there is "school policy", and then there is THE LAW. And they are two very different things.
"School policy" applies to students and faculty. A violation of school policy by a student can result in suspension, expulsion, and an unfavorable school record. Violation of school policy by faculty can result in suspension and/or termination. And good luck getting another teaching job after that.
"THE LAW", is the penal/criminal code, and it applies to EVERYONE. Violating the law can result in arrest, jail time, criminal record, thousands of dollars in fines, years of probation, etc.
Here in California, in regards to schools k-12, THE LAW says "any person...who brings or possesses any dirk, dagger, ice pick, knife having a blade longer than 2 1/2 inches, folding knife with a blade that locks into place, razor with an unguarded blade..." on school property is guilty of a violation of California penal code 626.10 (a). So, under California law, a person can legally carry a slipjoint onto school property as long as the blade is 2 1/2 inches long or shorter. But no locking folders, and no fixed-blades.
In regards to college campuses, THE LAW says "any person...who brings or possess any dirk, dagger, ice pick, or knife having a fixed-blade longer than 2 1/2 inches... is guilty of violating CA pc 626.10 (b). So, under California law, a person can legally carry any manual folding knife, of any size, open or concealed, or an openly carried fixed-blade with a blade no longer than 2 1/2 inches on college property. There is also an exception in the law for carrying/possessing fixed-blades with blades longer than 2 1/2 inches as long as they are being used for food prep.
Naturally any school has the ability to set their own policies that are more restrictive than the law, but again, those policies only apply to students and personnel. If my kids school has a policy that says "NO KNIVES PERIOD", that policy doesn't apply to me, and I cannot be punished if I violate that policy. But THE LAW does apply to me. That's why I only carry a slipjoint with a blade under 2 1/2 inches when I go to my kids school.
As far as kids carrying knives at school, I like knives about as much as anybody (more or less), but I don't think my kids, or any kids, need knives at school. The way many kids are today, with all the "behavioral problems", I don't want kids bringing knives to school, and I want school personnel to be able to intervene and temporarily confiscate any knives they see, as well as find out why the child brought a knife to school. I've been at school functions (elementary) where I've seen first hand what little monsters kids can be when they're playing, or when they get angry, and it can be pretty scary.
Children often possess little to no self-control, over themselves, or their emotions. They often have poor impulse control. And they often have no understanding regarding the consequences of their actions. So HELL NO, I don't want kids to be allowed to bring knives to school.
College however is a different matter. I'll worry about college when the time comes.