I have teachers that do both. My piano teacher stops me fairly frequently as I play, but as I make progress with the piece, he stops me less and less. Sometimes we make through a section before stopping, but he usually stops me while I'm playing. This approach is sometimes annoying and can be discouraging, because I as the student feel as though he's not seeing the progress I have made as a whole. On the flip side, he catches a lot of things that can be fixed before the next lesson so that we don't have to stop so much next time. My organ teacher however, NEVER stops me when I'm playing a piece, and I play as far through as I can go before she goes over my mistakes. So then, she can hear as a whole how much progress I may or may not have made. BUT, she doesn't always remember details, and we often end up going over the same thing week after week, because she makes general comments, and nothing specific and doesn't demonstrate as much. So there are ups and downs to both.