Career Change Advice

What's the best way to make a switch? I've been in banking for 11 and half years working every position from part time teller to management. However, I'm so tired of the banking world. It's not satisfying anymore, just going through the motions.

I went to school for museum studies and writing (a heck of a 180 from what I'm doing). I want to get into that industry. I've made a few applications, but I keep hitting walls. I'm finding museum industry is heavily volunteer driven.

Insight? Not even just about the museum field. Just how to go about making a career switch.