Schools in the rapidly growing southern and western regions of Fairfax County are being shortchanged in their share of psychologists, counselors, social workers and art teachers, according to a staffing study by the school system.

At the same time, schools in the older eastern and central areas of the sprawling suburban county have more staffing positions per student, the report on staffing inequities showed.

"The study brought to light the inequity that exists," Kohann Whitney, the School Board member from Centreville who requested the study, said yesterday. She said the survey shows that the school staff in the fast-growing districts, such as the one she represents, serve more children than they can help efficiently.

The study showed, for example, that the support staff in the fast-growing Vienna region serves 40 percent more students, but has the same number of art teachers as the Alexandria region where student enrollments have declined.

School Superintendent Robert R. Spillane said he will ask the School Board to divert more of its 1987 budget to increasing school staffing in the fast-growing areas. The school system traditionally had divided its new staff positions evenly among each of the school districts in the county.

Whitney praised Spillane's recommendations for changes, but said, "There are some inequities that still exist and I would like to see us move a little bit faster."

Whitney recommended hiring even more social workers and psychologists in the booming neighborhoods. Whitney said the alternative -- moving staff from one district office to another -- would be politically sensitive.