Sally Reis, a professor at the Neag School of Education at the University of Connecticut, recommends that you focus on teachers' needs when approaching them with your program. "Any entrepreneur who wants to deal with [schools] has to think about how to make teachers' lives easier," she says.
While your program might not directly address teachers' classroom needs, it will likely benefit teachers, students and parents indirectly by filling in the gaps in public education. A child who can dance, speak another language or perform in front of a group is more likely to feel confident in the classroom--and that can only be a good thing for everyone involved.
If there's no room for your program during the regular school day, you can provide after-school programs so that students get the benefits of your program while getting the supervision they need if their parents work. If you have your own facility, you could even shuttle students from school to your location every day. Considering that a 2000 Department of Education report found that more than 28 million families have parents who work outside the home, it's clear that quality after-school care is a must.