Our Web sites have many illustrations of these things.
Here are a few of them.  We need to make them more and more clear and interesting.
The Slippery Implication
Energy,  so what is it? -- really!
ENERGY...............Feynman's view
The simplest math
A Tensor is more than a lamp!
TENSOR.............Feynman's view
Ages 10-13, where it begins
A CASE STUDY   Children often exhibit charming naivete -- when the adult easily sees the error.
A CHILD'S VIEW   Adults often make similar errors of more sophisticated logic.  We all come to the boundary of sophistication where what lies beyond seems non-existant:  "Ivory-towered and quite out of touch with the real world." 
A MAGICIAN'S VIEW   "Richard Feynman [was] a magician of the highest caliber" -- "magic: seemingly beyond human powers."
POWERFUL TOOLS that too often gather dust in the attics of our minds.  A few of the simpler reasoning tools that add a lot of power to science.