More than 10% of the math teachers in the city’s public schools aren’t certified to instruct students to add and subtract, the state Department of Education said.

Tucked into a proposal to attract more qualified math teachers to New York, state education officials disclosed yesterday that 679 of the city’s about 6,000 math teachers lack proper certification, although they are certified to teach another subject.

The city responded yesterday by saying it has made “great strides” in reducing the number of uncertified teachers and vowed that all teachers would obtain proper certification by the 2007-08 school year.

“We are working closely and collaboratively with the state to put highly qualified teachers in the classroom,” a spokesman for the city Department of Education, Keith Kalb, told The New York Sun.

The proposal presented to the Board of Regents yesterday stated that the “educational community still must address the issue of teachers teaching subjects in which they are not appropriately certified.”

Faced with a perennial shortage of math and science teachers, Governor Pataki during his State of the State address last week announced a plan to offer free tuition to students at state and city universities who agree to teach those subjects in public schools.

The proposal presented yesterday by two state deputy education commissioners, Johanna Duncan-Poitier and James Kadamus, outlined eight possible steps to do so.

The recommendations include offering a reciprocity in teaching certification with other states in order to attract more teachers from outside the New York area.

Other suggestions include working with the business community on programs to prepare employees interested in teaching in the fields of math and science. IBM announced a plan in September that it would train its veteran employees for second careers as teachers. The program is geared to employees in their 50s who have worked for the company for at least 10 years.

While the proposal was generally met with support yesterday, one suggestion to reassign teachers roiled the president of the United Federation of Teachers, Randi Weingarten.

“I am adamantly against any forcible reassignment,” Ms. Weingarten said. “When you try to force people to teach a subject area that they don’t know or at a school they don’t want to be in, that is a way of asking them to leave the school district.”

Ms. Weingarten said the city reached out to her yesterday to talk about ways to attract and retain more qualified teachers and said that her efforts to address the issue were rebuffed during the union’s recent contract negotiations with the city.

The proposal suggests offering possible signing bonuses or housing allowances to entice more teachers into the hard-to-staff areas.