While extroversion is often highly valued by companies, there are many people like you who have a more introverted style that may be less engaging and more deliberative. That doesn't necessarily make you any less effective, but you have to be sure that some of the more negative features associated with being an introvert don't come to define you. The risk, as you've started to see, is that you become viewed as quiet and inactive, as opposed to thorough and deliberate. So you may need to go on an active campaign to let the important folks at your company know what your style is, recognize its strengths, and present yourself as more of a three-dimensional figure.
So you might focus on demonstrating your acumen in one-on-one interactions where you're more comfortable. And for your boss and your boss's boss, you might even want to articulate your style to them-perhaps tell them that "This is how I operate: I tend to listen more before saying something, and really think through a decision and consider all the variables." That way, they can comfortably describe your style and defend you if others were to critique you. You want them to see you as an active player who may have a different style but can still be successful, rather than a low-profile, inactive player who is not engaged.
In addition, you may want to find venues and situations that allow you to showcase your more extroverted side. So while you may not be so comfortable speaking in big meetings, maybe you're a fearless karaoke singer. Or perhaps you have hobbies or interests, such as skydiving or rock climbing, that demonstrate a more social, external approach and that you can drop in to conversation with your colleagues. Making people aware of these things can help them to form a fuller picture of you. Ultimately, you want to be in charge of framing people's perceptions of you, versus having them project their impressions on to you. Good luck.
Photo courtesy of Flickr user Ed Yourdon
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