Erin Ferrantino rarely has to consult the birthday chart in her kindergarten classroom to pick out the Octobers, Novembers and Decembers. This year, there was the girl who broke down in tears after an hour’s work, and there was the boy who held a pencil with his fist rather than his fingers.

Those two, along with another of Ferrantino’s students who were 4 when school started, will be repeating kindergarten next year.

“They struggled because they’re not developmentally ready,” said Ferrantino, 26, who teaches in Hartford, Conn. “It is such a long day and so draining, they have a hard time holding it together.”

Soon, Ferrantino may not have to be on the lookout for children with birthdays in the late fall. Connecticut, one of the last states to allow 4-year-olds to enter kindergarten, is considering changing its rules so that children would have to be 5 by Oct. 1, rather than Jan. 1, spurring a contentious battle over access, equity and persistent achievement gaps based on race and class.

The policy debate among lawmakers, educators and children’s advocates echoes the cocktail-party chatter in well-off neighborhoods, where parents have long weighed the advantages of delaying kindergarten on an individual basis, a practice known as redshirting.

Supporters of the earlier cutoff date in Connecticut say it would level an unequal kindergarten playground in which the youngest students are often poor minorities whose parents cannot afford to give them this so-called gift of time. But others worry that the change could leave thousands of 4-year-olds in educational limbo, perhaps worsening the readiness of those without access to high-quality preschools.

“We may actually be harming them by not letting them start until a year later,” said Sara Mead, an associate partner at Bellwether Education Partners, a nonprofit consulting firm in Washington.

While kindergarten began to flourish in the United States in the late 1800s as a way to teach children as young as 2 and 3 through play, it has become increasingly academic, particularly over the past decade amid an emphasis on standardized testing throughout public education. That, in turn, has spurred a widespread movement to limit the “children’s garden” to 5-year-olds.

Today, 38 states and the District of Columbia have established or are phasing in birthday cutoffs by Oct. 1, according to the Education Commission of the States, a nonpartisan interstate agency, with California the most recent to make the move. Connecticut is the only state that still has a year-end cutoff, although New York and New Jersey are among eight states that leave the decision to local districts. For most districts in New Jersey, that date is Oct. 1, while for most in New York, it is in December. (New York City’s is Dec. 31.)

In Connecticut, about 24 percent of the approximately 39,000 kindergartners who start school each year are 4 years old. But in the state’s poorest districts, 29 percent of kindergartners start at 4, while in the wealthy ones, that number is 18 percent. At the same time, about 2 percent of kindergartners in those wealthy districts start at age 6, compared with fewer than 0.1 percent in the poor areas. The proposed change in Connecticut would take effect in 2015.

“It’s a glaring weakness that we should have fixed long ago,” said Mark McQuillan, Connecticut’s previous education commissioner. “Many of the wealthy parents enroll their children at 6 or 6 1/2, and other families — particularly poor families — enroll their children as early as 4 1/2 because they need the school support. It’s a huge developmental span.”

There is research suggesting that children who enter kindergarten later perform better on standardized tests, but critics contend that the entry age often serves as a proxy for family background and preschool experience. In any case, they say, such benefits disappear by middle school.

Indeed, Mead and others point to research linking redshirting to higher dropout rates down the road as older students struggle to fit in with their younger peers, and to lower lifetime earnings as a result of a later start in their careers. And some parents and teachers say redshirting — a term borrowed from athletics, in which students are pulled from participation in order to begin their eligibility at an older age — can exacerbate problems like bullying and low self-esteem among teenagers.

Connecticut’s Department of Education has not studied the effects of age differences on achievement, but some kindergarten teachers have reported that their youngest students are more likely to miss class, have difficulty focusing and generally require more handholding.

Jennifer Dominguez, a kindergarten teacher in Hartford, said she felt so strongly that 4-year-olds were at a disadvantage that she held back her own son, Kobe, until he was 5; he will turn 9 on Dec. 30.

“The January birthdays are so much more mature and able to handle the curriculum,” she said. “The October, November and December birthdays, they’re just learning about what school is.”

Parents like Courtney Gates-Graceson, a lawyer and single mother in East Lyme, Conn., said boys, especially, might find the age difference harder to overcome. Her son, Sebastian, turns 5 on Sept. 29, and she decided to enroll him in a private preschool, at a cost of $14,000, rather than to start him in kindergarten.

“I don’t want his academic enthusiasm to be quashed if he can’t compete with the older kids in his class,” she said.

But what about those who do not have $14,000 to spend?

“Kids will have to wait around another year to get into school; that’s time wasted,” said Milly Arciniegas, president of the Hartford Parent Organization Council. “They’ll be 19 when they graduate — no thanks; that’s not the solution.”

Paul Wessel, executive director of Connecticut Parent Power, a statewide advocacy group, called the plan “an incomplete solution to a larger problem.”

Hartford school officials said children with late birthdays could be absorbed into the district’s free preschool programs, but other districts do not have that capacity. Connecticut education officials had called for expanding the state-financed preschool program, known as School Readiness, along with raising the kindergarten entry age, but legislators balked at the estimated $40 million cost. The program subsidizes preschool for 10,000 3- and 4-year-olds, primarily in 19 low-income areas.

Similar concerns prompted California, which voted last year to move its cutoff date to Sept. 1 from Dec. 2 one month at a time starting in 2012, to establish so-called transitional kindergartens for children with birthdays in the fall.

Karen Gasparrini, a kindergarten teacher in Stamford, Conn., said that without a quality preschool option, “all they’ll be is older; it doesn’t mean they’re better prepared.”

In Westport, Conn., an affluent district where nearly all children attend preschool, Elliott Landon, the schools’ superintendent, said he had noticed no difference in the 70 kindergartners who were 4 when school started.

“The earlier we get them, the better,” Landon said. “If they’re in need of remediation, we can do that; and if they’re in need of acceleration, we can do that, too.”