• Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation.Developmental Psychology, 41, 189–201.
• Seigler, Robert. “Cognitive Development.” Cognitive Devlopment. NOBA, 03 Nov. 2010. Web. 24 Feb. 2016.

The Author/professor known by Robert Siegler and his research colleagues at Carnegie Mellon University diagnosed the relationship between quantitative and qualitative changes in cognitive development and how that affects your ability to learn either continuously or discontinuously. Cognitive researchers have differentiated society into categories by their ability to accept change or to acknowledge new information more rapidly than others. The psychologist by the name of Jean Piaget and other researchers conducted that there are four stages of the cognitive development process that humans encounter through the different periods of life. One of the four stages that the Jean introduced was the sensorimotor stage that is typically anywhere from birth until the age of two. During this stage their thinking inside the brain relies primarily with their encounters and interactions of viewing how the world works and how people are. It is also hard for the brain to conceptualize objects for people at this time period. This is so because its difficult for them to know that the object still exists without them physically examining it. The second stage of the cognitive development is called pre-operational stages were in this stage a person can only achieve a one dimensional perspective of things. Things such as strategic word problems and other things that requires you to use your “out side of the box” capabilities would be very difficult.  When children are capable viewing life in a second dimensional or start utilizing their “outside the box”capabilities then this is called the Concrete stage of cognitive development. Even though they can view life in other perspectives they still cannot get a full understanding of complex problems and solutions. Finally in the formal operations period is when a person should be able to learn, accommodate, solve and think in a systematic scientific way. The Researchers and publishers of this article is trying to inform to the readers that cognitive development process is vital when come to thinking outside the box and people who have problems at these stages are at high risk of attentional fatigue.