It is my understanding, however, that people in the southern and eastern regions of Germany use "viertel vier" to mean "a quarter past three" and "dreiviertel vier" to mean "a quarter to four".
I want to make sure that this is, in fact, the case and there was not a mistake in the lesson. I would appreciate hearing your confirmation that this confusing regional difference does exist between the above-mentioned regions of Germany and Austria. It's an important point to know!