I was right. And the hat pattern is one I've used before. Unlike Mom, I'm not so good with hats, so it's good to have something to start out with. The basic idea is (for a 1-year-old hat)...
hat base: Cast on 78 stitches (with DK yarn); knit in a round for 3.25 -- 3.50 inches
hat shaping: knit 11, k2tog, and repeat, all the way around to the stitch marker.
Following row: knit.
Following row: knit 10, k2tog, and repeat, all the way around 'till stitch marker.
Following row: knit
Next: knit 9, k2tog and repeat, all the way around......
etc.!
the shaping/decreasing continues until you have 19 stitches for a round hat, or until you have 4 stitches for a pixie. obviously, we went with the pixie. It started out as a mistake on my part -- I misread the pattern -- but then we decided we liked it.
p.s. http://techknitting.blogspot.com/2007/01/jogless-stripes.html was a helpful introduction to the world of striping!