Portscan question

Hi all,

I'm a little bit lacking in tech literacy, so this might be a stupid query. But I'm running nortons av software on a macbook and I'm getting quite a few portscan attacks (well, vulnerability blocked notifications of portscans, anyway). I've contacted my isp, but they're disinterested - in fact, it took me about half an hour to find someone who even knew what a portscan was, which was a little concerning! (I found myself explaining it to their "tech support"...dire.) Should I be concerned? And is there a way I can block the specific ip address that is doing the scanning, permanently?

Any help would be much appreciated.  

winnie.