Jim Tanton is a very deep thinker and communicator about many aspects of mathematics. He recently was in residence in the DC area for a few years and was a mentor at Math for America – DC (based at the Carnegie Institution for Science), where I attended several of his highly entertaining and inspiring talks for new and experienced DC secondary Math teachers.

This article by him goes into what mathematics is all about, and how we teach [a part] of that in school. Here is the link: