I know a few folks who homeschool their kids - they've never mentioned Common Core, but they've said that in the homeschooling community, textbooks from the '50s and '60s are in demand to teach basics like arithmetic, American history, spelling, science, and grammar. (New developments - computers & electronics, recent history, current geography, etc., of course require more recent materials. Duh.)
And yes, they still do teach their kids how to write in cursive.