The remainder of the evaluation will come from observations from principals and other teachers, and other measures. If teachers are rated ineffective for two consecutive years, they would face firing through an expedited hearing process that must conclude within 60 days. Currently hearings can drag on for several months.

The changes, which Mr. Steiner, his deputy John King and Merryl H. Tisch, the chancellor of the State Board of Regents, described in an interview on Monday, are subject to approval by the State Legislature. Ms. Tisch said they needed lawmakers to approve a package of education legislation within the next 10 days, so that the state could meet the June 1 application deadline for the federal competition known as Race to the Top.

New York did not win one of the first Race to the Top grants. Last week, the State Senate voted to more than double the number of charter schools in the state, another move aimed at winning Race to the Top money. The Assembly has not voted on that issue, though pro-charter advocates have been furiously lobbying and running advertisements.

Testing data would be used for only a fraction of the teachers in the state, because many teachers instruct in subjects or grades that do not have an annual exam. Mr. Steiner and Ms. Tisch have criticized the state exams, saying they may have become too easy and predictable in the last several years. But Mr. Steiner said that they were “not useless,” and that the department was taking steps to improve them, including changes this year that broadened the material covered by the tests.

Lawmakers are likely to approve the changes if they are backed by the teachers’ unions. But Mr. Steiner said it remained unclear if the state was out of “choppy waters.”