Sensorimotor is the first stage in Piaget's theory of cognitive development. Although this stage appears primarily physical, the child is developing a connection to the world through interacting with her environment. For example, one of the major developmental milestones of this stage is object permanence, being able to understand that an object continues to exist even when it is not seen. An activity that shows object permanence is to show a child a toy and then to place it out of sight while the child is watching. A child able to find the toy is displaying object permanence.
In the preoperational phase, children are developing their ability to think symbolically. This is seen in rapid language development and acquisition. The ability to think symbolically is also seen in the activity of pretend play. Children in the preoperational phase begin engaging in pretend play, such as creating specific scenarios, creating situations with characters and plots. Playing "house" and assigning roles such as mother, father and baby are examples of typical pretend play.
Concrete operations is the stage in which children start to be able to use logic. Although this ability is not as developed as it is with adults, it allows children to take other's perspectives and to gain a more clear sense of the physical world. For instance, children are able to understand the concept of conservation. Activities that demonstrate this ability include showing a child two glasses that hold the same amount of water but are different shapes. A child able to recognize that a tall, thin glass does not necessarily hold more water than a short, stout glass shows the ability for concrete operations.
As children grow into adolescents, they develop the ability to understand and apply abstract ideas and engage in advanced reasoning. Activities that show this ability include engaging in advanced mathematics and understanding multiple sides of an argument. Mathematical activities, such as the ability to understand geometry and algebra, demonstrate this ability. Engaging in courses at the college level also generally demonstrates abilities connected to formal operations.