School principals matter. Any parent who has sat in on a PTA meeting will tell you that. So will researchers. The authors of the Wallace Foundation's landmark 2004 report, "How Leadership Influences Student Learning," found that leadership is second only to teaching among school-based influences on student learning, What makes principals so important? Start with their ripple effects. Great principals, in the words of political scientist Paul Manna, "can be powerful multipliers of effective teaching and leadership practices in schools."

It stands to reason, then, that state officials who are serious about improving public-school education, especially in the most troubled schools, would be interested in supporting the development of highly capable principals. They have considerable authority to do so. In addition to setting job standards for principals that undergird principal "pre-service" training and licensing, states oversee and approve this training (typically university advanced-degree programs) and licensure.

A synthesis of four Wallace Foundation-commissioned studies published earlier this year suggests, however, that many states are failing to assert their powers as well as they could.

Consider training. The report, "Improving University Principal Preparation Programs: Five Themes from the Field," concludes that fully 80 percent of school-district superintendents are dissatisfied with program quality. Surprisingly, many universities share their concern, according to the report. Thirty-seven percent of respondents to a survey of member institutions of the American Association of Colleges for Teacher Education agreed that current school leadership programs prepare graduates "not well" or only "somewhat well."

Licensing, too, requires sustained state attention. Some 62 percent of respondents to the superintendent survey said state licensing requirements were only moderately relevant to principals' responsibilities. That may be because the principal's job has shifted dramatically in recent years, moving from a focus on managing buildings to an emphasis on improving classroom instruction.

State policymakers can take steps to address all of this. For one thing, they can make sure that their states' principal standards are up to date by comparing what's currently on the books with "Professional Standards for Educational Leaders 2015," a revision of model principal standards by leading education professionals. For another, they can use their accreditation powers to approve only programs that focus on what today's principals need to know and be able to do.

Fortunately, a few states offer some bright spots. Illinois, for example, has started to tackle the problem of inadequate training by enacting more rigorous standards. The upshot is that principal-preparation programs and school districts in Illinois have started to work closely together to make sure training reflects the real-world needs of students and schools. Significantly, enrollees in Illinois' pre-service programs today primarily learn about improving instruction, and they spend up to a year as resident interns, working in schools alongside mentor principals. This is in keeping with what's described in "Preparing School Leaders for a Changing World," an examination by education scholar Linda Darling-Hammond and others of commonalities among exemplary leader-training programs.

Other states have scrutinized and overhauled principal licensing. In Massachusetts, for example, this involved introducing less reliance on paper-and-pencil exams and more reliance on real-life demonstrations of the aspiring principals' capabilities.

State policymakers interested in strengthening school leadership also have new opportunities emanating from Washington, D.C, thanks to the Every Student Succeeds Act (ESSA), the massive overhaul of No Child Left Behind, one of the leading sources of federal education funding. Through ESSA's Title II, for example, states have flexibility to use funds for state principal-preparation leadership academies, internships for aspiring principals and other measures. The law urges states to fund activities that demonstrate evidence of effectiveness, and here the news is good as well. The RAND Corp. has just published a review of evidence from studies of pre-service programs and other activities to promote better school leadership, and it found an ample body of research.

Each state is unique, so there's no one-size-fits-all approach to improving school leadership. But state policymakers would do well to consider their localities' needs and options so that every student can benefit from a great principal.