In math classes, teachers often focus instruction on the formulas and processes needed to solve different types of problems, but neglect to teach the concepts on which these tools are based. In this article, the author argues that before they can do this, teachers themselves need to understand "understanding math." Teaching mathematics with understanding means creating experiences in which mathematical interconnections can be made because, without them, there would be a real danger that questions put in isolation would make the learning process rather piecemeal and incoherent. It is vital, therefore, that students be offered a variety of models--real models--that take them from the reality of their world into the world of abstract mathematics and, where appropriate, back again. He suggests that teachers need to develop not only a profound understanding of mathematics, but also a corresponding understanding of how children learn. (Contains 3 figures and 26 endnotes.)