As far as I can tell, the speakers are not anyone in particular. Instead, they are just average teenagers. The only thing that really identifies them is their attitude towards people who are in positions of authority.
The whole song (and really the whole album) is based on the idea that authority figures build this wall between themselves and young people. It says that they build the wall, brick by brick, by the way that they treat young people. The speakers in the song are teens who feel that their teachers (in this case) have built this wall by their sarcasm and harshness towards their students.
The primary voice that emerges from Pink Floyd's work is the notion of alienated youth. In a setting where conformity in accordance to parental and social expectations drove how students and children were treated, the voice that arises from the work is one that demands the acknowledgement of individual autonomy away from the conformist voice of alienation. There is a call to revere childhood, individuality and the authenticity of experience. Failure to do so ends up resulting in conformity that robs individuals of their identity, making them more susceptible to being molded by extreme forces of social control. The way around this is to demand change and seek it out as the acknowledgement of voice is extremely essential to individual identity.
I've always thought of the speakers as students. Who else would even think about talking to teachers? I agree with the first answer that this is definitely a teenaged crowd - and here in America - education is mandated by law for teenagers.
I love the line "(we don't need) no dark sarcasm in the classroom" - I guess this makes me think these are the really smart students who maybe don't get the best grades, or kiss up to the teacher, or even show-out much in the classroom at all, but are not missing a single thing. There aren't many students who fully understand sarcasm in the first place, let alone dark sarcasm - which is the most cutting, the most demeaning, and largely the hardest to pick up on. Also, when they say, "...leave them kids alone..." it is almost as if they are other students feeling sorry for the rest of the class who just doesn't get it.
I feel that the speakers are meant to represent the band members at a younger age. They are expressing their angst at the impending journey into adulthood.