Human development is inclusive of cognitive development which its basic premises involves the thoughts construction process. This occurs through the ability to remember, being in a position to solve different problems and the capability of making individuals decisions from infancy, in the course of adolescence to adulthood. Teachers therefore have the responsibility of understanding how the children and the adolescents mentally develop which is considered as a gigantic component of the learning development. This therefore enables the teacher to accommodate all different students with different levels of understandings in classroom. There are many theories which discuss the cognitive development in children and adolescence thus this discussion is inclusive on some of these theories.To begin with, different theorists have discussed on the cognitive development while differing in some aspects but in one way or another they have some commonalities. In comparison of Piaget and Vygotsky approach on intelligence development, they both acknowledge intellectual development to take place when the acquirement of sign coordination occurs. They both believe that the invariant progression of steps for children and adolescence are the same and also they both feel that the cognitive conflict initiate the development. On contrast Piaget believes that for any learning to occur, there must first be the occurrence of specific development. Vygotsky approach on this is the opposite in that learning must take place before the occurrence of any specific development (Keenan, 2002).On developmental stages, the two theorists have some similarities all through from the time of birth to the adolescence. They both advocate on the social factors having significant position on developmental stages. They both acknowledge on the importance of children and adolescent learning culture symbol coordination. They both agree that some tasks are beyond understanding capacity range of adolescents and children where Vygotsky views that they can however get assistance from capable people. On contrast in developmental stages, Piaget takes cognitive development as a process that contains four stages. The sensory motor is his first stage which is from the time of birth to two years followed by preoperational stage which occurs at the age of two to seven years, then concrete operation that takes place in seven to eleven years and the last stage as formal operational which starts at eleven years all through to adulthood (Oakley, 2004). On the other hand Vygotsky considers two elements instead of stages. The two elements include: private speech and proximal development zone.In classroom applications of the two theorists, they too have some similarities and differences. On Piagets theory classroom application in a kindergarten classroom where children are on preoperational stage, there is the act of sharing then doing some acting what will be done afterwards. Some may be for the idea of making snowmen while others snow angles where they all have correct responses. Vygotskys theory application, there can be a consideration of a third grade experience of a classroom where there is classification of different rocks in reverence to their diverse characteristics. Formation of groups would allow the other students to speak out in their classification of rocks. This loud thinking gives an opportunity to the fellow peers to listen to their thinking process while being in a position appreciates other views on rocks thus promoting learning in different groups. There are similarities in the above different learning applications where in both case there is the act of listening to the loud thinking and also in both there is interaction with the environment even though using different theory applications (Keenan, 2002).