Mayor Bill de Blasio’s universal pre-K program has seen registrations increase by 12,000 children in its second year of operations, with double-digit percentage increases across income levels except for one group: those who need it the most.

New data obtained by ProPublica that compares pre-K registration with a student’s home ZIP code shows that the program added only 195 kids from the bottom 20 percent of ZIP codes by household income.

That is an increase of just under 1 percent for families that make less than $38,000 a year. All other income groups saw large percentage increases from 27 percent to 43 percent.

The stark contrast between those at the very bottom and everybody else is important because decades of academic research have shown that children from low-income families who attend pre-K benefit immensely, but those benefits decrease as you move up the income ladder and may even disappear beyond the middle class. The universal pre-K program was a hallmark of de Blasio’s campaign to make free pre-K education a right for every New Yorker and to narrow achievement gaps, which start very early in child development.

“I honestly don’t see how the mayor will narrow early disparities in children’s learning until he focuses more directly on poor communities, lifting low-income families,” said Bruce Fuller, a UC Berkeley professor who has analyzed the city’s universal pre-K program and provided ProPublica with his analysis of the newest numbers.

Students in the lowest 20 percent of ZIP codes are still the most represented across the program. They make up almost a third of this year’s 65,000 registrations. And city officials said they expect their numbers to go up. Last year, the Department of Education first announced 51,500 registrations, but an additional 1,620 students ended up enrolling. If history repeats itself (and assuming every single new student comes from the bottom group), enrollment growth in the poorest ZIP codes would reach nearly 9 percent this year. But even this hypothetical percentage growth would be three to five times less than the growth of the other income groups this year. It’s also 15 times less than the bottom income group’s growth in 2014 when it expanded by 138 percent.

“Once you successfully engage the first layer of poor income families it gets harder and harder to engage the deeper and deeper layers of families,” Fuller said. “You are now talking about going to the housing projects and knocking on doors, reaching out to the families in Spanish and Cantonese. You are talking about reaching immigrant families who might be mistrustful of government.”

This is exactly the kind of outreach city officials say they are doing.

“We have over 20 full-time people that are dedicated to reaching out to communities all over the city, who speak many languages,” said Josh Wallack, Deputy Chancellor at the city’s Department of Education who directly oversees the pre-K program. “And they have reached out to tens and tens of thousands of families, not only with live phone calls but by attending community events all over the city.” Wallack’s remarks are from an interview that took place last week before these registration numbers were obtained.

Harry Hartfield, the department’s deputy press secretary, stressed the same point in a statement prepared for this story. “We knocked on doors, called families directly, and went to community events across [low-income] neighborhoods to tell families about our free, full-day, high quality programs,” he said. “And we got the message out: two thirds of all students enrolled in Pre-K for All are from households below the median income.

A separate analysis of the data was featured in a story published Sunday. The article touted the mayor’s program with a similar statistic, reporting that 62 percent of children registered this year come from ZIP codes that are below the city’s median income of $51,865. This is true, but left unmentioned were the disparities between those who are close to the median and those who are very much below it.

Overall, eight out of the 12 ZIP codes that saw the largest drops in enrollments since last year fall within the bottom 20 percent. Officials note that in some of these ZIP codes, enrollment in mandatory kindergarten has also decreased, which could mean there are fewer children living in the area. Only four of the 40 ZIP codes that saw the largest increases this year were in the lowest income group.

While an analysis of median income by ZIP code provides only a proxy to understand who is actually making use of universal pre-K, this is the data that the city has been willing to release. It has not released income data for the particular families who enroll in pre-K.

Update, Sept. 18, 2015: After publication, de Blasio’s deputy press secretary Wiley Norvell offered the following comment:

“This is a 2-year expansion, and the first year was heavily focused on low-income communities that benefit most from high quality pre-K. In the ten lowest-income communities, enrollment more than doubled last year. And that focus continued this year, where we pushed and successfully enrolled more than 1,000 children whose families were in homeless shelters. Professor Fuller's bizarre allegation that low-income families aren't served by this new system has been rejected by early education providers and experts over and over.”