I just read about an eBook called Nix the Tricks on Dan Meyer's Blog. It's free to download and has some great ideas about little math tricks that we teach to students that end up keeping them from truly understanding the math concepts.
I've hated PEMDAS for a while now for precisely this reason. How many times have students (or, dare I say, teachers?) thought that you have to multiply BEFORE dividing because "M" comes before "D" in stupid PEMDAS.
Other tricks on the chopping block? FOIL, cross-multiply and divide etc. Get ready to rethink and reflect. This is an important read. Check it out!