You could say she was impressionable which I was too at this age and this is the the story of her first unhappy term as she gets to grips with school structures, rules and consequences.
Nancy's problems were less the stuff of theft, insubordination, refusal to apply ones self or bullying but more about what can be seen as maturity or rather the lack of age appropriate maturity at least in part because she was never really 'schooled' so failed to see how her impulsive reckless side so resulted in one child almost drowning and another catching a serious cold.
For Nancy this lead to the matter of her being 'asked' not because to return not formally expelled by Head Mistress Miss Cawdwell because she feels Nancy lacks the maturity a girl at boarding school needs. It also leaves the door open for her to return with a clean slate made easier for Nancy making a attempt in her last three weeks to do some good such as doing well in the swimming competition.
It's an enjoyable read not just for her spirit but also how working at channelling her interests starts to pay off.