Katy books

Im reading some of the Katy books by Susan Coolidge. They are set in the USA, about a widowed doctor who has 6 children, in a small town in the West. Katy is the eldest, rather harum scarum and thoughtless but warm hearted. She has 3 sisters, Clover, Elsie and the boyish Johnnie (Johanna). There are 2 brothers. Katy and the children are looked after by Aunt Izzie, the doctor's sister who is kind but strict... Katy has a fall one day from a swing, having been told not to play on it. She did not know that it needed mending and was not safe and she has a bad fall that jars her spine, and she is told that she may never walk again and that to have some chance of recovery, she will have to lie in bed and rest. She is utterly miserable, but receives a visit from a cousin, Cousin Helen, who also has a back injury that has left her crippled. Helen persuades her that she may recover if she does what the doctor tells her and tries to make a life for herself. She is only 12, and Helen tells her to keep up with her school work, and not neglect her education. Katy tries to follow Helen's advice.... but then Aunt Izzie dies.