A student asked my opinion of notan:
Notan is a very interesting way of seeing the black and white design of an image. To create a notan of an image you would remove all color and reduce the remaining values to two, black and white. On the other hand, a halftone image (black and white photo for example) contain a range of shades of grays between black and white, but a notan has no gray whatsoever. Its black and white only.
It is my opinion that notan is interesting but has limited use in teaching painting. The reason is that most notan interpretations of an image are so far removed and abstracted from the linear and value structure of an image that they rarely resemble the image anymore. That's why I think notan excels when it come to learning two-value graphic design, but is very limited when learning to paint in either grayscale or color.
I think it is extremely helpful for a student to learn about black and white value structure in painting. Because that information will give you the needed knowledge to paint your painting. However, I have found that notan, outside of an awesome graphic design appearance, has little direct usefulness in painting.
In summary, it is my opinion that to understand value structure (black, white and 3 to 5 values between) is far more useful to the painter than understanding notan.
Anyway, that's my take. I would be happy to discuss notan further if you would like. It's a fascinating topic.