Many people will be familiar with the feeling that their manager doesn't really believe they're working if they're not in the office. The reason isn't based on anything provable (after all, the majority of managers think that when it comes to them, they are much more productive when not chained to the office). It's not that they don't have faith in you, they just don't trust you. There's a difference.
The best definition of faith comes , appropriately I suppose, from the Bible. Hebrews 11:1 to be specific: "Faith is the substance of things hoped for, the evidence of things not seen". You hope for the best, and then the evidence (hopefully) supports that faith. Trust is different.
Sadly, there's no equally eloquent description of trust. Many models describe trust as built over time, based on the observable in three areas: shared goals, proof of motives and proof of competence.
Basically, faith starts with belief and is supported by what comes later. Trust is built over time based on the evidence.
Faith is important, because it starts with positive intent. We would love our bosses to have faith in us just because, well, we're us. It just doesn't always work that way. Why won't she trust us?
In a perfect world, our bosses would have faith in us, and that faith is supported over time. It looks and smells just like trust. If we aren't trusted though, it can be depressing and we often think very unkindly of those who mistrust us, even when there's no evidence to support that lack of trust. It's easy to be insulted and take offense.
What we don't know is how our boss reached that suspicious stage. Maybe she's always been the suspicious micro-managing type. Maybe she's been disappointed in the results of remote workers and team members in the past. Whatever the reason, it's more important to build her trust in you than to hope for her faith in your brilliance.
Remember, trust is evidence based. We need to consciously demonstrate our capabilities:
Shared goals are critical. Explicitly state how what you're doing ties to the overall team goals. Don't assume that people can make the connections. If you're not sure how what you're asked to do fits those goals, ask. Just the discussion alone will demonstrate your commitment and check that box off in your boss' mind.
Proof of competence is very objective. You meet your deadlines or you don't. The quality of your work is at or above expected levels or it's not. At best, it reaffirms her faith in you. At worst, it slowly builds "trust equity". You can help by making sure that you and your boss have clear metrics on deliverables. State them and meet them. Over time trust evolves.
Proof of motives is much more subjective and is the least-discussed component of building trust. It's largely internal - why do you do (or don't do) what you do? Did you miss that deadline because you just ran out of time, or did you fritter your time away on some other project you cared more about?
As a manger, find out what is going on with your team members. As a team member, confirm your commitment to the team and give honest answers about barriers to your success. Otherwise, she is going to draw her own conclusions and they may not be to your benefit.
Faith is a wonderful thing. Today's project and functional teams, though, are better off running on trust. It's subjective, it's built on measurable results and can be restored through hard work on both parts. Over time, it might even turn back into faith.