Can teachers and stuff really make...?

Props to eastacademic: he's exactly right. In addition to the cases he has cited, you should check out a concept called "judicious discipline." Basically, the teacher and the school can take away some of your rights for "compelling state interests." All of these are things that eastacademic has mentioned as well, but here's an example:

Say you're in a band class. The school as a whole does not have a policy against gum chewing, but the band director has forbidden it in his classroom. Also, gum chewing is not against the law and you have the right to put whatever you want in your body (so long as it's not specifically outlawed). Nonetheless, your band director has forbidden gum chewing in his classroom. Has he violated your rights? Not really in this case, because of "compelling state interests." Viz: If you play your instrument while chewing your gum, you can begin choking on it after taking a quick breath. It is in the state's interest to keep you safe at school, which you choking on gum that you yourself put into your own body is not safe. So, because of this possibility, and the fact that you chewing gum while playing your instrument gets in the way of your participation in class activities, chewing gum in this case is against "compelling state interests," so they can revoke that right temporarily. The same holds true for talking or saying what you want. Talking in class can be disruptive to the learning of others, which is also against "compelling state interests" because learning is one of the state's goals for you. Check it out.

A great question to ask - keep that mind working.

yes, teachers can quiet you.

Most likely the two cases you should look at are Schenck v. United States. and Tinker v. Des Moines.

In the Schenck v. United States case, it was held that your free speech rights are not absolute. this is the case where they famously said:

"The most stringent protection of free speech would not protect a man in falsely shouting fire in a theatre and causing a panic."

More to your point is the Tinker case:

"The Court held that students at public schools do not leave their First Amendment rights at the schoolhouse gate and can express opinions orally and in writing, as well as symbolically, as long as it does not "materially and substantially" disrupt classes or other school activities."

that .....as long as it does not..... is the key here.

The court recognized that schools have special characteristics that must be protected. Because of this, it is not just a rule - but a *LAW* in every state that teachers must uphold classroom order. We have a *responsibility* to protect our students from disruptions that prevent ~their~ learning.

So yes - I can make my kids shut it. (I have ways to do so that are nicer)

Yes, they can since you are a minor, and all of those wonderful rights do not fully apply to you as of yet. Second, you could choose to use your rights in class, which would not be illegal, but would go against school rules. As with any rule, you would then have to be willing to accept the punishment from breaking the rule. Of course you would probably wine that he or she is being completely unfair, which would make it clear that you are not ready to be an adult with all the rights of an adult.