I read it several years ago then lost it. Had a purple cover and was pretty old (I think published in the 60s or 70s but not sure).
It was about a girl who went to stay in a remote cabin for a summer with her dad, who was a researcher on the subject of psychic abilities. She wasn't happy about it, but her parents were divorced, so she had to go.
Lo and behold, their nearest neighbor is an old lady who has psychic powers and helps the girl/main character development her own psychic powers. The old lady has several kids including an adopted son also with psychic powers.
There is a climax where the girl gets stuck in the woods during a big storm/flash floods and has to call for help using her mind. So her father the researcher gets in on the whole psychic thing and also kind of seems to make "special friends" with the old lady. And the girl is invited to go to a school for psychic powers.
It's the first in a trilogy or series. The psychic powers are very low grade, not flashy. It was a really good book.