An elite corps of teachers whose certification makes them eligible for bonus pay in at least 31 states has tripled in the past year, the Education Department said this week.

The National Board for Professional Teaching Standards has certified 2,965 elementary and secondary school teachers from 48 states and the District of Columbia, bringing the number of so-called "master teachers" to 4,799.

The teachers spend about a year submitting videotapes of their teaching, lesson plans, and samples of student work and then take a test to prove they have mastered the subjects they teach and how to teach them. They have been praised by President Clinton, who has sought funds to help more teachers pay the $2,000 application fee, hoping to boost the "master teacher" ranks to 100,000 in the next seven years. There are 3 million teachers nationwide.

"With this announcement, we believe the national board is well on its way to reaching its goal," said Betty Castor, president of the private, nonprofit board of teachers, other educators and business leaders. The Southfield, Mich.-based board, founded in 1987 to increase teaching standards, has a $35 million budget partially financed by the federal government.

Critics say the system interferes with states' licensing procedures and unfairly increases the pay of teachers who can afford the time and the $2,000 fee to get the credential.

"This is about rewarding teachers for staying in the classroom," countered Castor. She said about half of the 35 states that reward teachers who earn the certification also offer financial help to teachers seeking it.

All states license teachers, but 42 test their teachers based on criteria ranging from specific subjects to whether they understand the basics of teaching. National board testing "says they can do a lot better," Castor said.

As the national certification of teachers has risen, so has state acceptance of the program. In addition to the 35 states that offer teachers some incentive to gain the credential, up from a dozen a couple of years ago, 31 help pay the cost of gaining the credential or increase pay for those who get it.