Procedures without Concepts

PEMDAS, "Please Excuse My Dear Aunt Sally"; "Keep, Change, Flip"; "Don't ask why, just invert and multiply"; "First find the common denominator..."; "FOIL-First, Outer, Inner, Last"; "Carry the 1"... "Start in the ones column and work to the left..." It's no wonder so many students (and adults!) think that they "aren't math people."  So much to remember; so little understanding of why.  How can we change this?