The children in Rosie Ferraro's preschool class sang songs about their toes, the American flag and a gingerbread man. They counted days on a calendar and counted each other.

When they started class in September at Fairfax County's Belvedere Elementary School, many of the children didn't know what a letter was. Now, all but the youngest child -- a 3-year-old -- print their names each day.

As Virginia's Democratic Gov.-elect Timothy M. Kaine prepares to take office next month, making classrooms like Ferraro's available to every 4-year-old in the state is among his most ambitious goals. Publicly funded preschool is offered to about 27,000 disadvantaged Virginia children, but, by the time Kaine leaves the governor's mansion, he wants to open it to all children who want to attend, regardless of family income.

Kaine's push for universal preschool comes amid a nationwide movement to expand state-funded pre-kindergarten classes aimed at helping the youngest children -- particularly those from disadvantaged backgrounds -- prepare for school. According to Pre-K Now, a Washington-based early-childhood advocacy group, over the past year state legislators nationwide added $600 million for pre-kindergarten programs.

"I really do believe we need to change the paradigm of public education, so it starts earlier in a child's life," Kaine said. "A child's brain is pretty much formed by age 5, but we put most of our education dollars into systems that pick up after that."

In a recent study of five state-funded preschool programs, the National Institute for Early Education Research at Rutgers University found that children who participated knew more letters than their peers, improved their vocabulary and learned more math. Studies suggest that all children benefit from high-quality preschool, but those from economically disadvantaged backgrounds have the greatest gains.

"The kids get to school, and they know more stuff, and they have more skills and they behave better," institute Director W. Steven Barnett said. "They do better in school. They are more likely to graduate from high school. They are less likely to get in trouble."

More than 40 states fund preschool classes targeted largely to disadvantaged children. Two states, Georgia and Oklahoma, offer universal preschool that reaches large percentages of children. Other states, including West Virginia and New York, are working toward such programs. In Florida, voters approved a constitutional amendment in 2002 that mandates universal pre-kindergarten for all children, but the program initially attracted far few children than officials had estimated it would.

Maryland educators are expanding a state-run preschool program that will make classes available to all eligible children from poor families by September 2007. And this month, D.C. School Superintendent Clifford B. Janey announced the addition of 36 pre-kindergarten classes in schools and the community.

Kaine's Start Strong plan, which he says would cost about $296 million a year after it is fully running by the end of his four-year term, is in its early stages. Many details -- including the required teacher qualifications and salaries -- have yet to be decided. But although the proposal appealed to many voters, some state lawmakers and educators say Kaine will face significant challenges as he works to offer preschool for all of the state's 100,000 4-year-olds.

Virginia legislators across party lines said money to expand preschool will be tough to come by because voters are clamoring for solutions to traffic congestion, the cost of health care programs is rising and public schools want more money to improve existing programs. And some lawmakers and educators question whether it makes sense to fund preschool for children whose parents are able to teach them at home or pay for private school.

House Appropriations Committee Chairman Vincent F. Callahan Jr. (R-Fairfax) called Kaine's plan laudable. He said, however, that he will be hard-pressed to support funding for preschool given the other needs of constituents.

"That program is going to have problems -- not that it's not worthwhile, but because of the competition," Callahan said.

Del. Brian J. Moran (D-Alexandria) agreed that lawmakers will have to weigh the need for improvements to the transportation system and funding for schools and social services. Universal preschool "is worth our commitment and investment," Moran said. "But it will have to compete with those acute needs."

Kaine said he intends to seek $74 million for the program in his first year as governor and add $74 million each year. By the end of his term, the program, which would be voluntary, would be fully funded. Officials predict that about 80 percent of families with 4-year-olds would enroll their children.

Kaine said he's convinced that the classes would pay for themselves eventually because years down the road, students would need less remediation, jails would house fewer minors and more children would graduate from high school ready for college or work. But, early on, he said, he'll have to "be creative when writing budgets."

Kaine's plan will build on an existing state-funded program that serves about 11,300 children. State officials said 25 localities didn't seek funds for the program this year, largely because there was no space for classes in public schools or local governments didn't provide required matching funds.

Kaine said he will set up advisory groups of parents, educators and businesspeople who will work to decide how to best provide preschool in their localities as well as a statewide council to oversee the process. Classes could be held at public schools or through a network of existing private schools -- a way to ensure there is enough space available.

Del. R. Steven Landes (R-Augusta), whose 3-year-old son attends private preschool, said that he backs current state funding for preschool for children from poor families but that new state funds might be better spent improving public schools or health care.

"I understand how important it is to have early-childhood education, but what is this going to do for those populations that really need the help?" Landes asked. "Families like my wife and I can afford to send our children to a private program."

In Ferraro's classroom, where all the children are eligible for free or reduced-price lunch, books and posters with the alphabet are everywhere and music is nearly always playing. Each child draws pictures or writes letters in a journal.

Dalcy Cortez-Veliz said that when her daughter, Paola, started in September she could sing the alphabet but didn't really grasp the concept of letters. Now, the 5-year-old picks up books more often and sounds out words.

"At the beginning, she didn't recognize the letters," Cortez-Veliz said. "She is absolutely more into spelling now."

Cortez-Veliz, who works from home arranging flowers, said Paola didn't attend preschool last year because the family -- her husband is a construction worker -- was making a little more money and did not qualify for a publicly funded program. Still, she said, private preschool was simply too expensive for a family with three children.

"I hope it becomes available for families who are stuck in the middle," Cortez-Veliz said. "I have a lot of friends in that situation. They can't go to Head Start because their incomes are a little above, and they can't pay for private school because it's a little too much."

As adults watch, Fabricio Pierola, waving an American flag, leads his pre-kindergarten class in song at Belvedere Elementary School in Fairfax County.

Fabricio, left, pre-kindergarten teacher Rosie Ferraro and Neo Upod work on letters in a class where most students started the school year not knowing what a letter was but since then have earned to print their names.Erida Dervishi, above, practices counting at Belvedere, where students have learned to count days on a calendar. Gov.-elect Timothy M. Kaine's push for preschool comes amid a nationwide movement to expand state-funded pre-kindergarten.

At right, pre-kindergarten classmates Matias Zurita-Cordova, left, and Moises Pedrazas read together at Belvedere.