My take is this:
Beginning classes are an introduction to the lathe, tools , Safety, and concepts ( sharpening, bevel, etc )
More than one session
Spindle turning between centers. Starting with a dead drive and progressing to a prong drive.
Introduction to face plate.
Tools: spindle roughing gouge, spindle gouge, and parting tool.
Skills: Emphasis on the basic cuts, cutting with the grain direction.
There are plenty of quick projects that give the student a feeling of accomplishment.
I think that a 3 legged stool as a 'final project' is good as it may emphasize repetition of basic cuts on the legs and an introduction to the different grain presentation of face plate turning on the seat.
1st level Intermediate classes or perhaps advanced basic:
Introducing new tools, more Safety, more concepts ( sharpening, tool presentation, measuring, etc )
Spindle turning between centers with the new tools, progressing to chuck held ( not between center ) turning
Tools: scrapers, skew, chucks (jam, 4 jaw ), drill chuck
Skills: Start with the new tools between centers ( dead or prong drive ). New cuts with the skew. Chucking methods.
Weed pots, Plate, platter turning, progress to box making.
Hollowing, measuring and fit, chucking, and design flow between separate parts.
Intermediate:
Introducing more new tools, more Safety, more Sharpening ( no longer a concept ), more concepts ( tool presentation, form, curve, etc )
Bowl turning from green wood, bowl from dry wood, larger boxes.
Tools: spindle roughing gouge, spindle gouge, bowl gouge, thickness measurements, chucks ( screw or 4 jaw )
Skills: Cutting the bowl blank, grain orientation, cuts on the outside and inside of the bowl, reverse turning ( between centers, jam chuck, etc ).
Using the different cutting edges of different bowl gouge grinds for better finish cuts.
Depending on the number of classes a green bowl can be rough turned and then to completion a couple of weeks later with some 'magic' tricks ( dishwashing detergent, alcohol soaking). The dry wood bowl can be completed in a class period of that instant gratification.
Advance Intermediate:
Introducing more tools, Safety, sharpening, and skill building
Beginning hollowing, advanced spindle, ( finials )Deeper hollowing ( vase shapes ) , goblets
Tools: small hollowing tools, spindle gouge, bowl gouge, '1/4" skew'
Skills: blank preparation, hollowing through a small opening, turning thin spindles, hollowing form with steep sides ( vase )
Turning hollow ornaments with finial, long thin spindles, goblets, vase forms.