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Vicki Valentine was a child star in the late 1930s and early 1940s. She appeared in over forty movies, among them Little Vicki for President, Little Vicki vs. Big Rhonda, and Hell Hath no Little Vicki, a war-themed movie whose poster showed her as a gunner in a bomber plane. When she grew up, she generally preferred to be called "just plain Vicki" rather than "Little Vicki" or "Little Miss Vicki," but apparently still reserved the right be called "Little Vicki" in a professional (i.e., dancing-related) context.
Vicki eventually became a dance instructor, and had her own studio—Lil' Vicki Valentine's School of Dance—in Springfield Mall. In her studio, Vicki kept her child-star movie posters on the walls. As an instructor, Vicki had a reputation for being very strict, but was also very successful, teaching many people how to dance. Lisa Simpson and Ralph Wiggum joined one of Vicki's dance classes. Ralph discovered that he was a natural at dancing, but Lisa just didn't have any knack for it and kept falling down.
Typical for performers, Vicki had a well-developed ego to go with her sense of professionalism. When Lisa borrowed a pair of high-tech automatic tap shoes from Professor Frink, the shoes went out of control, and Lisa ended up dancing onto the stage and interrupting a recital in which Vicki was starring. Vicki took Lisa's interruption as a personal affront and a deliberate attempt to upstage her, and matched Lisa (or rather, the shoes) move for move, until the shoes short-circuited and took Lisa off of the stage. When Vicki learned that Lisa had been using automatic tap shoes, she was highly offended, but understood Lisa's using the shoes out of a strong desire to be a dancer.
 Behind the Laughter