That's right, it must be possible to install an app that enables to program from the iPad (I don't owe one, so I may be wrong on that), but unlike the calculator, the programming environment is not included with the device, so many students who were not exposed to programming before will not even think of installing it on the iPad.
If you don't want to install something new, there's a pre-installed app called Safari which has a full programming language rather fast runtime and extensive display capabilities.
Soulver, Pythonista, Pixie Scheme, Scheme Programming Language, Lisping.