Sean you are correct that this is a security issue, but i am betting that it has nothing to do with the firewall ports being opened. MinecraftEdu does not require any ports to be opened to connect internally from client to the server.
You should check that your network settings are not blocking incoming connections.
If this is a Windows machine, open your Network and Sharing Settings by right clicking on the server computers network icon at the bottom right.
In here, you will see View your active network. Usually this is set to home, work, or public.
If it is set to work, it will preload firewall and connection settings that are most likely blocking your connections.
1. Go to Control Panel > System and Security > Windows Firewall
2. Then select Turn Windows Firewall on or off
3. In these settings, make sure that your network is allowing incoming connections by unchecking the option that reads: Block all incoming connections, including those in the list of allowed programs.
Hope that helps.