QUOTE(TSax @ Nov 5 2006, 06:27 PM)

The circle of fifths/fourths has been used quite a lot in the jazz classes I've been to. In jazz it's most common to go around it in the 4ths direction. If you do that, starting at C and moving to F then Bb etc you'll notice that if you think of that note as the key, you're adding a flat (or subtracting a sharp) from the key signature with each move.
Jazz chord progressions often move in fourths, probably the most common progression is a ii, V7, I e.g Dm7, G7, Cmaj7 - the root notes are moving in fourths. Another place you'll find chords moving fourths is the bridge of Rhythm Changes where dominant 7th chords move around the cycle, 2 bars on each of 4 different chords - on alto it's usually B7x2, E7x2, A7x2, D7x2 resolving back to Gmaj for the A section.
If this doesn't make a lot of sense at the moment don't worry too much, I've heard it repeated so often (and I'm sure you will too) that it does sink in eventually.
Because the chords often move in 4ths it can be useful to practise patterns in 4ths, maybe start practising 1, 3, 5, 7 of each major chord, 1 beat per note so
C, E, G, B
F, A, C, E
Bb, D, F, A
etc then maybe speed it up so you're playing quavers and come down the chord as well
C, E, G, B, C, B, E, G
F, A, C, E, F, E, C, A
etc
then flatten the 7th so you're practising the dominant 7ths, then the third as well so you're practising minor arpeggios. Getting to the point where you know the 1, 3, 5, 7 of any chord without having to think about it is really useful.
Thanks, TSax. I don't understand all of what you said, but you have given me a lot I do grasp and can be getting on with.