In a Principals of Biomedical Science class, ninth grader Bemnet Gebrechirstos looks at human blood smears under a microscope. (Sarah L. Voisin/The Washington Post)

The District’s mix of schools — including traditional public, public charter and private — offers parents one of the widest varieties of educational choice in the country, according to rankings a Washington think tank plans to release Tuesday.

Only New Orleans and New York City were rated higher on the Brookings Institution’s Education Choice and Competition Index, which graded more than 100 cities and large suburbs on the policies governing choice and availability of education options, including magnet schools, charters and virtual education.

“The thing that of course stands out about the District of Columbia is that 40, 45 percent of kids are in schools of choice — which is very high with respect to the rest of the nation,” said Grover J. Whitehurst, director of the institution’s Brown Center on Education Policy and a key figure in developing the index.

Brookings ranked Fairfax County30th out of 107 cities and suburban areas. Prince George’s County was ranked 41st; Montgomery County 47th; Prince William 63rd; and Loudoun was tied for second to last.

Whitehurst said the District has room to improve, particularly when it comes to designing admissions and assignment policies that try to match parents with the schools they prefer.

Admission to oversubscribed charter schools in the District is determined by lotteries, for example. Students can apply to many schools, but they have no better chance of getting into their first choice than into their 18th choice.

That can be frustrating for parents, who often feel less like they’re making an educational choice than leaving their kids’ future to fate. It can also encourage families to hold onto seats in multiple schools, which means that months into the academic year, wait-listed students are still gaining admission and changing schools.

“This is one of the most robust cities for choice in the country, but there are a lot of aspects of our choice system that aren’t optimal for parents and families and, in many cases, for schools,” said Scott Pearson, executive director of the D.C. Public Charter School Board.

In contrast, New Orleans parents rank schools in order of preference. A computer algorithm — developed by a Nobel Prize-winning economist — then assigns students to schools with the aim of maximizing the number of satisfied families.

Pearson said that system has its own drawbacks, but D.C. charter school leaders are considering it along with models used in other cities.

The Brookings report also criticized the application process that D.C. Public Schools uses for its selective high schools. School officials said the group misunderstood its system, which is new this year and was developed by the consultants who created the matching system in New Orleans.

Incoming freshmen used to apply to multiple schools and receive and weigh multiple acceptance offers. Now, they rank their choices in order of preference when they apply. Schools, in turn, rank their applicants, and a computer algorithm matches students with the most preferred choice to which they were accepted, school officials said.