Capitalization of "School" as an adjective

It would be capitalized if it was preceded by the name of the school. For example:

Students at the Brooklyn School of the Arts often collaborate on assignment with their mobile devices. The students were asked about cheating habits, and their mobile devices. Such questions would allow us to learn how the School culture affected cheating.

However, it would not be capitalized if you were using it like this:

Schoolkids in the 21st century are using cellphones more than ever in schools. The New York Times asked 1000 students about their cheating habits and cellphone usage. Such questions would allow us to learn how the school culture affected cheating.