This pattern, which works beautifully for scarves and shawls, is what I call Broken Rib stitch. But if you Google "broken rib stitch," you get a different pattern, one that I don't especially care for, as the texture isn't very distinct. In a nutshell, this pattern is 4 rows of 2x2 ribbing broken up by 2 rows of knit stitch (which equals one strip of garter.)
If you want to try this pattern, cast on an even number of stitches which when divided by 2 is uneven, e.g. 14 or 38 or 62. This makes the edges look neater.
Row 1: K2, P2, repeat until last two stitches, which should be K2
Row 2: P2, K2, repeat until last two stitches, which should be P2
Row 3: same as Row 1
Row 4: same as Row 2
Rows 5 and 6: K
Repeat 6 rows for pattern.
If you're interested in knitting shawls for a good cause, check out the
Prayer Shawl Ministry--but I must admit I don't like their suggested pattern. It's not very distinct. I like a textured pattern you can see!