Mrs. Appleyard Doesn't Know the Poem She Assigns (Dramatic irony)
At the beginning of the novel, Sara is left at school as punishment for misbehaving. Mrs. Appleyard assigns her a poem to memorize, thinking it will be to her academic benefit. However, Mrs. Appleyard actually incorrectly identifies the author of the poem, despite remaining vehement that Sara is unintelligent and bad at school. In this instance of dramatic irony, Mrs. Appleyard condescends to her student despite not knowing what she is talking about, reflecting her lack of understanding of her own situation.
Mrs. Appleyard Is Disappointed That Irma Returns (Situational Irony)
Mrs. Appleyard is disappointed by Irma's return. She immediately assumes that Irma's returning without Miranda and Marion actually makes her look worse than if all three girls had never come back. In this moment of situational irony, Mrs. Appleyard shows she would prefer for the girls to have all remained gone, going against the reader's expectation that she would be happy to see at least one of her students safe.
Mrs. Appleyard Dislikes Dora Lumley (Dramatic Irony)
Mrs. Appleyard takes an intense dislike to Dora Lumley, finding her dull and irritating. However, she actually has more in common with her than she does with Mlle. de Poitiers, who she likes more. Dora is similarly inflexible in the way she thinks about the rules and has no qualms about harshly rebuking students. This is displayed when she insists on telling Mrs. Appleyard about the incident in the gymnasium. In this instance of dramatic irony, Mrs. Appleyard shows distaste for the person at the school who most closely resembles her. Once again, the reader sees her complete lack of insight about her character.
Sara's Guardian Pays Her Tutition (Situational Irony)
Sara's guardian, Mr. Cosgrove, writes a letter to the school with a check enclosed for Sara's tuition. This not only reveals that Sara is missing, but also demonstrates that Mrs. Appleyard was simply penalizing Sara because she did not like her. Her guardian not only paying the tuition but also clearly being well off, as he is investing in mining abroad, demonstrates that Mrs. Appleyard has just been harboring a grudge. In this example of situational irony, the reader discovers that Mrs. Appleyard has not accurately represented a number of facts about Sara and that her treatment of her is almost entirely based on a personal grudge.