Wireless AP set-up

I have put together a wireless network for appro. 300 students on my campus so students can access the internet. I have each AP using a unique SSID and the same channel (11). Unfortunatley ever so often 1 or 2 may lose connection to the internet for various reasons. The problem I face is trying to find which 1 may still have intenet access, as you will still connect to the APs and get an IP ADD however you will not browse the net. IT proves quite frustrating at times as we sometimes have to move through 4 APs before picking up 1 that still has intenet. My ? is should I use the same SSID for all and change the channels. Will this help? Can someone please assist me with this problem.
Thanks