In 1993, a dozen children became the face of a million New York City public school students when a lawsuit was filed on their behalf.

Among the dozen were three girls: Sumaya Jackson, who was 6 and dreamed of becoming a dancer; Alina Lewis, a teenager who thought about becoming a teacher even though the elementary school she had gone to seemed on the verge of falling down, and Erycka DeJesus, who traveled far from her district in Queens to go to a Manhattan high school that wasn’t overcrowded. Their parents charged the city’s schools with failing to provide them the level of education guaranteed by the state constitution.

For 13 years, the lawsuit has churned through an obstacle course of appeals and politics while the three girls have grown. Ms. Jackson, now 19, is studying at Juilliard to become a dancer after attending a private high school. Ms. Lewis, 27, teaches at a public school in Brooklyn. She buys books and supplies with her own money to make up for what the school lacks. Ms. DeJesus is 30 and sends her 5-year-old son, Jah’Neil, to kindergarten out of his district, where she says the schools are overcrowded.

“It’s kind of sad this lawsuit has been drawn out for so long,” Ms. DeJesus said. “I have a family of my own now, and I realize what not having just certain basic things, how it impacts you.”

A hearing in Albany tomorrow could bring the lawsuit closer to its end. The coalition that filed the lawsuit, the Campaign for Fiscal Equity, is hoping the appellate court will order the state to pay between $4.7 billion and $5.63 billion a year in operating aid to New York City public schools. In the past, the Court of Appeals has declined to specify the amount the governor and Legislature must pay, leaving it up to them to decide. The state has already pledged $9.2 billion in capital aid to the city that will be phased in over five years, but the Legislature has resisted court rulings ordering it to allocate the rest of the extra funding to city schools.

Yellow buses full of CFE supporters are driving to Albany today for a rally on the steps of the court before the hearing. If the appellate court rules in their favor and orders the Legislature to pay the city at least $4.7 billion, supporters say, their celebration will be tempered by the fact that the money comes too late for many students.

“An entire generation of children has gone through the New York City schools since the lawsuit was filed,” the director of the CFE, Geri Palast, said. “We believe strongly another generation of children shouldn’t suffer.”

Some opponents of the campaign note that funding for city schools has doubled during the course of the lawsuit with little effect on student performance. The reading scores of city fourth-graders have gradually improved, but those of eighth-graders have stayed flat.

Opponents say this is evidence that more money won’t make a difference in the effort to improve city education. They also say the lawsuit has wasted millions of dollars on litigation that could have gone to schools instead.

Ms. Lewis, who buys her own school supplies for her social studies classes, says the extra money is exactly what the schools where she attended and now works need.

“It’s only now I realize the things I didn’t have in high school compared to other people … all those extra things, and smaller classes,” she said. “In the last school I was in, it was just the bare bones, the classes were so dreary and everything was so old, we didn’t even have screens for overhead projectors.”

This year, she moved to a new charter school, Brooklyn Latin, where conditions are better.

“I feel like we’re super lucky,” Ms. Lewis said. “Everyone else that is in public school deserves that, too.”

Ms. DeJesus, a mother of two who is studying speech pathology at Lehman College, said she thinks of her public school days often as she studies for a college level physics class that she is failing. If she doesn’t pass, she can’t earn her degree. Looking back now, she says more funding might have helped her school buy supplies for science labs and hire more teachers.

“I don’t remember ever getting any real science in high school,” she said. “How could you be prepared when you have 33 people in a classroom and no textbooks you can take home because there were not enough to go around?”

She added: “I look at myself, and I don’t want this to happen to my children.”

Ms. Jackson, whose older sister Asmahan was also a plaintiff and is now a public school teacher in Buffalo, ended up going to a private school. She wanted to be in smaller classes and participate in extracurricular activities such as music and dance, though her parents made the choice reluctantly — her father is Robert Jackson, a City Council member who heads the Education Committee.

“The school I went to was a really, really good public school,” she said. “But I wanted to be in a small environment.”

At the private Dwight School, she took classes in the International Baccalaureate program, similar to the Advanced Placement program, competing against students who had attended private schools with small class sizes and individualized attention from teachers.

“They had an advantage,” Ms. Jackson said.

Overall, however, Ms. Dejesus, Ms. Jackson, and Ms. Lewis say their experiences in the public schools were good ones, but mainly because their parents were so involved and made sure they went to the best schools in the city. They say their role in the lawsuit has been to represent other children who aren’t so fortunate.

“It should be not necessarily that everybody gets the same,” Ms. DeJesus, said, “but that everybody gets what they need.”