I use many different approaches to the art of improvisation and find it particularly useful for the older beginner, as I link sound with enhanced reading ability. My approach is to teach common chord progressions, with a variety of left hand patterns based around these progressions. Students can then play using only a lyric sheet with chord symbols; they then have access to many free songs from such sites as ultimateguitar.com
From this a student progresses from the reading of lead sheets, to improvising their own melodic ideas over a given chord progression, or even making up their own chord progressions.
Any of these approaches is a useful introduction to the study of music composition, which I also teach. They also make reading traditional music notation easier, as I link reading fully notated music to an understanding of chord progressions, in a more holistic approach. This is also in keeping with current educational thinking which puts sound before symbol.