Does your accent affect how good a teacher you are, and how easily your students can understand you? This is probably more a British thing, since the UK has such a wide variety of accents, but in my experience, it's other English-speaking people who have the most trouble understanding different accents, whereas foreigners don't seem to notice. Those with a strong accent, does it affect the way you teach? Do you tone it down, or just try to speak clearly in your accent?
