So here’s a cautionary note when you’re co-learning with your child: They don’t necessarily want another coach. Kathleen Jen, a 52-year-old mother of two boys (now college-aged) in the Chicago suburb of Glenview, was inspired to pick up karate about a decade ago after taking her sons to classes. On a whim, the head of the dojo began offering daytime courses for parents. Those classes ended, but Ms. Jen was hooked. “You’re learning something that you’ve been watching for two years,” she said.