Formal Operational Stage of Piaget's Cognitive Development Theory: An Implication in Learning Mathematics

IntroductionJean Piaget a well-known psychologist belonged to Switzerland. He developed Cognitive Development theory in 1952 and was known as Piaget's Theory. He was concerned with children cognitive learning and proved that how they responded to their surroundings. Piaget's theory centered on a rule that cognitive development starts in a sequence of four separate, universal stages. These four stages work for all time in similar order and each stage constructs on the basis of the prior stage. Piaget stated that cognitive development was a reformation progress of mind as a result of genetic, biological maturation and surrounding practice. Children pass through four stages of cognitive development up to the adulthood (Wadsworth, 2003).Cognitive development process is the formation and composition of thinking processes. It includes particularly identification, recall, solve difficulties, problems, hindrances, and make decisions about something from childhood to adulthood. Piaget's theory of cognitive development is concerned with information, knowledge and understanding, how a human being gains knowledge, builds knowledge as well as applies knowledge (Wadsworth, 2003). In view of Piaget (1964) cognitive development in early period contains processes which are based upon some actions and in later period cognitive development involves mental operations. Ojose, (2008) asserted that Piaget's theory on cognitive development stages are Sensorimotor (0 - 2 years), Pre operations (2 - 7 years), Concrete operations (7 - 11 years), and Formal operations (12 - 16 years).Cherry (2014) explained that in view of Jean Piaget, children grow within four stages of cognitive development. Each stage is characterized, how children understand the world around. According to Piaget, children are like little scientists. They try to discover the world around them. Piaget proposed that there is a qualitative change in kids during these four stages. During the sensorimotor stage (0 - 2 years), infants gain knowledge through sensory practices, using different things. Piaget (1977) distributed the first stage into six sub-stages having specific time of each sub-stage with composition of actions such as visualization, seeing, hearing, investigation, physical and motor practices e.g. catching, sucking something, and trying to stand. Piaget explained that ability to count numbers or things like one cock, two cats, three dogs, four tigers etc are additional features of sensorimotor stage. According to Essa (1999), language and some symbolic actions are developed in preoperational stage. However, thought process is not consistent up to this stage. Children comprehend simple categorization, ordering, function, games, etc. Piaget (1977) explained that at the preoperational stage (2 - 7 years), children gain knowledge through imaginary play. They try to use their senses and acquire opinion of other people. During the concrete operational stage (7 - 11 years), children start thinking more logically, but their thinking may be inflexible. Children make an effort with abstract and theoretical thought.Cherry (2014) stated that the formal operational stage (12 - 16 years) of Piaget's cognitive development theory involves increase in sense or intellect, the ability to exercise deductive way of thinking plus understanding of conceptual thoughts. In this period, children build up their ability to reflect on abstract concepts and develop ability of logical thoughts (use general principles to find out specific results), deductive reasoning, and systematic arrangement. In abstract concepts, children think about probable result and effects of any activity. Abstract concepts are helpful in long-term planning. Deductive logic is required especially in science and mathematics. Children are able to solve a problem quickly in an organized way. Brain and Mukherji (2005) stated that in formal operational stage, actual things are no longer required and intellectual operations can work 'in the mind' using conceptual words. …