I will be teaching Arduino programming this coming school year and have at least a dozen libraries installed on my computer. Is there any way for me to replicate Arduino on multiple other computers so that I don't have to install the libraries on each one?
You might be better looking ate the EDU program and depending on the hardware being used also CREATE.
Both used extensively in EDU surroundings with great success.
Bob.
The libraries are stored in the libraries subfolder of your sketchbook folder. You can find the location of the sketchbook folder in the Arduino IDE at File > Preferences > Sketchbook location. So you could just copy the libraries folder from your computer where you have all the libraries installed to each of the other computers.
If you want to be able to copy the IDE and libraries along with any extra hardware cores you installed via Boards Manager all as a single package, you can put the Arduino IDE in portable mode by creating a folder named portable inside the Arduino IDE installation folder, then install the libraries and hardware cores. They will be installed under the portable folder. Portable mode can be a bit tricky. The Arduino IDE needs write access to this folder and, depending on your security settings, Windows can be very strict about the C:\Program Files and C:\Program Files (x86) folders. So you might need to install the Arduino IDE to a different location. I don't think it's possible to use portable mode on macOS.
More information on portable mode: