> I would like to see every elementary school have a math specialist, who knows advanced math, to help students with their overall understanding when they get off track. Helping a kid master some mechanics does a little to get them back on track, but diagnosing misunderstandings takes more math expertise than most elementary teachers have.

The classic example of this is "Benny's Rules", eg. http://math-frolic.blogspot.co.uk/2012/11/bennys-rules.html