There have been far too many cultural, societal, and legal changes to claim any correlation between school prayer and positive or negative behaviors.
While I'm positive there have been many factors affecting positive and negative behavior in school students over the years, I'm equally certain that school prayer is at least a significant factor, because if nothing else it teaches conformity and how to behave respectfully and civilly in a given situation, even if you don't agree with or believe in the prayer.
There are people who are not sports fans and want to eliminate sports programs from schools because they think it's a waste of time and money, and children can get hurt. They dismiss sports as irrelevant. But by doing so they are eliminating the lessons about life that come from playing sports. Sports teaches you how to work hard and be a constructive member of a group. And to be a leader. Sports gives you discipline and persistence, the drive to better yourself. It teaches patience, responsibility, creativity, and professionalism. There are many things that formal classroom education can not teach to students that can only be experienced by being a team player and getting the experience working hard to achieve a goal.
The elimination of any and all religion from public schools we have eliminated many of the life lessons that are only learned (or at the very least best learned) from religion. Our very society and our laws are religious based, and the lessons we must learn in order to have an ordered civil society can clearly only come from religion. You and others may disagree, and I'm a devout agnostic, but the results are plainly evident. Religion teaches people how to be good people, the concept of kindness, to have a good heart, the ability to treat others with kindness, love and understanding. It teaches the difference between right and wrong. It teaches charity, and for the right reasons. It teaches people how to overlook another's flaws and foibles, to not "correct” these faulty attributes with hostility, to be able to actively identify with the other human and interact with them in a positive way. Prayer in schools also, oddly enough, teaches respect and tolerance for others' beliefs, especially if you do not share their religious beliefs. It teaches you how important a person's beliefs are to them, whatever those beliefs are, and to respect them for it.
You can't learn these things unless you also learn their context and practice them within that context. Violence, and students disrespecting and talking back to teachers, is rampant in schools. They have all been told not to do that, but they haven't learned why, they haven't learned the context, they haven't learned why it's important. While I don't agree with, or even believe in religion, I know and understand how important it is to those who do, and I can respect that.
This isn't to say they should be promoting or giving Bible lessons in school. Not at all. Not even close. There should not be teaching of a religion in schools in the same manner that academic subject are taught. There should absolutely be a separation of church and state in public primary schools. But that doesn't mean that there needs to be an artificial elimination of the important thoughts, ideas and beliefs that are an important component of people's lives. Primary schools are the very places that we send our children to prepare them for life when they grow up. If they grow up without having an understandable frame of reference that religion teaches people, we have a society like we have now, and it ain't pretty.
Here's one illustration that you might find interesting. Back when I worked for Olan Mills (back when they still existed - they've since been sold to another portrait company) they had two primary divisions: the Studio Division and the Mobile Division. The Mobile Division included the Church Division as well as the Club Plan Division, where we'd go to small towns too small for a permanent studio and work out of motels instead of studios. The Church Division was where we went into churches, synagogs and mosques to take pictures and give the members a church directory. The Church Division was 80 percent of Olan Mills' business.
In the Studio Division, where studios are located in larger cities, where there were at one point 600 of studios, the rate of bounced checks was about two percent, about three per week per studio. That was, at the time, just about the national average for bounced checks (thanks to electronic transactions, the rate is now nationally about half of one percent). In the Club Plan Division, mostly small towns, the rate of bounced checks was about one percent. In the Church Division, the rate was so small that it was startling. The term used was "non-existant." One year I remember they had literally 10 checks bounce,, in a division that was the equivalent of 2100 permanent studios. Ten. That's a whopper of a life lesson, I'd say, and they learned it somewhere.
If I hadn't learned anything in my time on this planet, I might see a cause & effect relationship where my bias directs me to look.
For one, I think you know me better than that. I'm far too aware and cautious of illusory corollary to make such an stupid and irresponsible mistake. Second, you should know me well enough to also know that I'm hardly biased in favor of religion. I'm pragmatic and realistic enough to
not let my bias
against religion color the reality. It is what it is, and just because I'm not a believer doesn't mean I should pretend, or convince myself, that it's something else, something that it's not.