Public schools have been under pressure for more than a decade to improve. Now, many school systems are considering a new idea: management by private companies. Education entrepreneurs say they can remake America's schools -- and make a profit in the process. But critics say companies can profit only by shortchanging students or cutting the pay of teachers or other school employees. Despite the criticism, one company is now managing nine public schools in Baltimore, and a second venture will open three new schools in Massachusetts in 1995. Supporters and critics alike will be closely watching students' achievement scores and the bottom lines of the management companies as well.