The lesson that we can learn about children is based on the difference between the nurse's idea of what it means to play together and the children's own idea of what it means to play together. What is fascinating about this short story is the way that the children are engaged in completely separate activities in the same room and don't seem to even acknowledge each other's existence. Note the following description:

The little girl took a picture book, sat down under the table with her back to Tom, and slowly, carefully, examined each page. "It's got a crooked wheel," Tom said, "that's what it is." The little girl made no answer.

We have two children both involved in their own activities and yet both are content and happy to be together even though it appears they are apart. The Nurse's response to this seems to impose an innaccurate view of the situation on these two children and causes problems whereas if they had been left to themselves they would have been happy. The lesson perhaps is that children play in ways that are difficult for adults to understand, and can actually "be" together even when they appear as if they are not.