John and I recently wrote our first Research Sampler column for MAA Online's Teaching and Learning Section. It is called, "Of What Does Mathematical Knowledge Consist?" We take as our starting point the deliberations of this past summer's ICME-8 Working Group on Forms of Mathematical Knowing, but continue on from there.
Our column will appear regularly every three months. It is an expanded version what we used to write for the now defunct UME Trends. The address is http://www.maa.org/t_and_l/. We would appreciate your comments/reactions.