How encouragement design works practically?
The fact that you can only encourage but not force the teachers to participate puts you squarely in the world of Local Average Treatment Effect (LATE) and Intention to Treat analysis.

Essentially if you use the voucher as a instrumental variable, you will get an estimate of the effect of the voucher on "the sort of person who you can encourage to take a class by giving them a voucher".

Read the Instrumental Variables section in Mostly Harmless Economics, to get a good easy to understand explanation of exactly the situation you are interested in.