I think the place where our path splits comes at the question of what kind of rights students in a school system have by definition. Runaways and truants, for instance, are status offenders. Their right to freedom of movement is automatically excluded by compulsory attendance laws. When the law makes you be in a certain place at a certain time or be subject to arrest, you do not have freedom of movement. The courts, applying the Fourth Amendment, have held that school lockers are not protected from unwarranted search.
Kids have their rights to freedom of assembly rigidly controlled on campus.
They are regularly told to sit down and shut up, bringing the matter of free speech into serious question, and what they can write on school assignments is controlled by the system. You may write a wonderful technical treatise on RNA replication in human brain cells, and it may win the Nobel Prize for chemistry , but it won't get you past the essay portion of your American history test. You may have noticed by now that the Second Amendment right to bear arms doesn't apply in schools. In fact, the only right that hasn't come into question yet is the right to resist quartering troops. Let's face it, students in school systems, even colleges, are deprived by the nature of their status of various civil rights, many of which they waive by social contract.