Sorry. Anarchism and socialism (i mean REAL socialism, not the shit "socialist" governments of China, Korea and Russia) are just illusions that can inspire us, but are not real or sustentable. They are asintotes.
Real Anarchism is just letting everyone pick their own 'Game rules' to use your classroom analogy, and not forcing one game on everybody.
Of course, but no one can play a game is each of them have their own rules ;-) if every of them deal with each other, then there is no individual thinking anymore.