You do not report it on Schedule C. You just enter your W-2. It is not business income. The district is handling it correctly. All payments from an employer to an employee are treated as wages and are included in your W-2. It's part of your employment as a teacher. It doesn't matter what they call it or what you call it. Except in rare special circumstances, an employer does not issue a 1099-MISC to an employee.
