There is conclusive evidence that smoking causes cancer, yet people still smoke. The evidence from probability is overwhelming that it is foolish to purchase a lottery ticket, yet millions of tickets are sold. There are hundreds of other situations similar to this, so I don't see why P.J. is surprised that teachers do not pay much attention to the data--teachers are people too. (If you did not take the time to read the article indicated in the comment to P.J.'s last blog, I suggest you read it as well.
It is a very interesting take on why and how we resist data that tells us things that run counter to what we want to believe and on what happens when we encounter data that provides evidence for something we do not want to believe.)
I have two initial thoughts about this data-resistance.
First: let us get to the heart of what we do as teachers. We wish to provide our students tools so that they can make intelligent decisions as they live their lives. We want them to learn to think clearly about little things and big things, so they can contribute to society at large and so they can make good personal decisions regarding their well being and safety. I hope everyone agrees with that. As a result, we teach students how to collect, analyze and draw inferences from data. The assumption is that if they understand what is true, then they will make informed decisions. It appears that we are wrong. There is considerable evidence that people will ignore data and continue acting according to old habits. Even intelligent, well-informed mature people will ignore the research if it provides an "inconvenient truth." Why is this, what can be done about it, and what are the consequences for education?
It seems true that people trust their own experiences much more than they trust research, most likely because that--experience--is the way we learned to learn. Children try to walk: they fail; they try again until they get it. They learn that the way to learn is to try and to trust experience. Not only does the child learn to walk, talk, and generally function in the world, but the child learns a good way to learn, namely: try, and then trust personal experience.
Second: most classroom teaching is still approached in one way: there is stuff to be learned; it is the stuff that the curriculum wants students to be learned; we have an obligation to have our students learn it. The students usually do not experience the curriculum. That means they might not believe it, because it is not something they personally experienced. If we want students to believe data and live by it, then students need to experience it. That means that we need lessons, beginning at a very young age, in which students state their beliefs, students collect data, the data contradicts those beliefs, and then the students have a way to test their beliefs against the data. The best example I can think of has to do with physics and falling objects. I think of these because they confronted my beliefs when I was a child, and I still remember being proved wrong. There was an exhibit at the museum where one ball was dropped and another was projected from the same height at the same time, and both balls hit the ground at the same time. I had to see the demonstration several times before I could accept the new information about how gravity worked.
The problem is further complicated by the way our culture celebrates people who just have a "gut feeling" that they should try something, and when it works they are celebrated as heroes. A particular instance of this is found in the book Moneyball, where the baseball culture ridiculed and ignored evidence that ran counter to long standing beliefs about baseball, even though considerable amounts of money were at stake.
Even the stories of great scientists seem to celebrate hard work and good fortune rather than a careful analysis of data. Perhaps we need some more stories, plays, films and TV shows about the importance of careful analysis of data.
There may be no better reason to reform mathematics education than to restructure what we do so that our students learn to look at data and make intelligent decisions accordingly.