Bonjour David (@dbonner),
honestly I was "fearing" that you were using BLE due to the Arduino board characteristics (a NANO33, in this case).
Nevertheless, there are already many topics in this forum dealing with this type of interface between AI2 and an "on field" device, specifically the Nano33.
For example by writing "nano33" in the search tool, you will access to:
https://community.appinventor.mit.edu/search?q=nano%2033
where many topics related to the connection between an AI2 app and that specific type of Arduino board are collected.
I believe that, once got the connection part working, the remaining part of the app building will be essy and your students will appreciate the friendliness of the development environment and the power of visual interface creating.
My hint is then to (teach your students to) proceed with little steps and don't do the "big bang approach", like many young guys often do. As a first step just try to make a simple app that is capable to exchange data between AI2 and the Nano: on the AI2 just implement a couple of pushbuttons that send a character each (i.e. 'A', 'B') to the BLE. You need an extension to do that:
On the Nano a simple code that can show on the SerialMonitor everything is coming from the BT. Second step, is to transmit from the Nano any character got from the Serial Monitor to the app and show these characters into a label in the AI2 app.
To help in debugging all the above you can use a free app named Serial Bluetooth Trerminal that you can download from Google Playstore.
The road to the target seems to be long and harsh, but is not that true. 
Bonne chance !
Ugo.
(Edited: corrected typos)