Apparently, according to Kate Tuttle's "I love you, now do your homework :)" in today's Boston Globe. One snippet:
Dr. Laura Prager, a child psychiatrist at Massachusetts General Hospital and mother of two teenagers, texts with her kids. It’s a method she adopted when her older child, a son now in college, went through a phase of not answering her phone calls. “But if I texted him,’’ she says, “he answered me right away.’’
For a teenager who’s out and about, at school or sports practice, texting is infinitely preferable to fielding phone calls from mom, especially in front of peers, Prager points out.
Most anecdotes in the article reference daughters texting with mothers (although this example is from a son). I wonder whether there's a gender difference.