I adopted a 4 month old kitten three weeks ago. She was bottle-raised in an animal shelter with siblings, without adult cats. My kitten and the littermates were considered properly litter trained at the shelter, using hooded litter boxes without an entrance flap. She is the only cat in the household.
She now has an open litter box (hooded is not an option due to space problems) and she is happy enough to use it. Only, she seems to be going through the motions without doing it properly.
Typically, she will go into the box, and make digging motions with the front paws, without making too much of a hole. Most times, she will turn around, but sometimes she even skips that. She then squats a little, but not deep, and sometimes raises her hindquarters back to almost standard position while she urinates. Then she makes a few more digging motions with the front paws, without actually aiming at the wet spot, and gets out of the box.
The problem is, sometimes the bad squatting means that she will simply overshoot the box wall and the urine will land on the floor outside the box. She doesn't show any concern over that (e.g. no going over to inspect the smelly puddle).
From what I can tell while observing her, she is not doing it deliberately. She doesn't seem to be unhappy about anything, to avoid the box, or to urinate intentionally outside. Also, it doesn't look like she is spraying - she is female, too young, and doesn't try to take the spraying position with intentionally raised hindquarters. It just looks like she has a vague instinct for the required motions (digging, squatting) but she hasn't gotten the hang of what they are for or how they fit together into a proper, clean toilet-going. So she does them half-heartedly, and metaphorically and literally misses the point.
She also displays a rather dominant personality (I suspect she has never taken a beating from another cat, since she was on the large side within the litter) and shows much less fear than I am accustomed to from cats, which would point to her not caring much to cover her toilet leavings.
Without the example of an older cat, are there ways to teach her to use the toilet better? A lower squat would be a solution, but I don't know how to get this information through to her :)