holomorphic said:
You would need parental permission to gather such data, and they would probably consider it more than a little weird for a teacher to do this.
Not just parental permission. The amount of bureaucracy that you need in order to create a publishable human study is unreal (and unfortunately necessary).
If you do a study involving children, you'll need an approval from an institutional review board. If you haven't set up an IRB, and the Feds catch you doing human studies, the school district could lose their federal funding.
It's a crazy system, but one thing that they teach you when they make you do human studies training is "here are the horrible things that happened that caused us to create this system." Here is a example. Let suppose you perform treatment X, and you find out that people in group X are doing a lot worse than people that don't. At this point you have a major ethical dilemma because if you stop treating people with X, you don't know if it's a real effect, but if you don't, then you may end up with a kid being a grade level behind.
Universities with teaching schools have committees (IRB's) that discuss these issues. They will have a meeting to figure out if the results of the experiment are worth the risks, and with kids, the answer is usually no.
Also I know this stuff because my wife has a Ph.D. in education, and trying to put together a valid education study is *really* hard and the type of stuff that they teach you in education grad school. Also as with physics, some people that are excellent education researchers make horrible classroom teachers and vice versa.
If you want the full chapter and verse...
http://answers.hhs.gov/ohrp/categories/1570