It is an environment where you are forced to dress a certain way (or the same as everyone), you can't chew gum, you are electronically searched as you enter every day, and your personal storage spaces are subject to random or unannounced searches.  (In my public school in the 80's, I was physically beaten--aka paddled--twice for being late to class too many times, though they have since discontinued that practice.  My parents were never notified that this was done to me, and their permission was never explicitly sought.)  If I didn't tell you it was kids at a school, you would think it was North Korea I was talking about.

"Daddy, the principal raped me."

"What, AGAIN?"

"Yeah. (sobbing) I was caught passing a note in class!!"

Schools step way over their line of authority when they attempt to do the job of law enforcement. A decent school superintendent has policies that clearly identify what issues can be handled in school and what requires the principal to call 911.

they should also be required to register on the state's sex offender list.

The campus cops are employed to 'keep it quiet' about the thefts, rapes and other violence on campus.  Campus PR is what matters.

From my reading, it seems that circuit courts have dealt with varying interpretations as to how much clothing must be removed in order to reach a clear definition of "strip search."  Apparently, however, the Supremes have not.

From the link (PDF):

The Eleventh Circuit has considered a police officer's direction for someone to strip down to their underwear to be a "strip search."

Likewise, the Fourth Circuit understands a search of an adult arrestee in his boxer shorts to be a strip search.

The First Circuit "recognize[s] that a strip search may occur even when an inmate is not fully disrobed."

Statutes defining a strip search in several states confirm our understanding of the term "strip search." California, for instance, defines the term as "requir[ing] a person to remove or arrange some or all of his or her clothing so as to permit a visual inspection of the underclothing, breasts, buttocks, or genitalia of such person."

Perhaps the following is the key comment & may lead to some form of national standard:

The Fourth Circuit has recognized that this definition of a strip search is "uniform" throughout the Union.
See Amaechi, 237 F.3d at 365 n.15.

One thing is clear under any standard -- the shocking strip searches that are described in some cases have no place in the schoolhouse. See Doe v. Renfrow, 631 F.2d 91, 92-93 (CA7 1980) ("It does not require a constitutional scholar to conclude that a nude search of a 13-year-old child is an invasion of constitutional rights of some magnitude"),

Not too obvious, apparently, since Stevens also cites Justice Brennan's dissent to denial of cert, a dissent that ended "Schools cannot expect their students to learn the lessons of good citizenship when the school authorities themselves disregard the fundamental principles underpinning our constitutional freedoms."