SAN FRANCISCO — For years, a school principal’s job was to make sure stu­dents were not cre­at­ing a ruckus in the hall­ways or smok­ing in the bath­room. Vig­i­lance end­ed at the school­house gates.

Now, as stu­dents com­plain, taunt and some­times cry out for help on social media, edu­ca­tors have more oppor­tu­ni­ties to mon­i­tor stu­dents around the clock. And some schools are turn­ing to tech­nol­o­gy to help them. Sev­er­al com­pa­nies offer ser­vices to fil­ter and glean what stu­dents do on school net­works; a few now offer auto­mat­ed tools to comb through off-cam­pus post­ings for signs of dan­ger. For school offi­cials, this rais­es new ques­tions about whether they should — or legal­ly can — dis­ci­pline chil­dren for their online outbursts.

The prob­lem has tak­en on new urgency with the case of a 12-year-old Flori­da girl who com­mit­ted sui­cide after class­mates relent­less­ly bul­lied her online and offline.

Two girls — ages 12 and 14 — who the author­i­ties con­tend were her chief tor­men­tors were arrest­ed this month after one post­ed a Face­book com­ment about her death.

Edu­ca­tors find them­selves need­ing to bal­ance stu­dents’ free speech rights against the dan­gers chil­dren can get into at school and some­times with the law because of what they say in posts on Face­book, Twit­ter and Tum­blr. Courts have start­ed to weigh in.

In Sep­tem­ber, a fed­er­al appeals court in Neva­da, for instance, sided with school offi­cials who sus­pend­ed a high school sopho­more for threat­en­ing, through mes­sages on Myspace, to shoot class­mates. In 2011, an Indi­ana court ruled that school offi­cials had vio­lat­ed the Con­sti­tu­tion when they dis­ci­plined stu­dents for post­ing pic­tures on Face­book of them­selves at a slum­ber par­ty, pos­ing with rain­bow-col­ored lol­lipops shaped like phalluses.

“It is a con­cern and in some cas­es, a major prob­lem for school dis­tricts,” said Daniel A. Domenech, exec­u­tive direc­tor of the Amer­i­can Asso­ci­a­tion of School Admin­is­tra­tors, which rep­re­sents pub­lic school superintendents.

Sur­veil­lance of stu­dents’ online speech, he said, can be cum­ber­some and con­fus­ing. “Is this some­thing that a stu­dent has the right to do, or is this some­thing that flies against the rules and reg­u­la­tions of a district?”

Inter­views with edu­ca­tors sug­gest that sur­veil­lance of stu­dents off cam­pus is still most­ly done the old-fash­ioned way, by rely­ing on stu­dents to report trou­ble or fol­low­ing stu­dents on social net­works. Track­ing stu­dents on social media comes with its own risks: One prin­ci­pal in Mis­souri resigned last year after accu­sa­tions that she had snooped on stu­dents using a fake Face­book account. “It was our chil­dren she was mon­i­tor­ing,” said one Twit­ter user who iden­ti­fied her­self as Judy Ray­ford, after the news broke last year, with­out, she added, “autho­riza­tion” from chil­dren or parents.

But tech­nol­o­gy is catch­ing on.

In August, offi­cials in Glen­dale, a sub­urb in South­ern Cal­i­for­nia, paid Geo Lis­ten­ing, a tech­nol­o­gy com­pa­ny, to comb through the social net­work posts of chil­dren in the dis­trict. The com­pa­ny said its ser­vice was not to pry, but to help the dis­trict, Glen­dale Uni­fied, pro­tect its stu­dents after sui­cides by teenagers in the area.

Stu­dents mocked the effort on Twit­ter, say­ing offi­cials at G.U.S.D., the Glen­dale Uni­fied School Dis­trict, would not “even under­stand what I tweet most of the time, they should hire a high school slang ana­lyst #shoutout2GUSD.”

“We should be mon­i­tor­ing gusd instead,” one Twit­ter user wrote after an instruc­tor was arrest­ed on charges of sex­u­al abuse; the instruc­tor plead­ed not guilty.

Chris Frydrych, the chief exec­u­tive of Geo Lis­ten­ing, based in Her­mosa Beach, also in South­ern Cal­i­for­nia, declined to explain how his company’s tech­nol­o­gy worked, except to say that it was “a sprin­kling of tech­nol­o­gy and a whole lot of human cap­i­tal.” He said Geo Lis­ten­ing looked for key­words and sen­ti­ments on posts that could be viewed pub­licly. It can­not, for instance, read anyone’s Face­book posts that are des­ig­nat­ed for “friends” or “friends of friends.”

