District public school teachers and staff have been accused of using improper force to punish students in 195 cases since September, and investigators have substantiated 77 of the incidents, the school system's top security official said yesterday.

Because the District's definition of corporal punishment is broad, such allegations can range from touching an arm to attacks with rulers and fists. School Superintendent Paul L. Vance said the number of substantiated cases is unacceptably high.

Seventy-eight reported cases could not be substantiated, and 40 cases remain under investigation, said Patrick V. Fiel, the school system's security chief. Officials were unable to say how many cases have resulted in teachers being disciplined.

Recent incidents include a case in which two teachers at Taft Diagnostic Center in Northeast were indicted for allegedly ordering a group of students to beat up three other students in March. One of the students suffered a broken tooth, a black eye and bruises. In a case that remains under investigation, a teacher at H.D. Cooke Elementary in Adams-Morgan was accused of pushing one student to the ground and threatening to kill another.

Vance held a news conference yesterday to announce that school officials will hold a training session today for teachers and principals to explain the corporal punishment law and what type of physical contact is disallowed. Vance said the training comes in response to a report in The Washington Post in August detailing a number of cases in which students said they were seriously injured by teachers.

There were 234 cases of corporal punishment alleged during the 12 months ending in September, some of which resulted in black eyes, bruises and other injuries. School officials could not say how many of last year's cases were substantiated.

Since September, the school system's security staff has conducted corporal punishment training for teachers and other staffers at 25 of the system's 148 schools, Fiel said. Those sessions, held in response to principals' requests, were not described at yesterday's news conference. Fiel said the number of cases reported this year could stem partly from the training and increased awareness of the law.

Corporal punishment, once widely practiced, is outlawed in District schools and also is banned in Maryland and Virginia. Twenty-three states allow the practice.

Definitions of corporal punishment vary from one jurisdiction to another, making a comparison difficult. School systems in the Washington suburbs report few, if any, of the more serious types of cases that have occurred in the District.

The District's definition of outlawed behavior includes the use or attempted use of physical force, either as punishment or to change "the behavior, a thought or attitude of a student." That definition is too broad, some school officials say, and they are considering changing it.

At today's session at Backus Middle School in Northeast Washington, school administrators plan to train principals and teachers union representatives from every school on the city's corporal punishment law and the investigative and disciplinary process that follows.

"What we're trying to do now is get out in front of this . . . to have some preventative training," Vance said.

Vance said he did not do the systemwide training earlier because "it wasn't at the top of my list of things to get done." He said it also took time to plan the sessions and involve the teachers' and principals' unions.

At the news conference, school officials did not cite the number of corporal punishment cases reported this year. Afterward, Vance said he was unaware of the number of cases confirmed by school investigators. "If it's 77, that is too many," he said.

Barbara Bullock, president of the Washington Teachers' Union, who is working in conjunction with Vance on the training effort, said teachers need information about what is allowed. She also asserted that many of the reported cases are untrue.

"What we want to know is, what can you do?" Bullock said. "As it stands now, there are children out of control. And what we want to do is get control. . . . We have to do something to provide a quality education for all students, and the teachers are concerned because they spend a lot of time trying to correct these behaviors."