Three weeks before school begins, Montgomery County Public Schools is facing roughly 500 teacher and support staff vacancies, mirroring a national shortage of educators that has left school systems scrambling to fill positions. The school system — Maryland’s largest with roughly 160,000 students — is trying to recruit and hire teachers in a more competitive environment than in previous years, Schools Superintendent Monifa B. McKnight said Monday during a media briefing on the system’s staffing. The school district’s biggest hiring needs are for special education instructors, elementary school teachers and school psychologists.