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*At the same time, the child is able to identify the properties of objects by the way different kinds of actions affect them. This is the process of "empirical abstraction".
*By repeating this process across a wide range of objects and actions, the child establishes a new level of knowledge and insight. This is the process of forming a new "[[cognitive]] stage". This dual process allows the child to construct new ways of dealing with objects and new knowledge about objects themselves.
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This process may not be wholly gradual, but new evidence shows that the passage into new stages is more gradual than once thought. Once a new level of organization, knowledge and insight proves to be effective, it will quickly be generalized to other areas ''if they exist''. As a result, transitions between stages can seem to be rapid and radical, but oftentimes the child has grasped one aspect of the new stage of cognitive functioning but not addressed others. The bulk of the time spent in a new stage consists of refining this new cognitive level; however it does not always happen quickly. For example, a child may see that two different colors of Play-Doh have been fused together to make one ball, based on the color.
It is because this process takes this [[dialectic]]al form, in which each new stage is created through the further differentiation, integration, and synthesis of new structures out of the old, that the sequence of cognitive stages are logically necessary rather than simply empirically correct. Each new stage emerges only because the child can take for granted the achievements of its predecessors, and yet there are still more sophisticated forms of knowledge and action that are capable of being developed.
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At the same time, by reflecting on their own actions, children develop an increasingly sophisticated awareness of the "rules" that govern them in various ways. For example, it is by this route that Piaget explains this child's growing awareness of notions such as "right", "valid", "necessary", "proper", and so on. In other words, it is through the process of [[objectification]], [[Introspection|reflection]] and [[abstraction]] that the child constructs the principles on which action is not only effective or correct but also ''justified''.
One of Piaget's most famous studies focused purely on the discriminative abilities of children between the ages of two and a half years old, and four and a half years old. He began the study by taking children of different ages and placing two lines of sweets, one with the sweets in a line spread further apart, and one with the same number of sweets in a line placed more closely together. He found that, "Children between 2 years, 6 months old and 3 years, 2 months old correctly discriminate the relative number of objects in two rows; between 3 years, 2 months and 4 years, 6 months they indicate a longer row with fewer objects to have "more"; after 4 years, 6 months they again discriminate correctly" (''Cognitive Capacity of Very Young Children'', p. 141). Initially younger children were not studied, because if at four years old a child could not [[Conservation of quantity|conserve quantity]], then a younger child presumably could not either. The results show however that children that are younger than three years and two months have quantity conservation, but as they get older they lose this quality, and do not recover it until four and a half years old. This attribute may be lost due to a temporary inability to solve because of an overdependence on perceptual strategies, which correlates more candy with a longer line of candy, or due to the inability for a four-year-old to reverse situations.
By the end of this experiment several results were found. First, younger children have a discriminative ability that shows the logical capacity for cognitive operations exists earlier than acknowledged. This study also reveals that young children can be equipped with certain qualities for cognitive operations, depending on how logical the structure of the task is. Research also shows that children develop explicit understanding at age 5 and as a result, the child will count the sweets to decide which has more. Finally the study found that overall quantity conservation is not a basic characteristic of humans' native inheritance.
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