Being an early educator, Piaget's theories play an important role in my beliefs on education. I agree that children follow through Piaget's developmental stages. Young children make meaning through play and interactions with the environment. Piaget also points out that much of the learning occurs through socialization. In the early years that is called play.

http://www.parentingscience.com/benefits-of-play.html

http://www.naeyc.org/content/research-news-you-can-use-play-vs-learning

That being said, it seems to me that it is the educator's responsibility to create an environment that motivates children to move through the various stages. I do not believe that you can or should force an unready child to move through more quickly. Yet, some children move more quickly through the stages than others. It then becomes the teacher's responsiblity to help guide a child, whether moving slowly or quickly. Attention needs to be paid to the environment and how it encourages students to grow. That classroom needs to scaffold the child ready to take off learning and the child who needs a little more time.