What I wish is that all the non-math folks would cut a few dozen squares, from graph paper if necessary. Color some as full squares, color some as HST, color some as the next step that I don't have a name for (like an hour glass) and color those. Then go to the table and play with the squares. Maybe find a few of the old faithful quilt block designs and discover there is no MAGIC FORMULA to most quilt blocks. Just simple designs.
I'd guess that most of those folks could ferret out the patterns of many quilts for themselves in very short time.
Oh, and throw in a few rectangles along the way, too.