The State Board of Education approved a preliminary budget Friday totaling more than $965 million - a 9.1 percent increase over the 1988-89 budget of $884 million.

Part of the increase is related to actual growth in the number of children who must be educated - an estimated 4,849 who will be added to the rolls, bringing the total to approximately 434,000.The board also will ask the Legislature to cover a shortfall in retirement and Social Security bases related to changes in these programs for state employees. The total recommended increase for these categories is is $3.7 million.

Growth in the Area Vocational Center programs also indicates an increase, said Laurie Chivers, financial officer for the State Education Office. The office seeks $400,000 to support that growth.

Also targeted for an increase is health insurance, which is increasing in cost 20 to 30 percent yearly. An additional $14.5 million is needed to help school districts meet the need.

The budget proposes an increase in the basic county mill levy, from 21.28 to 23.28. The proposal would put the controversial 2-mill shift provision passed two years ago by the Legislature permanently into the basic mill levy.

An increase in the weighted pupil unit from $1,204 to $1,264 and cost-of- living increases for school personnel would add $23.9 million to the budget.

The board also will ask for one-time-only money to help schools meet federal asbestos standards; to give the area vocational centers up-front money instead of funding them the following year based on the current year's enrollment; to institute a program that would allow students to accelerate their school experience by earning proficiency credits; and to give alternative educational-delivery systems a start.