What constitutes a profound understanding of fundamental mathematics?
It includes four key features. The first is Connectedness. A teacher’s knowledge of mathematics should be fully connected. The teacher must be able to see how math concepts relate to one another so that they can build new knowledge upon what students already know. The second feature is Multiple Perspectives, which means having the ability to approach mathematics in a variety of ways. Teachers who develop multiple perspectives for each basic math topic have complete knowledge of that topic. Thirdly, teachers must understand that elementary math consists of Basic Ideas. These basic ideas that recur throughout math learning create a solid foundation on which to build future math learning. The last feature is Longitudinal Coherence. What is taught today becomes the base for future knowledge, just as current mathematics teaching builds upon students’ previous knowledge, however fragmentary that knowledge may be. With this profound understanding of fundamental mathematics, we as teachers wil
