I would do some channel analysis like Rich suggested if you have not already to see how many AP's you can see/hear from a given classroom. You have your channel selection to Auto which is probably going to lead to having multiple AP's on the same channel, at least from my experience (depending on how dense your deployment is ).
Apple devices are usually good at using 5ghz if they are somewhat current. You can look at increasing the Min. Basic Rate, especially on radio 1. Unless you have a really sparse AP deployment, you want higher than 6 Mbps from my experience for radio 1. This *can* help with roaming.
If you have floor plans, go through your AP's, mark them on the floor plans,note the channel each is running on and the last six of one of the BSSID's for each AP. Without even doing any onsite testing, if you look at the floor plan and have AP's next to each other on the same channel, you are going to have all kinds of issues like you are describing. You can use the plans as a guide to setting the channels manually which is pretty easy to do using 20mhz wide channels on radio 1 once you get an idea of signal penetration. Not sure of the size of buildings you are dealing with, so maybe this isn't practical, but I have done this and refer to them regularly. Another option would be putting the maps into oneview (if you have that) to get a look at the channel layout.
As suggested though, you need something to give you a look at what your dealing with. Other suggestions include AirPort Utility, Wifi Explorer or inssider. All depends on what kind of device you have.
