on this stage. The formal operational stage usually emerges when adolescents are between the ages of 11 and 15. In this stage adolescents can think logically about abstract concepts or hypothetical situations, and then use reasoning to solve problems (2.2) (Berk, 2000). This theory is relevant to teaching a high school math class because it tells me that almost all of the students that I teach will be able to think abstractly, so I can give them problems that require them to think and work on their own (2.5).
The formal operational stage can be implemented in math teaching strategies by giving students problems that force them to think abstractly. Students start to learn how to think abstractly in Algebra when they learn that variables represent a specific quantity. In Algebra students can manipulate and solve equations without needing to refer to a concrete example. If I teach Geometry in the future, I will give my students a problem that requires them to prove that two angles in a polygon must be the same. This type of problem uses formal operational thought because it forces the students to think about what makes an angle congruent. While children may think very concretely, formal operational students would be able to understand that even if two angles look the same in the picture that does not necessarily mean that they are congruent. Students in the formal operational stage can see past the physical aspects of a picture to solve a problem.