Brainy Academy, Brooklyn

You won't find a single screen in most of Brainy Academy's classrooms—no smart boards, no computer monitors, no TVs. In fact, students spend very little time passively taking in information at all. In nursery-school sessions, enrichment classes, and private tutoring meetings alike, instructors are guided by the principles of Montessori learning, which help develop problem-solving skills and creative thinking through hands-on activities.

That doesn't mean that the programs lack structure. Kids prepare to compete on a global level with the Singapore Math system, and an analytic approach to English swiftly lays the foundation for advanced reading and writing skills. The school's methods are suited equally to expanding learning capacity in kids with learning difficulties and in those ready to move beyond their peers. (Several programs are designed to prepare kids for the citywide gifted and talented test.) Summer Russian, lego science, and English programs keep children in touch with academic concepts and away from roving gangs of philosophers trying to teach them arguments against math's existence.