When the story begins, Jerry is anxious for some freedom from his mother's watchful and protective eye. However, "Contrition sent him running after her." He felt badly for wanting this independence and doesn't leave her on this first day of vacation. This year, he's much less interested in the "safe beach" they've always frequented in the past; he wants to go to the "wild bay," alone.
The next day, he gets his chance, and when he looks back at her beach, he feels "relieved at being sure she was there, but all at once very lonely." He misses her but soon becomes distracted by some older "boys -- men to Jerry" who come along and take turns diving off the rock. They eventually amuse themselves by swimming through a tunnel in the rock, and since Jerry cannot do it, he begins to clown around to refocus their attention on him. It doesn't work, and they leave him, crying like a child. Cried out, he "swam out to where he could see his mother. Yes, she was still there, a yellow spot under an orange umbrella." He seems to want to be free of her, but -- at the same time -- he wants to know that she is nearby.
As he begins to grow more confident in the water, he feels that his old beach "now seemed a place for small children, a place where his mother might lie safe in the sun. It was not his beach." And next time, when he goes, he does not ask her permission first. It is at this point that "A curious, most unchildlike persistence, a controlled impatience, made him wait" to attempt swimming through the rock yet. His ability to delay gratification provides evidence of his growing maturity (he was unable to do so earlier when he accosted her for goggles), as does the fact that it doesn't occur to him to ask her, anymore, if he can go to the bay without her.
In the end, after his experience in the tunnel has seriously frightened him, Jerry does return to her, still a child -- at least, for a while. He calls her "'Mummy'" and clearly wants her approbation and praise for his new ability to stay underwater for three minutes. When he tells her this news, "It came bursting out of him." Jerry has obviously begun the process of maturing, though it seems that one's progress toward maturity is not a straight line, and we can see that in his fluctuating relationship with his mother.