The stories are all too familiar, and yet somehow we’ve come to believe that with really good teachers and longer school days and rigorous testing we can transform children’s lives. We’ve imagined teachers as lazy, excuse-making quasi-professionals — or, alternately, as lifesavers. But the truth, of course, is more complicated. Quality schools and quality teaching clearly can make a difference in children’s lives, sometimes a huge difference, but we too often attempt to impute to teachers impossible powers. (After more than 15 years of reform in Chicago, the dropout rate has been markedly reduced but is still an astonishing 40 percent.)

Consider that in Chicago, many elementary schools have a social worker just one or two days a week (they’re shared among schools) in communities where children face myriad pressures and stresses. Class sizes in kindergarten through third grade hover around 25, even though the Tennessee STAR study, conducted in the 1980s and renowned in education circles, found that small classes of about 15 during those early years can make a big difference for students’ long-term outcomes. In Chicago, slots in after-school programs for 6- to 12-year-olds have been reduced by 23 percent since 2005, according to Illinois Action for Children, an advocacy organization. Earlier this year, the city shuttered half its mental health clinics. A promising mentoring program, Becoming a Man, which was found by a University of Chicago study to have reduced violence and increased graduation rates among its participants, is oversubscribed. Forty-five schools want its services, but it has only enough money to work in 15. Last year, at an Aspen Institute conference, the education historian Diane Ravitch was asked her wish list to improve schools. At the top of her list: universal prenatal care — which, of course, has nothing to do with the classroom. Or so it would seem.

Of course, Ms. Ravitch wanted to make a point. As we slash services in deeply impoverished communities and reduce school budgets, how can we expect that good teachers alone can improve the lives of poor children? Poverty, of course, can’t be an excuse for lousy teaching. But neither can excellent teaching alone be a solution to poverty.

It’s been too easy to see this dispute as one between two hotheaded personalities — Mr. Emanuel and Ms. Lewis, or as a play for respect. Rather, as I spoke with teachers on the picket lines last week, it became clear that it was about something much more fundamental, and something worth our attention: top-notch teaching can’t by itself become our nation’s answer to a poverty rate that, as we learned the other day, remains stubbornly high: one of every five children in America live below the poverty level.

In Chicago, 87 percent of public school students come from low-income families — and as if to underscore the precarious nature of their lives, on the first day of the strike, the city announced locations where students could continue to receive free breakfast and lunch. We need to demand the highest performances from our teachers while we also grapple with the forces that bear down on the lives of their students, from families that have collapsed under the stress of unemployment to neighborhoods that have deteriorated because of violence and disinvestment. And we can do that both inside and outside the schools — but teachers can’t do it alone.