When an employee gives notice to a manager, the relationship instantly and fundamentally changes. The relationship is no longer manager/employee and instead becomes a peer to peer relationship.
From: 9 Tips for Quitting a Job Gracefully
9. Be conscious of the shift in the balance of power.
The moment you quit is when you go from being your boss's underling to your boss's equal. After all, you are no longer beholden to your boss for a job. At the point of quitting, any more work you do for your boss is out of kindness and respect for the custom of giving notice.
While the employee does technically still work for you -- and yes, he/she does still receive a paycheck -- keep in mind that he/she is essentially doing you a favor by sticking around for the month-long notice period. In many cases, the employee could just start early at the new company and leave you high and dry.
Remember, this person has short-timers syndrome, which is not to be confused with laziness. Remember what it was like when you started a new role and what that stress and excitement was like.
As a result, a good way to view your former subordinate turned peer is as if he or she is a volunteer who has agreed to help train his or her own replacement. Don't look at him or her as a resource on the project after the notice period, as the purpose of the notice period is to transition, not to squeeze out the last few drops of productive work from said employee.