But with Facebook’s announce­ment this month that teenagers will be per­mit­ted to post pub­lic sta­tus updates and images, Geo Lis­ten­ing and sim­i­lar ser­vices will poten­tial­ly have access to more infor­ma­tion on that social network.

Glen­dale has paid Geo Lis­ten­ing $40,500 to mon­i­tor the social media posts. Mr. Frydrych declined to say which oth­er schools his com­pa­ny works with, except to pre­dict that by the end of the year, his com­pa­ny would have signed up 3,000 schools.

David Jones of Com­pu­Guardian, based in Salt Lake City, said his prod­uct let school offi­cials mon­i­tor whether stu­dents were research­ing top­ics like how to build bombs or dis­cussing anorex­ia. His cus­tomers include five schools, but he, too, is opti­mistic about mar­ket growth.

“It helps you boil down to what stu­dents are hav­ing what prob­lems,” he said. “And then you can drill down.”

But when does pro­tect­ing chil­dren from each oth­er or from them­selves turn into chill­ing free speech?

John G. Pal­frey Jr., head of Phillips Acad­e­my in Mass­a­chu­setts, said he favored a mid­dle ground. He fol­lows his stu­dents on Twit­ter if they fol­low him, for instance, but he is wary of auto­mat­ed tools that try to con­duct what he called Nation­al Secu­ri­ty Agency-style surveillance.

He briefly con­tend­ed with this ques­tion last year when stu­dents cre­at­ed a blog where they could anony­mous­ly share “secrets.” Many posts were on the fringe, Mr. Pal­frey recalled, and some teach­ers and stu­dents were con­cerned that children’s iden­ti­ties could be deter­mined from their writ­ing pat­terns. The blog’s stu­dent founders were per­suad­ed to add a note of cau­tion, warn­ing par­tic­i­pants that their iden­ti­ties could be discovered.

Mr. Pal­frey offered an offline anal­o­gy. “We wouldn’t want to record every con­ver­sa­tion they are hav­ing in the hall­way,” he said. “The safe­ty and well-being of our stu­dents is our top pri­or­i­ty, but we also need for them to have the time and space to grow with­out feel­ing like we are watch­ing their every move.”

That fine line seems to be equal­ly con­found­ing the courts.

In the Neva­da case, a 16-year-old boy bragged on Myspace about hav­ing guns at home, and threat­ened to kill fel­low stu­dents on a par­tic­u­lar date. He also cit­ed the 2007 mas­sacre at Vir­ginia Tech, in which a trou­bled stu­dent killed 32 people.

The boy end­ed up spend­ing 31 days in a local jail and was sus­pend­ed from school for 90 days. He then sued the dis­trict, say­ing his free speech rights had been violated.

The Ninth Cir­cuit Court of Appeals dis­missed the claim. It called his threats “alarm­ing” and so spe­cif­ic that they pre­sent­ed “a real risk of sig­nif­i­cant dis­rup­tion” to the school. Admin­is­tra­tors were jus­ti­fied, the court ruled, for penal­iz­ing what was osten­si­bly off-cam­pus speech.

“It’s going to be more and more of legal issues,” said Gretchen Ship­ley, a lawyer who rep­re­sents school dis­tricts. “The abil­i­ty to mon­i­tor is grow­ing so quickly.”

The Indi­ana case offers a con­trast. In the sum­mer of 2009, two incom­ing 10th graders at Chu­rubus­co High School post­ed what the court called “raunchy” pic­tures of them­selves. Once school offi­cials found out, the girls were sus­pend­ed from extracur­ric­u­lar activ­i­ties for the school year. The girls sued, say­ing their free speech rights had been vio­lat­ed. The school con­tend­ed that its stu­dent hand­book bars con­duct that could “dis­cred­it” or “dis­hon­or” it.

The court found that pro­hi­bi­tion too broad. The stu­dents’ pic­tures, “juve­nile” though they were, did not cause “sub­stan­tial dis­rup­tion” at school, the court ruled, and even though it was just “crude humor,” it was pro­tect­ed speech. “No mes­sage of lofty social or polit­i­cal impor­tance was con­veyed, but none is required,” the court said.

This arti­cle has been revised to reflect the fol­low­ing correction:

Cor­rec­tion: Octo­ber 30, 2013

An arti­cle on Tues­day about some schools’ efforts to mon­i­tor their stu­dents’ off-cam­pus Inter­net post­ings for signs of trou­ble described incor­rect­ly the vic­tims of a shoot­ing at Vir­ginia Tech in 2007. The vic­tims includ­ed non-stu­dents; not all of the 32 killed were students.