At  the Chronicle’s Forums, I found this by Conjugate:
I found once, years ago, a nice piece on writing a teaching statement in math. It appears to have vanished from the web site where I found it. But it gave advice roughly like this.
First, start off by listing the courses you have taught, as well as the variations in them (if you know how they vary from other courses). Write a little bit about how you think it is appropriate to teach those courses, and what it is appropriate to expect of those students. This will organize your thoughts, and will provide you with the “clay” (so to speak) with which to mold your statement.
Now, generalize. So I talk, for instance, about math classes for non-majors, and the differences in how I handle them from classes for majors. I talk about classes in which I expect students to be able to prove theorems, and proof rubrics for different kinds of proofs.
What have you tried that has worked? What will you try to address problems that you’ve noticed in the past? How strict are you about late work, and how often do you assign homework, and what kinds of projects or assignments are most useful for what kinds of classes?
Put all this into a heap, call it your rough-draft teaching statement, and then edit it. Have others look at the result; they will give you good, solid, experienced and contradictory advice. “No, leave out this paragraph; it makes you look unprofessional.” “What? Why did you leave out that paragraph? It goes straight to the heart of what a search committee is looking for!” Take from the contradictory advice the somewhat reassuring observation that all these people got jobs despite making errors in one anothers’ views, so that you really can’t go too far wrong with what you’ve got. Send that sucker out, after making whatever changes they suggest that sound right to you.
That’s a useful introduction to a different way to do the teaching philosophy statement. I think I would be interested in doing that.