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My teacher says that it's more than enough for non-music major students to learn scales up to the key of C# (maj, clockwise) for my entire life. I also know some teachers think it's necessary to complete the study of circle of fifth before moving onto advanced music literature. I'm curious to find out how much of circle of fifth do you teach your students and in what sequence? Thanks so much for sharing.

I wonder if this isn't a case of a teacher not knowing well the fingerings for the flat scales? There is so much music written in Bb, Eb, and Ab, that to ignore them seems odd at best.

Just so you know, I do teach all my students all scales and chord progressions, I-IV-I-V-V7-I.

Some students learn it better by building it up bit by bit; others understand more easily if they can see the whole picture from the start.

Sorry if my previous post was confusing. In my handout, the circle of fifth (for major scales, skipping the relative minors for convenience of discussion) consist of the following ones in the order that my teacher plans to teach:
C -> G -> D -> A -> E -> B -> F# -> C# -> Cb -> Gb -> Db -> Ab -> Eb -> Bb -> F
So we are skipping G#, D#, A#, Fb, Bbb, Ebb, which involve double sharps or double flats.
I guess I'm trying to figure out what "all scales" typically include?

This is a completely different question. No scales are being left out, rather,you're confusing enharmonics, which are identical scales with different names. There are only 12 keys in an octave and thus only 12 possible major scales. Many have two names, ie, Cb or B; C# or Db, etc.

For me as a student, I find it easier to learn bit by bit or key by key, then eventually I see the big picture.

Yes, but remember that's just you, and other students are different.

Right, but those key signatures only share the same scale on a 12-et keyboard instrument like piano, not an archicembalo or a harpischord. My teacher does play harpischord too... I guess the conclusion is double sharps and double flats are beyond the scope of typical piano lessons then.

Hummm, the last harpsichord I played only had twelve keys per octave. In fact, I've seen hundreds of harpsichords, and have yet to see one with 13 or more keys per octave.

Some older keyboards (can't remember which instruments specifically), before the temperaments of the Baroque period took hold, were built with split keys to accommodate the tuning systems then current.

David, I believe you, but now, I'm going to have to revisit the instrument museums in Berlin, Nurnberg and Munchen to "look" more closely!

I just had a discussion with a student about the older tuning systems that led to wondering about extra keys. Must go search to see if I can find a picture of one of those keyboards.

Here we go:

http://www.flickr.com/photos/ana_sudani/396791619/

http://www.h-pi.com/eop-keyboards.html

There is also a picture and a short explanation on Wikipedia, listed under "Split sharp".

I have a split sharp on my small harpsichord, but it has nothing to do with different temperaments - it's actually to accommodate two extra notes without making the keyboard longer. The low C# has a split portion which plays A, the D# has B, and what appears to be a B is actually tuned to low G.

That was the other possible reason for split keys: to get a couple more of the most-used low bass notes without adding another octave to the keyboard.

Very interesting. However, considering the tuning system in use back then, the woof tones would have precluded writing music or using modulations into keys very distant from C, G, D, & F. The dominant of the dominant of F, Eb, would have had a lot of sour sounding notes. Gb would have been unbearable. Enharmonic keys signatures were a non-issue.

i love this circle of fourths exercise. a fellow church musician gave this to me years ago. One simply plays the music thru the fourths. It sounds great and is great fun to play.

one plays the Ist, and then the Vth in the left hand, hits upon the seventh in the right and starts the next measure a fourth up. Once you get the hang of it, it's pretty easy. I can email you a better copy if you pm me.

Hmm, well there are no fourths, it's all fifths. I know it looks like fourths, but alas it's not (turn a fourth around and it becomes a fifth).
The way you describe, it is a cycle of Dominant fifths. V > I
Also your example is "wrong" it should be the other way around: sharps to the right, flats to the left.
(I know there are examples depicting flats left, etc)

i should have mentioned that it is the circle of fifths, just 'played' backwards.