She appears to be a cynical and sarcastic person, commenting that Bart will see a lot of F's in the future. She is also the one initially responsible for making Bart feel miserable and unable to fit in at school, which leads to his crave for attention through mischievous behavior. It is presumed that she either quit or was fired, prior to the current kindergarten teacher.
In "Lisa's Lifeline" of The Lisa Book, it is mentioned that Lisa convinced the kindergarten teacher to quit and join the military, through logical argument. It can be implied that this is the very same teacher.