The Calvert County Board of Commissioners yesterday adopted a $31.5 million fiscal 1984 budget that includes $580,000 for Maryland's first county-wide computer system for teaching mathematics and reading.

The program is scheduled to be implemented this fall in elementary schools, supplementing traditional instruction in mathematics and reading with one hour of individualized instruction on the computer each day. School officials say it is the first such system in the state.

"By teaching with computers in kindergarten through fifth grade we expect to blow our kids' test scores right out the top," said schools superintendent Eugene M. Karol.

In approving the overall $31.5 million county budget, the commissioners spared residents any tax increases by drawing on almost $2 million of an anticipated $5.5 million surplus from previous years, according to James Allman, county director of administration and finance.

In addition to money for the instructional computer system, the public schools will get just over $16 million, most of it for teachers' salaries, Allman said.

The state superintendent of schools recently declared an impasse in contract negotiations between the county and the Maryland State Teachers Association. An arbitrator is scheduled to begin mediation July 21.

Should a settlement be reached, funds have been set aside in budget for a $400 annual across-the-board increase for the county's 400 teachers, administrators, librarians and guidance counselors, Allman said. The school system has an additional $300,000 it could use for teacher pay increases, he added.

If a negotiated settlement exceeds the amount on hand for pay raises, school officials would have to seek supplemental funds from the county, Allman said.

The county's 220 full-time salaried workers-- primarily courthouse and parks and recreation employes--will get an annual increase of $800 each, and the county's 100 to 200 part-time employes will get an increase of 40 cents per hour.