Another reason for the staffing inconsistencies is that prospective educators tend toward certain subject areas and away from others. On top of early-childhood education, the DOE report suggests that there are few shortages in high-school English, for example. And Education Week reported in 2013 that colleges were overproducing elementary-school teachers.

On the other hand,teachers specializing in special education and English as a second language are in high demand; this has been the case for years, though shifting demographics in student populations suggests that the demand is rising. Science positions also tend to be understaffed, particularly in physics and chemistry, as are those in math. Despite the ever-growing emphasis on STEM education, science and math teachers have long been in short supply because it’s hard for public schools, many of which are drastically underfunded, to compete with private-sector salaries in their recruitment of young adults with those skills. A number of states also report a shortage of foreign-language teachers.

So, in theory, while prospective high-school English teachers might struggle to find a job in New York’s middle-class suburbs, special-ed teachers in, say, Indiana or California are likely to find plenty of offers.

The takeaway? Solutions to the teacher-shortage problem must take into account its complexities; across-the-board initiatives to increase the number of education majors are unlikely to address each state’s specific set of issues. Teacher-training programs could do a better job of providing students with concrete information about the employment realities—which subject areas need teachers and which ones don’t. Given that 14 percent of 20-somethings are unemployed, that information is certainly valuable. And greater certification portability would reduce barriers to relocation, while streamlined recertification options could help teachers who struggled to find work or were laid off during the recession return to the profession.

Some districts and states have experimented with added incentives for teachers. In Philadelphia and in rural areas in South Carolina, for example, there have been proposals to create low cost housing or “teacher villages” to provide incentives for teachers to work in those communities. States could offer bonuses and other perks to teachers in the high-need subjects and locations. At least one study found that these targeted bonuses are successful, though others haven’t been as optimistic about the efficacy of such perks—at least with regard to retaining effective educators. As the Kentucky teacher Paul Barnwell has argued, schools—particularly those serving high-poverty student populations—should do more to support their teachers with resources and training, particularly since many of the teachers placed in struggling schools have the least experience.