The Maryland State Board of Education, spurred by recent national reports about the declining quality of education, yesterday asked the state legislature to fund a scholarship program to attract the "best and the brightest" to teach in its classrooms.

The legislation, which school officials said is the crucial element in a major statewide plan to raise teaching standards, would provide money for tuition and fees to about 300 high school graduates a year who agree to enroll in teacher-training programs and then return to Maryland public schools for four years. Board officals estimate the program would cost about $2 million a year.

In other action, the state board also sent to Gov. Harry Hughes an austere budget request for $890.76 million in state funds for the fiscal year beginning in July 1984, an increase of 5.9 percent over this year's state funding. In an effort to raise additional money, the board also approved the creation of a foundation to solicit funds from private sources for public education.

The scholarship program is designed to address a problem that is "not just a national problem," said Herman E. Behling, assistant state superintendent for certification and accreditation. "Historically, we have not attracted the brightest people into teaching. This is an attempt not only to get a better level of teaching, but also to get the best and the brightest."

The proposed legislation follows the release this month of a Carnegie Foundation study that showed college students enrolled in teacher-education courses scored on the average 80 points less on the Scholastic Aptitude Test than other college students.

The scholarship program is only one of a number of steps Maryland plans to implement to improve the quality of teaching. Earlier this summer, the Maryland board decided to spend $215,000 to design teacher-competency tests, teacher-evaluation programs and teacher-training programs in areas such as science and mathematics where there are severe teacher shortages. Teaching students who plan to specialize in these areas should be given priority in the scholarship competition, the board recommended yesterday.

"We hope the scholarships will only be one arrow in our quiver," said state board spokesman Gus Crenson.

To qualify for the scholarship money, which will not exceed the cost of tuition and fees at the University of Maryland, a high school student must have at least a 3.5 grade point average, and a college student, 3.0. Tuition and fees at the University of Maryland are expected to run $1,410 next year. If a student does not return to teach in Maryland public schools after completion of training, he or she will be required to pay back the money.

In approving the creation of the private foundation, school officials said it should provide a much needed and visible forum for public schools to compete with other public institutions for donations from private corporations and institutions.

Such a foundation is not a new idea. In the Washington area, Fairfax County has started a similar foundation and in the District, the Washington Parent Group Fund has provided money to 16 public schools.

In California, one of the first states to embrace the idea of private funding, about 200 private foundations were created after public funding for local school jurisdictions there plummeted as a result of voter approval of Proposition 13, which limited property taxes. In some California jurisdictions, the foundations have provided as much as $200,000 to local public schools.