New York City public-school principals looking to control costs by shedding teachers forgot Lesson No. 1 about schoolhouse politics: The faculty can never shrink, only grow.

“Displacing teachers is not a viable solution,” union boss Randi Weingarten says. “Fewer teachers in a school means increased class size, a reduced range of . . . services and less time for teachers to spend with students.”

Ah, yes. The class-size trope.

Weingarten & Co. bemoan rooms with as many as – gasp! – 21 kids in the younger grades, on average, and up to 26 kids in the older grades.

But here’s Lesson No. 2: Teachers get to use different math than everyone else. Because, in reality, the system’s 1 million students share more than 78,000 teachers – producing a student-teacher ratio of, get this, 13-to-1.

So why do classes run so much larger than 13?

Ah, you see, a teacher on the payroll isn’t necessarily a teacher in front of a chalkboard.

So where have all the teachers gone?

Gone to rubber rooms, every one.

Or they’re on sabbatical.

Or “excessed” – that is, let go (though they still get paid, under rules of their contract).

Meantime, special-ed classes – where the maximum number of kids is 12 – suck up armies of teachers.

For Weingarten & Co., of course, the more teachers, the more dues income to bribe – er, contribute to – politicians.

Any additional teaching is purely coincidental.

But if principals can’t trim faculty headcounts, how are they supposed to achieve their share of City Hall’s mandated budget economies – given that some 85 percent of their outlays are for personnel costs; that is, for teacher salaries?

They’re not, of course.

That’s the point.

Teachers are special, don’t you know.