Whether or not this person has any association with your school will not lessen the feelings of invasion of your personal space and fears for your safety. It is a natural reaction to have heightened suspicions of everyone - particularly in your field of work.
If it can be of any comfort for you, most attempted break-ins are opportunistic, poorly planned or prepared, and as much as can be known to the invader, anonymous (since any associations create for easy suspects).
Are you living in the same suburb as the school? Are there other schools in your area? Most likely it is a random attempt to gain entry by some idle loiterer who had no idea.
Check your security footage to see if there are any earlier appearances (during the day, or people just hanging around nearby). If you still feel uncomfortable, it may be time to install lockable gates, upgraded surveillance, or get a big angry dog on the property (who will also be your support in times of need).