The Montgomery County Board of Education began its painstaking review of the school system's budget last week, calling staff members before the board to answer questions, page by page, about the 600-page document detailing $339 million of expenses expected in fiscal year 1982.

Local residents will have a chance to testify to the school board next Monday, Wednesday and Thursday before the board runs through final work sessions on the budget at the end of this month. Final action is due in early February.

Superintendent Edward Andrews characterized the budget as offering no new educational programs, although it is substantially larger than the current year's $309.1 million budget because inflation has sent utility bills skyrocketing and necessitated a cost-of-living increase in teachers' salaries. The pay raise alone will cost the school system an additional $21 million to $24 million; the exact amount cannot be calculated until 1980 Consumer Price Index figures are announced by the federal government Jan. 24.

Current teachers' salaries range fromm $12,103 to $25,535.

Other increases in the budget result from the higher cost of placing handicapped youngsters in private residential institutions; an estimated 41 percent increase in the cost of heating oil, natural and propane gas and electricity; higher medical care costs for school employes; and regular salary increments for school system personnel who have not yet reached the top of their salary schedules. These total $8.76 million.

The budget adds six positions for art, music and physical education teachers; 10 positions in the gifted-and-talented program; and two career-preparations and four counselors' positions in high schools.

Officials expect countywide enrollment to drop by another 1,500 students, so the budget eliminates 140 jobs, most of them elementary and junior high school teachers', with a corresponding reduction in monies for textbooks and instructional materials, for a savings of $2.3 million. Another $1.2 million will be saved by consolidating five area administrative offices to three, and by cutting 77 jobs in both the area offices and the centrol office.

Andrews said no one will be fired, however. The staff reductions will be achieved through attrition and demotions.

Federal grants covering a variety of programs are expected to decline from $2.26 million this year to $1.4 million, and state funds are expected to increase, from $45.2 million to $48 million. The remainder of the budget falls to the county government.

A windfall for the school system lasst month was $600,000 in federal impact aid, with perhaps another $1.2 million sstill to come. Impact aid is money reimbursed to local jurisdictions from the federal government to compensate for the loss of property tax revenues on tax-exempt federal property.

Last year the school board did not include revenue from impact aid in its budget for fiscal 1981 because it was told Congress planned to discontinue those payments to some jurisdictions, including Montgomery County. School officials said they believe the move to cut that aid got lost in the transition of administrations, and they were pleasantly surprised to get the first of what they hope will be three checks. They are not, however, including federal impact aid in the new budget, since they still expect it to be cut.

The impact aid can be used for any basic educational expenses, and Andrews said the money will go toward wiping out a utilities deficit of $841,000 caused by higher fuel-oil prices.

In early projectons, the County Council said it could cover either $329 million budget or a $335 million budget, depending on whether the council increased the property-tax rate.

The school board and the County Council are expected to disagree on how much is needed to run the school system. Last year that difference was nearly $5 million. The Board of Education asked for $314 million and got $309.1 million.

"The atmosphere of the work sessions (this year) with the school board is going to be painful," said Council President Ruth Spector. "In certain areas, such as class size and the closing of schools, the philosophy of the board is not always attuned to what the majority of the council wants.

"Is it always best to have two teachers for smaller classes rather than one good teacher for a slightly larger class?" she asked, citing an example of the differences.

Andrews said the new budget assumes the school system will hire the best teachers it can, but he expects to be challenged by the council, as he has the last two years, over average hiring-level salaries. The council has not given the school system the salary average it has asked for, and Spector questioned again this year the necessity of having so many teachers with master's degrees.

There are 823 teachers in the school system who hold bachelor's degrees, 158 with bachelor's degrees plus 15 credits toward a master's, 3,174 teachers with master's degrees or the equivalents, and 2,166 teachers with master's degrees plus 30 graduate credits toward a higher degree.

Salaries for those with bachelor's degrees range from $12,103 to $18,637. Teachers with master's degrees earn from $13,555 to $24,568, and those with master's degrees plus 30 credits are paid from $14,522 to $25,535.

Public hearings on the budget before the Board of Education are scheduled for 8 p.m. on Jan. 19, 21 and 22 in the Educational Services Center auditorium in Rockville.