Of the 50 million U.S. students who returned to public elementary and secondary schools in recent days, more than 2 million did so at charter schools.

Just two decades after Minnesota passed the first charter law, about 5,600 of the schools have been established in 41 states and the District of Columbia. Contrary to claims of some teachers unions and education bureaucrats, this is good news.

Yet rising enrollments also point out the need for better oversight, particularly when it comes to charters’ “authorizers” -- the bodies that get state permission to create the schools, draw up their founding contracts (the “charter”) and oversee their boards.

Although charters come in every shape and size, they are all free public schools that have a large degree of autonomy over hiring, finances, curriculums and instruction methods. In general, they accept all interested students or, if demand exceeds capacity, use lotteries. Do they work? Education statistics are as slippery as eels -- most studies are limited in geographical scope and duration, and advocates from all sides tend to poach data selectively to support their claims. That said, there is no doubt that charter schools have improved the test scores of many students, particularly the most vulnerable.

One of the best studies, a 2010 survey by the consulting company Mathematica Policy Research that compared students enrolled at charter schools with those who applied but lost out on admission in a lottery, found that overall performance was roughly similar but that low-income and low-achieving students at charters showed significant gains over peers at traditional public schools. (It found that outside of urban centers, charters have an overall detrimental effect on achievement.) A Rand Corp. study in 2009 noted that students attending charter high schools in Chicago and Florida had higher ACT scores, graduation rates and college entrance rates than their peers. Anecdotal evidence suggests that competition from charters has led to innovation and improvement at traditional schools.

Another pattern emerges from the data: Some states outperform others. Arkansas, Colorado, Illinois, Louisiana and Missouri have shown consistent educational improvement. Charters in Arizona, Florida, New Mexico and particularly Ohio have struggled.

What do the higher-performing states have in common? One factor is well-conceived rules concerning school authorizers, which can be municipal school boards, state education departments, universities, city governments, nonprofit groups and so forth. (There are about 1,000 authorizers nationwide.)

These variations have given us a wealth of data on what works and what doesn’t. Several charter advocacy groups, including the National Alliance for Public Charter Schools and StudentsFirst, headed by former Washington schools chief Michelle Rhee, have created model legislation that state lawmakers should heed as they enact and refine their laws. Several best practices involving the role of authorizers stand out:

-- Accountability. Each authorizer should be required to provide the state with regular reports on the academic and financial performance of all schools it supervises, as well as the results of audits on its own operating expenses. Arizona, which has been a locus of charter-school scandals, is a cautionary lesson: State law does not require authorizers to submit annual performance reports or mandate any formal review process by an authorizer oversight body. Illinois, where charters have done well, has a strict law: Among other requirements, every other year authorizers send the state board of education a report with details on the schools’ academic and financial performance, progress made toward reaching the authorizer’s strategic vision, and audited operating costs.

-- Performance-based contracts. In charter applications, authorizers should be required to set minimum standards for student and teacher performance, which can serve as the baselines for renewal. Florida does well here: It mandates that each charter explain how the school will measure progress, based on incoming students’ previous academic achievement.

-- Transparency. Too often, groups wanting to start schools (and their communities) are left in dark all through the charter application process. States should establish timelines for charter approval, insist that all authorizers meet in person with members of the applicant group, hold a forum for residents to give input, and make public a detailed explanation when an application is denied. Arkansas is a leader here: Charter applicants use a standard form created by the state education department, and denials must include a list of specific reasons.

-- Caps. Many states put limits on the number of new charters that can be opened each year. This arbitrary limit is foolish: Demand is high, and states should give themselves maximum flexibility to add the schools they need.

-- Multiple schools. Many states limit charter-school boards to oversight of a single school, another pointless cap. Those that demonstrate success should be able to oversee several, so long as each school maintains fiscal and academic autonomy.

-- Government funding. A 2010 analysis from Ball State University found that charter schools receive 19 percent less funding per student than regular public schools get. Schools need government guarantees that their students will receive the same state and federal aid that they would get at traditional public schools in the district.

-- Collective bargaining. In at least seven states, charter schools are generally required to give educators the same collective bargaining rights as other public schools have. Yet freedom from traditional practices is the basis of a charter’s creativity, so long as this doesn’t interfere with other protections, for example against discrimination.

Charter schools are no panacea. But like most reform efforts of the past two decades, including the much-maligned No Child Left Behind law, they have benefited millions of students and provided guidance for future innovation. With more consistent state oversight, charters can be left to plot their own course.

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