Mathematics Stack Exchange:

My 13-year-old sister has a problem which, given the way math is currently taught, I doubt is anything but all too common. She has a low grade in her math course and only ever attempts to memorize formulas and tricks, but never actually learn any of the reasoning behind the math. Cross multiplication is the perfect example.
She knows that from
35=x10
.. she can “cross multiply” to get
30=5x
.. and from there get x=6. She has absolutely no idea what any of this means, however. She’s simply memorized a pattern and is applying that pattern to a recognizable arrangement of numbers.