Fear of Elevators

I think fear of elevators is called "clautophobia" but I cannot find a clear consensus on that. Whatever it's called, Rebecca has it. Which is very surprising to me considering her usually mellow personality and the fact that I have rarely seen her be afraid of anything. But today was the second or third time that she freaked in the elevator at Ben's school. For a while I avoided using the elevator because I knew she didn't like it, and then today I forgot and I put her in her stroller to go in to get Ben this afternoon. So of course I had to use the elevator to go up to the second floor where Ben's classroom is since I had the stroller. She started screaming bloody murder as soon as the elevator door opened and again on the way back downstairs even though I took her out of the stroller and held her on the way down - it didn't make her feel any better. I really don't understand what about it scares her. Should I practice avoidance or try to desensitize her?