Having read "A Mathematician's Lament," by Paul Lockhart, I think I can understand where the educators who conceived of this particular math problem might be coming from. (That is of course assuming they're operating from the same premise as Lockhart, which they may not be).

I agree that this is really not a very good way to teach math, but saying that it takes 108 steps is slightly misleading, because the entire process can actually be summed up in only two steps:

Step 1: Draw 18 circles.
Step 2: Draw 90 lines inside the circles, distributed equally among them.

So yes, while that whole process will almost certainly take much longer than simply dividing 90 by 18, lets not arbitrarily exaggerate the number of steps involved.