Chancellor Joel Klein likes to say that many of the teachers who’ve lost their jobs and remain on the city’s payroll aren’t trying to find new work. But a back-of-the-envelope analysis of teachers in the reserve pool shows that even if all of them doggedly pursued open positions, nearly a quarter are trained for jobs that are disappearing.

Most teachers in the absent teacher reserve — a pool of people cut from schools when they were closed or enrollment dwindled — are certified to teach core subjects that every school offers. But the most recent data shows that almost a quarter of teachers in the pool are only licensed to teach classes like swimming, jewelry-making, and accounting, among other subjects that are nearly extinct in the public schools.

The pool also includes music, dance, and art teachers for whom getting a new position will be difficult in a year when schools will have to lay off thousands of teachers.

As of November, there were 1,247 teachers in the pool, working as substitutes and collecting salaries that totaled $134 million. After announcing a deal to close the notorious rubber rooms for teachers accused of misconduct or incompetence, Chancellor Klein said last month he would turn his attentions to the ATR pool.

But the composition of the pool raises questions about Klein’s claim that its members ought to be fired because they don’t try to get new positions once they’ve lost their old ones. Teachers hold particular licenses, and they can only be hired for jobs in that license area. An elementary school special education teacher can only be offered an elementary school special education position, and if there aren’t any, that teacher is out of luck, no matter how much he or she wants to work.

The vast majority of reserve teachers do hold licenses that make them eligible for jobs that open up regularly. The most popular license among teachers in the pool is for elementary school classroom teaching. Dozens of others are eligible to teach in areas that traditionally have shortages, such as math, science, and bilingual education, although with this year’s layoffs, those shortages may not exist.

The legacy of large high school closures is apparent: The pool contains 17 accounting and business teachers, 12 typing teachers, and half a dozen electronics teachers. Two Creole language bilingual social studies teachers were clearly excessed from Tilden High School, a school that’s being phased-out and that offered the only Creole-English bilingual program in the city.

A set of data from last summer shows that in addition to the teachers, the pool also contained dozens of school support staff members. These employees provide essential counseling and administrative assistance but are but not required, making them especially vulnerable when budgets are cut. As of last June, there were are 72 high school guidance counselors in the pool, 14 librarians, 17 psychologists, 29 secretaries, and 38 school social workers.