I'd do the math in a programming language. First I'd make some
  awesome graphics, transforms, skewing, rotating, flipping,
  translating - all that good stuff.

  I'd HAVE to get the math right because it's in a programming
  language. Get the syntax wrong and it doesn't work. Get it
  right, and it does. INSTANT results.

  THEN once I have an intuitive grasp of the what those "magic
  words" actually ACCOMPLISH...

  ..THEN go over the math in greater details. but not until I've
  successfully written a little video game with the magic words
  first.   The way they teach it, archaic manner, in special weird
  math language, to me, is unnecessary in 2015.