Other forms: uncomprehendingly
Someone who's uncomprehending doesn't really understand what's going on. If you try to ask directions in English during your trip to Bulgaria, your words might be met with an uncomprehending expression.
When you comprehend something, you understand it. So by transforming comprehend into an adjective and adding the prefix un-, or "not," we get a word that means "not understanding." When your teacher asks you a question and you don't respond, she may not be able to tell if you're uncomprehending or just not paying attention.