In elementary school, we're taught that by adding 1 plus 1, we get 2. But when it comes to Connecticut's teacher shortage, the numbers don't sum that easily.

Consider the following two facts:

1. For several years, numerous Connecticut school districts have struggled to fill vacancies, in what has widely been called a "teacher shortage." As of last spring, the state's schools had more than 1,000 open positions.

2. Total staffing levels across Connecticut have increased across most categories since the COVID-19 pandemic and remain about as high as they've ever been.

Counter-intuitively, both statements are true, state data shows. And according to Marguerite Roza, director of Edunomics Lab, a research center based at Georgetown University, the two are closely related to each other.

The explanation, Roza says, starts with the federal Elementary and Secondary School Emergency Relief fund, established in 2020 and bolstered in 2021 as a way to help K-12 schools nationwide through the COVID-19 pandemic. ESSER left districts nationwide flush with cash, portions of which went to hiring new staff.

But as some school systems, particularly wealthier ones, brought in more teachers at higher salaries, those with lower budgets were stuck hiring from a smaller pool of candidates.

"When ESSER came and we had a bigger jump of hiring, we sort of depleted the labor force," Roza said of the phenomenon. "And hiring in some districts meant that we took staffing away from other districts, and so there's this kind of predatory hiring going on."

In Connecticut, the data supports this theory. The state had 437 more certified general education teachers and 50 more certified special education teachers during the 2021-22 academic year than during the previous one and remained above pre-pandemic staffing levels during the 2022-23 year as well, according to figures from the education department.

A closer look, though, shows that this increase was fueled largely by wealthier districts, many of whom increased staffing levels during this period. In some poorer districts, the story was different:

* Hartford had more than 20 fewer general education instructors in 2022-23 than it had two years prior, as well as dozens of fewer special education teachers and paraprofessionals.

* New Haven was down more than 30 general education instructors and about 20 special education teachers in 2022-23 as compared to two years earlier.

* Waterbury had 125 fewer general education instructors, as well as fewer special education teachers and paraprofessionals, than two years prior.

According to a December 2022 report from the Office of Legislative Research, 71 percent of teaching vacancies in Connecticut were in "Alliance Districts," a category that includes 36 of the state's lowest-performing school systems serving about 44 percent of all students in the state. And exceptions for teacher certificate standards — often a sign of a school system in desperate need of staff — have been largely concentrated in the poorest districts, including Hartford and Bridgeport, state data shows.

Fran Rabinowitz, executive director of the Connecticut Association of Public School Superintendents, said hiring in wealthier districts has exacerbated difficulties for poorer ones, particularly when it comes to special education and other areas of particular need.

"There continues to be shortages in shortage areas and in the challenged districts, both rural and urban districts," Rabinowitz said. "Many of the teachers from those districts are probably migrating to other districts."

Kate Dias, president of the Connecticut Education Association, the state's largest teachers union, says that's exactly what has happened. While some teachers have left the profession out of frustration, others have simply moved to jobs in districts offering better working conditions.

Essentially, salary increases and sign-on bonuses in wealthier areas has been good news for teachers — but bad news for poor districts that can't easily keep up, at least without more help from the state.

"I think you've seen a migration towards salary," Dias said. "If I have my choice, I pick to work in a district that's going to pay me substantially more."

The result, Dias said, is that staffing levels have become "an equity issue," with low-income districts — and the teachers who work there — left struggling.

Still, some signs point to an improved situation for challenged districts. New Haven, for example, is down to 73 classroom vacancies, from more than 100 last winter, which a district spokesperson attributed to higher salaries, new recruitment initiatives and improved retention efforts.

Hartford has seen a similar trend, a spokesperson said, with 146 vacancies currently as opposed to 223 a year ago.

Dias said things feel "a little bit calmer than last year" but that some districts continue to struggle to fill openings, creating difficult conditions for teachers there. One job-listing site showed 937 open positions across Connecticut as of Tuesday afternoon, and the state's education department continues to list special education, bilingual education, technical education, math, and science among shortage areas.

"I don't think people are at the same panic-level as they were a year ago," Dias said. "But I don't know that the situation has dramatically improved."

For better or worse, the shortage should ease next year when ESSER funding expires and many districts are forced to cut costs, including through possible staff reductions. Instead of hunting for teachers, some school systems will soon find themselves letting staff go or rooting for retirements.

Last spring, Connecticut legislators sought to mitigate this fiscal cliff by appropriating an additional $150 million to K-12 schools, particularly those in low-income places, but districts would likely need more than that to fill their gaps entirely.

As a result, Roza says, the education landscape a year from now could look far different.

"Starting in '24-25, I think we're not going to hear as much about the shortage," she said. "Because by then districts will be actually crossing their fingers and praying that their staff will leave because they want to use attrition to potentially shrink their budgets."