Theory:

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The narrator

The narrator is a curious person with an appreciative mind. He goes to the school to learn more about the unique system followed by them. Although the profession of the narrator is not mentioned in the lesson, it could be assumed that he was either a writer or a columnist. Since E. V. Lucas worked as a writer and an editor in his real life, it could be assumed that the narrator was drawn from the writer's real life. The narrator was probably at the school to do an article or story on its unique system. Another critical aspect of the character is that he has undergone a great transformation by the end of the lesson. In his words, he became ‘ten times more thoughtful than he had ever thought he would be’.
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Miss Beam

Miss Beam is the headmistress of the school. She has a kind and an authoritative look. Miss Beam is in her middle-age, and her hair has started to grey. Her plump figure gives her an approachable and comforting appearance. According to the narrator, her presence can make a homesick child feel comfortable.

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The young girl

The young girl is on her blind day. She expresses her feelings and experiences of the special days. She can be seen as a representative and the voice of the student community. It is through her conversation with the narrator that we get to learn more about the school and its unique system.