My name is Reuel Smith.  I’m a doctoral student in Mathematics Education.  For twenty-four years I was a classroom teacher in the New York City area with the great majority of those years spent teaching wonderfully bright, creative, hardworking kids in an independent all girls’ school in Manhattan. During my teaching years I taught at every level from 6th through 12th grade and as a graduate student many years ago taught freshman calculus at the University of Tennessee and introductory statistics at the University of North Carolina. Although I tremendously enjoyed these years of classroom teaching, my overriding interest has become curriculum development, as more and more I have come to believe that excellent teaching is necessarily based on excellent curriculum, a curriculum that asks students the right questions and provides them with a well thought through sequence of mathematical experiences. I am primarily interested in researching ways to help provide K-8 classroom teachers with straightforward access to contextualized curriculum in which core skill acquisition and problem-solving capabilities complement and support one another. I’m particularly interested in how deep conceptual understanding can be achieved within the framework of teaching fundamental skills. Also of interest is the nature of mathematical "proof" as it pertains to young learners: what constitutes stronger and weaker proof in their minds and what sort of "proof" is most effective as an aid to a robust understanding of core mathematical concepts and skills.