Both the proverb and the common teacher complaint beg the question of what is understanding. When we began the University of the University of Chicago School Mathematics Project, we felt that understanding could not be treated as something that happens automatically or magically or something that combined the best of the ideas of tangible objectives yet was flexible enough to cover what we perceived to be the wide variety of understanding that were possible. As of this quest, a multi-dimensional approach to understanding developed. This approach has influenced both our curriculum writing and our evaluation.