Thanks for writing and for your interest in the NYC Schools Gap App Challenge. No, I'm afraid that DOE employees are not eligible to enter the challenge.
Per the Official Rules:
"E. The following individuals, teams, and Organizations are not eligible regardless of whether or not they meet the criteria set forth above:
(i) the Sponsor, the Administrator, and any advertising agency, contractor or other organization involved with the design, production, promotion, execution, or distribution of the Competition (collectively “Promotion Entities”); all employees, representatives and agents of such Promotion Entities; and all members of any such employee, representative or agent’s immediate family or household."