build a pinhole camera and record an image with it.
shoot 10 head and shoulder portraits of strangers. no zoom or cropping allowed.
do a light study of an outdoor object over the course of 24 hrs.
record 100 diff. images of one object.
photograph an object in an out of the ordinary setting. (example: hotdogs. shot in bookcase, in a flower arrangement, etc)
depth of field study
shutter speed study
I did stuff like this for 3 yrs while studying fine art b&w. I've also taught courses to a few diff art classes at various middle and high schools. I've got tons of assignment ideas to share.
Once we get past the basics, we could get into stuff like studio lighting w/ a single source (using gobos and reflectors), or manipulating lighting on a white and/or black box to produce a diff. exposure on each side. (black on one side, white on one side and 18% grey on one side.)
First assignment though, if you want to REALLY learn photography would be to read three books by Ansel Adams called "The Negative" "The Camera" and "The Print".
All of my post neg. manipulation was done by hand, but some photoshop technique stuff (no filters allowed) might be fun. Hand coloring, tinting, burn/dodge, etc.