From the wildly famous work by sociologist Annette Lareau, we know that middle-class parents adopt "concerted cultivation" to intensely develop their children's skills/talents, as well as communication and negotiating skills, through hectic schedules of formal activities, while working-class and poor parents use a "natural growth" strategy, which leaves children to play on their own and develop their skills spontaneously and often among extended family. There are benefits and costs to each one. Please see Lareau's book for a more detailed discussion of her research findings, which is also easy to read. From this review (since I am still at Census training and not at home near my books), "according to Lareau, middle-class children are more likely to be argumentative, complain of boredom, demand attention, and have weak ties with siblings and other relatives." The natural growth strategy also has costs because society, especially schools, values the skills learned through concerted cultivation. Concerted cultivation is a new strategy (since I think the late 1960s), which has become a response by parents to deal with the ever increasingly competitive educational and career markets.
The Census data reveals some surprising trends in parenting. I would highly recommend the Census' child well-being report and the even more fascinating tables. For example, see Table D8: Daily Contact: Mealtimes with Child, Characteristics of Families. Overall, 56.5% of parents have dinner daily with their teenagers. Those with lower incomes and especially the lowest incomes are more likely (67.9%) to have dinner daily with their teenagers than those with higher and especially the highest incomes (48.7%). Let me know any other interesting trends you find.