Tandrink - I've given lessons for more years than I'd like to admit. Sounds to me like you're giving the guy money to give you tab sheets.
I work from standard notation, but also work with my students on learning by ear and by imitation - what one might call an 'oral tradition' method. Typically, I'll have my students play what we worked on the previous week. We isolate trouble spots, and I show them specific techniques to help them through the trouble. By practicing just the part of the passage they have trouble with, they're not spending gobs of time playing through stuff they can already do. That usually takes up about 20 minutes or so. Then we work through the next week's lesson, taking special note of sections that might be troublesome when practicing. While it's based mostly on reading, I will also ask my students to LISTEN to me play a section (never the whole thing) and WATCH my hands, especially if there's a move up or down the neck.
Music instruction should be a balance of learning from notes, learning by ear (especially important for folkies), and music theory. I'd suggest finding a new teacher. Might you be in the Central New York region???