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Thank you for your letter.
I do know that unless you semi-isolate a child from popular culture via homeschooling that that child is going to be influenced more by the culture than the parents.
However, I firmly do not believe the solution is to surrender to culture. You mentioned peer groups. Parents have some influence over this. When my daughter was hanging with lots of people who became involved with drugs, I found ways to redirected, I made it clear that I expected more of her, and I actually limited (in a rather subtle way) her contact with them. When she was fourteen, I told her she couldn't spend much time at the homes of other teens unless I met their parents and I approved of them. I only approved of parents who tended to supervise.
This worked, as did getting her involve with a church.
As to the media, at home parents have complete control. Where parents fail is that they don't want to do without their television. It can be as simple as not having cable or unplugging the television. Adults should be willing to make some sacrifices for their children.
My main mistake was that, when she was 17, I allowed my daughter to date a boy (who seemed okay) who was nearing 21. That was a bad mistake. He wasn't dreadful, but his influence on her didn't improve her future. When she turned 18 she moved away with him and refused to go to college. In less than a year, they had broken up.
I believe that if I had been just a bit stricter (and also if I hadn't been depressed), I could have persuaded her to begin college.
But enough about me and my mistakes.