There is a sign at MacArthur Elementary School in Alexandria that proclaims: "We the Kids."

It doesn't signify a children's move to overthrow the government; it is part of the first institute of its kind on the East Coast aimed at bringing the study of law into the elementary classroom, according to the institute's director.

About 20 instructors from Alexandria, Fairfax County and Arlington are participating in the 2 1/2 week George Mason Institute on Law-Related Education, which began Monday.

They are learning how to set up a mock trial, how to make law discussions palatable in the classroom and acquiring a background in areas such as the rights of children, civil rights cases in Virginia and school law. A principal aim is to introduce pupils to aspects of law they deal with on a day-to-day basis.

According to the program's director, Jack Henes, the Alexandria school system has been moving since 1971 toward a curriculum that includes law. "When the desegregation process began I thought there should be some changes in the curriculum," said Henes, who directs social studies for the city's schools. "All socio-economic groups can relate successfully to law."

Henes said he noted that adolescents had the highest crime rates and said he hoped students in the schools might benefit from what they heard in the classroom.

A similar training program for secondary teachers was held last summer.

Mary Lynda Gowran, an intitute staff member who is also an Alexandria teacher, conducted a six-week course in the law for eight-graders following last year's program and said she noticed some interesting developments.

Students started visiting stores that advertised sales and asking store personnel about how limited their "limited supply" of sale items was or whether the store was really going out of business as advertised. Some students wrote letters to manufacturers complaining about faults in their parents' cars. Others questioned school rules, asking that they be changed and that all regulations be posted at the beginning of each academic year.

Gowran said she thinks mock trials, which were conducted in the secondary schools, will also work well in the primary schools. Such trials work well for both lower and upper achievers, said Gowran; "I found the low-achievers could reason well and accurately" in a trial situation.

As the study of law is introduced into elementary school classes this fall there will be discussions of things the pupils can relate to - such as the laws that govern the TV commercials that interrupt the "Pink Panther" cartoons on Saturday mornings.

The institute is divided into two major fields: street law (criminal law, juvenile law, welfare and landlord-tenant law) and conceptual law (First and Second Amendment rights). Participants also discuss the reasoning process of children.

The program, which gives its participants three hours of graduate school credit, is financed by a Law Enforcement Assistance Administration grant. According to Henes the $18,000 grant is being split between the Mason Institute and a similar program in Madison, Va.

Sponsors of the Mason Institute include the Young Lawyers Conference of the Virginia State Bar, the Virginia Council for the Social Studies, the Virginia State Department of Education and George Mason University.