Managing Conflict

Lately, I have been facing conflict at work. I have tried numerous times to explain how I feel about it and why to my supervisor, but my efforts have not really been successful. Through course readings, I have found that one strategy that I started to use and will use more often, it is a challenging strategy. I think this strategy would work best for me because most times, I just try to avoid conflict altogether. Because avoidance was my usual managing technique, I never felt as though my issues were resolved, they were just suppressed. Along with the challenging strategy, I would like to use probing as well. I need to ask more questions if there is a misunderstanding. I believe that these two together will help me to manage this conflict more effectively. I believe this because at times, the atmosphere is one where I am supposed to do a task without question. Many times, this can cause conflict within myself because many times, I feel like an explanation would be okay. 

Does anyone have any other suggestions about how to deal with conflict in the work place?