Nathan,
I would suggest you look at a Webapp with an HTML form instead of using copying spreadsheets for this. Having a script attached to a spreadsheet means it would need to be authorized by each teacher for them to be able to run it. Also when you copy a spreadsheet, the new sheet will have to be re-authorized.
In the end you will wind up with many spreadsheets in your folder with no easy way to search through them.
Having a form (whether Google Forms or a Webapp with HTML) allows you to record the data in one spreadsheet which will condense info and allow you to easily search and manage the data.
George