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A QUAINT idea about school discipline is that students who are unruly and disobedient, or who get in minor scrapes or hallway shoving matches, will be dealt with sternly by teachers and principals. If only. In fact, in a staggering number of such cases, the students, who are often preteens in elementary and middle schools, are referred to police and the courts — a wildly disproportionate response that can stigmatize children at school and, in some cases, be a stain on their records for years.

In the most comprehensive study on the so-called school-to-prison pipeline, published by the Center for Public Integrity in 2015, Virginia schools were the worst offenders, shunting disobedient kids to law enforcement at nearly three times the national rate. The state's record amounted to a criminalization of rowdiness and run-of-the-mill juvenile behavior, as well as an abdication of responsibility, lack of training or both on the part of adults who nominally run things at public schools.

Based on Education Department data collected in the 2011-2012 school year, researchers found that Virginia was reporting students to the authorities at a rate of about 16 for every 1,000 students; the national average was 6. Just as striking, the report said, was that the most frequent reporters were middle schools, whose students are usually 11 to 14 years old. Nearly half of criminal complaints were issued to students younger than 14 — in some cases much younger.

Typically, the complaint lodged against students is disorderly behavior, a catchall that can mean anything from a temper tantrum to a balled fist to a brawl. State law doesn't require that law enforcement be notified of such conduct by minors, but many Virginia schools do it anyway. In the state, and nationally, students referred to law enforcement are disproportionately African Americans and children with disabilities. In Virginia, where blacks are 23 percent of the student population, they were nearly 40 percent of those referred from schools to juvenile courts.

The impulse prompting schools to hire police has spread since the massacre at Colorado's Columbine High School in 1999. It amounts to a massive overreaction on the part of educators who, though justifiably determined to maintain safety for students in their care, ended up adopting hair-trigger policies. A more level-headed approach would emphasize de- ­escalation training for the police and security officers who work in schools, diversion programs to deal with relatively minor offenders without turning them over to the courts, and clearer rules set by the schools themselves.

Gov. Terry McAuliffe (D) has spoken out forcefully against disciplinary policies that criminalize conduct once handled in school. A new state law is in place to encourage local school boards to develop alternatives to suspending students, including counseling, community service and mediation. That's a promising start. Lawmakers will have to keep the pressure on to tamp down what amounts to massive overreaction on the part of school authorities.