I don't think that the problem - wanting to show that you are an international person of mystery - is solved by listing the high schools you attended.
this isn't because the high schools don't prove it, it's because
- most recruiters will skim this section, looking only at your last school
- even if they read them, how evident is it that you are in different countries?
- even if that is evident, how does that prove you know the languages you know?
- also, you're making them jump from the idea "oh ws6079 went to 7 international schools" to the idea "oh man, ws6079 is totally able to handle culturally diverse scenarios how awesome!!!1"
As noted by @RobM, you're more able to make the statements you want to make in the cover letter you write. There you can mention the schools, citing them as proof to the statements.
If you do want to list "International Exposure" in your CV - and it isn't a bad idea - then do so under a heading, maybe one titled "International Exposure". There you can list the time you spent in various countries, and the languages you picked up.
If I'm misreading the question, and you were in one country the whole time, I don't think that the schools themselves really provide strong evidence of "international exposure", so I would probably skip the CV entry (but the cover letter story is fine). That is just my thought though. I never went to an international school.
@Pepone's thoughts on the popularity of the school do stand - for some schools. I would be more interested in hiring a member of my old high school, for example, so seeing it on the CV would be useful. You'll typically know if this is the case with your high school.