The problem is compounded by the teaching of order of operations in a vacuum; devoid of any context. Students are expected to simplify such expressions as 72 – (6+3)+15/3x5 as a form of Sudoku, a stand-alone puzzle that has no further application but to say they have done it. This takes away a students’ ability to use common sense to check her answer. If order of operations is embedded in formulas for compound shapes, or a model for solving story problems then students can rely on their grasp of what sort of answer is in the ballpark as a preliminary check for correctness.
I think the remedy is for educators to build context and teach from there. I have a series of questions that I'm developing to try it out, I'll let you know how it unfolds.
There is a great rant to accompany mine at http://www.youtube.com/watch?v=y9h1oqv21Vs. Check it out!