The changes in how teachers are recruited, certified, evaluated and rewarded included in the new state budget are a huge victory for Gov. Andrew Cuomo. More important, the changes are a huge victory for students and for the best current and future teachers.

At the end of marathon negotiations, Cuomo got practically every reform he wanted, and the unions lost ground.

In broad strokes, a system will almost certainly be in place after legislation is voted on this week to recruit great education majors to state colleges in return for full scholarships, a huge boon for young people who want to make a life in this city as educators. The changes will also make the process for teachers to get accredited and tenured more rigorous. It will be harder to game teacher evaluations. Teachers whose students fail to make measurable progress can no longer be rated effective or highly effective -- no matter how well they do on subjective evaluations like classroom observation. Great teachers will be in line for $20,000 bonuses, bad ones will be removed more easily, and schools where students aren't achieving will get meaningful outside help in the form of distinguished educators brought in to oversee turnarounds.

All this comes with a 6 percent school-aid increase for the 2015-16 school year that should go a long way toward getting schools the resources they need.

This significant achievement in reform probably could not have happened without the unexpected deposing of Assembly Speaker Sheldon Silver and the ascent of Carl Heastie into the job. Critics will say Heastie lacked Silver's negotiating dominance, but in fact he prioritized the extra school aid, and got what he wanted.

The state Education Department, which has no commissioner, and the Board of Regents, responsible for filling that post, now face huge responsibilities. Many teachers can't be rated effective unless their students show growth on tests, so the annual standardized exams in English and math need to be top-notch, and ever improving. Every aspect of the system must work fairly so students can get what they need and teachers can provide it.