The Fairfax County School Board last night approved the closing of one elementary school and considered another, while taking a look at a proposal to build three new elementary schools in the western part of the county.

With only one abstention, the board approved the closing of John C. Wood Elementary, a Fairfax City school whose enrollment will be absorbed into Layton Hall Elementary next fall. Action is scheduled Jan. 13 on a proposed voluntary merger of Chapel Square Elementary into Wakefield Forest.

The closings and construction proposals, contained in the school system's proposed five-year capital improvement program, reflect continuing trends toward declining enrollments in the beltway area of Fairfax County and increased crowding in the western region.

Wood and Chapel Square are in the central eastern part of the county, while the three locations where new schools are proposed -- Centreville, Herndon/North Reston and Oakview -- are in the outer crescent.

The staff recommended against studying further consolidations during the 1982-83 school year.

The board also took under consideration projections that there would be about $2 million less in state and federal aid than budgeted for in the current year. The biggest single cause is reduction of the sales tax receipts estimate.

Projected expenditures also were down--by $840,000--largely because the cost of fuel oil was overestimated.

In other business, the board named E. Wayne Harris to be Area Two superintendent. Harris has been an aide to the divisional superintendent since 1980.