The only way I know to help move the reference process along is to provide the recommender with a resume/bio sheet to work from. Often the teacher doesn't know you beyond their classroom and it is helpful to give them some context to work with. By giving your reference plenty of lead time, you should feel confident that the result will be beneficial. No one likes to feel like they are under the gun, so don't set up this dynamic with the person you are asking to do you a favor. Make your deadline/timeline clear, touch base in a few days for a status update, but don't pester the person.