Lisa Jacobson sees many Type A parents at the 150-employee tutoring company she founded, Inspirica, in New York. “If you’re a Type A parent with a Type A kid, it’s pretty simple. You speak the same language,” she says. “Type B parents with a Type A child are amazed at the child they spawned. They’ll call us and say, ‘We want a tutor who is going to just calm her down.’ ”

Problems arise, though, when “drive trumps compassion” and Type A parents push their kids too hard, criticizing them when they are already doing their best or piling on unreasonable demands, Ms. Jacobson says. Still, she adds, a little push can work. After graduation, many students say “they are glad their parents pushed them one level up from where they would have been.”