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How can I demonstrate my productivity to management?

My university has a module for software development with a real client. Some of my team members work in the computer lab all the time, which is an extremely noisy environment with lots of interruptions and distractions. There are about 30 people always talking. People always go on Facebook, YouTube, or tell jokes to each other in addition to doing "work". Some of my team members work 3 hours every day in this environment.

I attend our weekly team meetings and use our online project management system extensively. I address all emails and have a chat client on busy, but I do get messages. I use online resources a lot when solving my problems. However, outside the team meeting and pair programming sessions, I do most of my work in a quiet environment where I can focus and concentrate and I block out all external as well as internal interruptions. I focus on my task 100%. I find that I'm about 10 times more productive this way than in the lab and I can get a lot of work done.

The problem is that our tutors or "management" don't see me doing work in the lab. Thus, I do not appear to be working to them. Thus they think I do no team work. How can I convince them that I do team work because I have lots of communication with my team, but at the same time I like to work on my own? I would like to prove that, just because I work alone a lot and don't necessarily do all of my work in the lab, I'm still a productive member of the team.

UPDATE Management told me that the problem was that I spend working in a team 60% of my time, and I work alone 40% of the time. They told me I should spend 99% of my time working with my team face to face in the lab, aka office.