As a female exhibit manager, I supervise a male employee who ignores my ideas and direction because of my gender. He is much more cooperative with male superiors. How should I deal with this issue?

Such friction may be due more to a lack of rapport than a lack of respect. If your employee has worked with his male superiors longer than he has worked with you, and if they share similar backgrounds, he may respond better to them for precisely those reasons. You can cross that particular bridge, however, by soliciting his opinions on work-related matters rather than just telling him what you want done. This will communicate your respect, which usually earns cooperative behavior in return.

But if that approach fails, it may be because he does indeed possess the sexist attitudes you suspect. In that case, I suggest a formal meeting in private, which will help impart the gravity of the situation to him. You might open it with a statement along these lines: "My position of authority and my ideas seem 'invisible' to you. I'm sure you can appreciate how frustrating this would be if you were in my shoes. How do you think we can resolve this matter?"

Whatever specific actions he suggests and you agree to, the most important part of the exchange is actually your recruiting him to solve the problem. By doing that, you will also make it easy for him to save face and buy into the remedies that he'll help prescribe.