I think usually when a problem like this comes up, it depends on how well you know and get along with the problem coworker. If you think you can communicate with them in a positive and effective way, then I'd say go for it. If not, then maybe in the longer term you should work on your relationship with the coworker...even if you never get to the point where you like them personally, a better working relationship has got to be a good thing. Not to mention the practice getting along with people you don't naturally click with.
In the short term, if you don't feel comfortable talking to them about it, then I think resolving these kinds of disputes is part of a manager's job. I would say in general it would be a bad idea to complain to other people about them (although I'm guilty of that myself...working on it!)...I would bring it directly to the managers attention, in as constructive a way as possible.
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