An independent group determined Friday math achievement levels for children in grades 4, 8 and 12.

The achievement levels may serve as national standards of student performance and may be used in measuring progress toward the national educational goals, said the National Assessment Governing Board, an independent agency that sets policy for the National Assessment of Educational Progress, a congressionally mandated testing program.The board, on a 19-1 vote, approved what children in each of the three grades should know in math at three levels - basic, proficient and advanced. Tests taken by children in 37 states in the winter of 1990 will be scored based on these achievement levels.

"We believe the board's effort is one of the most important ever undertaken to describe what American students ought to know and be able to do in key grades as they move through school,"said Roy Truby, executive director of the assessment governing board.

Children at the "basic" level have a partial mastery of fundamental knowledge and skills, the board decided, and answered 45 percent of questions on the test correctly.

Children at the "proficient" level have demonstrated competency over challenging subject matter and are well prepared for the next level of schooling, and answered 70 percent of questions on the test correctly.

Children at the "advanced" level have shown the kind of superior performance needed in 12th grade and show readiness for rigorous college courses, and answered 90 percent of questions on the test correctly.

The board set the following achievement levels for the "proficient" level:

-Grade 4: Should understand numbers and their applications to situations from the students' daily lives.

Should be able to solve varied math problems, including whole-number computations; use patterns and relationships to analyze mathematical ideas; relate physical materials, pictures and diagrams to mathematical ideas; and find and use relevant information in problem-solving.

-Grade 8: Should be able, with and without a calculator, to solve problems involving everyday situations requiring decimals, fractions and proportions.

Should be able to compute with integers; classify geometric figures; read, interpret and construct line and circle graphs and understand the basic concept of probability. Should be able to translate verbal problem situations into simple algebraic expressions.

-Grade 12: Should have a considerable command of the use of numbers and operations involving all forms of real numbers - whole, fractions, decimals, negatives - and should be able to set up algebraic problems.

Should be able to select, interpret and use measurement relations and formulas in problem situations. Should be able to handle advanced algebra and geometry and should be able to plot a graph and use coordinates.