Alexandria's 15 public schools will open Tuesday with a new superintendent, Paul Masem, and 9,400 students, about 500 fewer than last fall.

The number of school-aged children living in Alexandria has declined in the last decade because of a decline in low-income housing, an influx of well-to-do adults who do not need or want to use the public schools and an increase in the cost of housing that frequently puts units out of the reach of some families with children. The enrollment has steadily declined from about 13,000 students in 1977 to about 10,500 in 1984 and an estimated 9,400 students this fall.

A new math program, called Quest, will be piloted for first and second graders at Polk Elementary School on Polk Avenue, and at Patrick Henry Elementary School on Taney Avenue. At the Cora Kelly Magnet School on Commonwealth Avenue, a $564,450 grant from the U.S. Department of Education will fund several new staff positions and programs.

The city's only high school, T.C. Williams on King Street, will have a new $260,000 running track, as well as new windows, additional air conditioning, a new science lab, and renovated bathrooms that include facilities for the handicapped.

Other building improvements made during the summer include a new gymnasium floor at John Adams Elementary School on Rayburn Avenue, a new front entrance at MacArthur Elementary School on Janneys Lane, and air conditioning for one-fourth of Hammond Junior High School on Seminary Road, which was not air conditioned.

Masem, 48, who succeeds Robert W. Peebles as superintendent, said he looks at the job as a challenge. Peebles retired for health reasons in July after seven years at the post.

"I had choices and I came here {to Alexandria} because this is an exciting and challenging job," Masem said last week at a luncheon for 23 new teachers.

"Alexandria is a microcosm of what is going on in education all over the country, and we are on the cutting edge with all the problems and opportunities" going on in the United States, Masem said at the luncheon.

Masem said he will emphasize making central office personnel and other staff a support for teachers. He has also pledged to visit school classrooms one day a week.

The nine-member Alexandria School Board, which has met on Wednesday nights for at least 30 years, this fall will hold its sessions at 8 p.m. on the first and third Thursdays of every month.

Timothy Elliott was reelected last spring as chairman of the board, and Lynnwood Campbell Jr. will be the new vice chairman. Billie Hughes, 41, was hired in June as clerk of the board.

Georgeanna Yahner, who retired in June as executive director of educational facilities after working for the Alexandria schools for nearly 30 years, will be succeeded by Philip Oliver, 56, a retired U.S. Navy captain, who will oversee building maintenance and improvements.

Other personnel changes include three new principals. Robert Yeager, 44, is the principal of George Washington Junior High School on Mount Vernon Avenue. Cecelia Krill, 42, is principal of Jefferson-Houston Elementary on Cameron Street, and Phyllis Bushell-Past, 45, will head Mount Vernon Elementary on Commonwealth Avenue.

Yeager and Krill worked previously for the Alexandria schools, and Bushell-Past comes from Owensboro, Ky., where she has been vice principal of a middle school.

Students will also be welcomed with higher lunch prices, up from 85 cents to 90 cents for kindergarten through sixth grades, and from 95 cents to $1 for students in seventh through 12th grades.

The $564,450 federal grant will fund a "writing-to-read" computer lab at Cora Kelly Magnet School for students in kindergarten through sixth grades.

According to Connie Cookson, mathematic curriculum specialist for kindergarten through sixth grades, the new Quest mathematics program for first and second graders is unique because students learn math by always using objects they can manipulate to understand concepts such as multiplication and subtraction.