We’d never met. But when I walked into my class at American University a few weeks ago, I knew instantly who she was. She came up quickly, like someone who didn’t have much time.

She was a grad student working at AU for the Service Employees International Union to organize adjunct professors like me. She hoped I would sign up. What surprised me was my reaction. I wished she hadn’t come.

How could I feel that way? When I was 17, and the New York’s teachers union went on strike, my mother, a teacher, spent days terrified of being fired if she refused to cross the picket line. I scoffed at her timidity.

What made me so timid? People like Wisconsin Gov. Scott Walker (R) want to take away most bargaining rights teachers have, but I think organizing adjuncts is a reasonable response to one big but little-known change in higher education.

The change isn’t what today’s college students learn. It’s who teaches them. That image of the cloistered, tenured professor, sitting in an office overrun with books? Forget it. Today, 47 percent of those teaching undergrads are adjuncts.

We have no offices. Or benefits. Colleges cut costs by hiring adjuncts for low salaries and few perks. Since some adjuncts actually do what they teach, schools can offer their students instructors who know what they’re talking about. That’s good.

The problem is, there are two kinds of adjuncts. I’m one: the hobbyist. I take teaching seriously but have a business. My adjunct salary isn’t vital. Don’t tell AU. I’d probably pay them to teach there.

Then there’s the second kind, who make up almost half of all adjuncts: those who want full-time teaching jobs, especially the 28 percent who take as much adjunct work as they can find. They teach at three or four campuses, tend bar to supplement their incomes, hold student conferences at Starbucks, and keep books in the trunks of their cars. Schools can let them go at a moment’s notice, and do. They need a union.

“If SEIU has its way,” wrote one critic in November, “America’s colleges and universities will find themselves in a headlong free-fall to the bottom.”

Not true. It will strengthen them.

One reason is something unionizing adjuncts won’t change. I calculate that AU takes in at least $25,000 in tuition for my course — after a heavy discount for student aid. AU pays a teacher like me $4,000 to $5,000 for it — way more than the $2,500 national average. Most other costs are fixed. Adjuncts contribute a lot to the school’s bottom line. Even a whopping salary increase wouldn’t change that.

But there’s something a unionized workforce can change. It can make teachers better. How? By making it more attractive to stick around until we get good. A 2000 Harvard Educational Review study, and others, lend credence to the idea that better salaries, working conditions and the training that unions bargain for don’t just motivate teachers. They improve learning.

I see the advantage of experience in myself. Each year I think of new approaches. Today I use many of them. Sorry, early students; I’m better now.

Better teaching should matter in Washington, where schools lure students excited about adjuncts who have held high-power political jobs. Yes, a senator knows a lot; even senators need to teach for a while before they learn how.

For my mother, the memory of her union organizer father made her decide. “It was the center of his life,” she said. She mustered up her courage, defied a principal she adored — and joined the strike.

Like her, I love teaching and my bosses. I didn’t want my signature to imply that they resemble the managers of decades past who hired thugs to go after striking workers.

But that fear, I realized, stereotypes both administrators and unions. I signed.

I hope AU proves smart enough to say, “Do it. Collective bargaining is fair. We’ll still cut costs — and improve AU.”

Because in the end, the issue is a matter of common sense: the idea that treating people well makes them work well.

Collective bargaining gives adjuncts a better deal. And it does more. By encouraging the conditions that better prepare us for that moment we first stare out at our classes, it creates an advantage even Scott Walker might like.

A better deal for those staring back.

Bob Lehrman, a novelist, former White House aide and author of “The Political Speechwriter’s Companion,” was American University’s adjunct of the year in 2010. He co-directs the university-sponsored blog Punditwire (www.punditwire.com).