When there is consistent and widespread hearsay from others, you should hear what they are saying.
Surfing the net and falling behind on one’s work go hand in hand. You should meet with this employee to discuss both issues. First, give her feedback regarding the fact that she is behind on her work. Be sure to provide specific examples.
Secondly, let her know that you have heard from many sources that she is spending excessive amounts of time surfing the net. She may deny this, or perhaps she will say that it was work related. If it is work related, you can ask to see some documentation.
Your company should have a policy that allows you to monitor employee Internet use. If so, you may want to check with your IT department to see if they have any information on her virtual whereabouts.
Since her possible shenanigans are going on while you are not around, it might also help for you try to be around more often to provide additional coaching, guidance, and feedback. This whole matter should be written up and then signed by both of you. She needs to understand that if these problems continue here, she is not likely to continue here.
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