Hundreds of city teachers show up at schools they’ve never seen before every Monday morning, DNAinfo.com reports. The lucky ones get assigned to classrooms, maybe to teach the subject in which they were trained. Others do paperwork. And some waste hours doing nothing. On Thursdays, they get a notice from the Department of Education telling them where to report the following week, and the cycle repeats. This is what the DOE calls the Absent Teacher Reserve, a pool of nomadic educators who are paid their full salaries to work as substitutes. Most have been “excessed” by budget cuts or school closings and have been unable to find new jobs. Others have been liberated from the department’s notorious “rubber room,” or have survived “unsatisfactory” ratings, and were deemed fit to keep teaching…