One way Anne matured is that she has really thought about what she has said about her mom. What the text says is,”...letters dealing with the subject ‘Mummy’ in such a hot headed way that I was quite shocked…”. What she means is that in the past, she has written about her mother so badly, she was shocked. So that means she will probably not talk about her mom in such a bad way again, which shows she has matured.
Another way Anne has mature is that she doesn't argue with her mom all the time anymore. In the text it states,”The period