ABSTRACT
In order to prepare mathematically literate citizens for the 21st century, classrooms need to be restructured so mathematics can be learned with understanding. Teaching for understanding is not a new goal of instruction: School reform efforts since the turn of the 20th century have focused on ways to create learning environments so that students learn with understanding. In earlier reform movements, notions of understanding were often derived from ways that mathematicians understood and taught mathematics. What is different now is the availability of an emerging research base about teaching and learning that can be used to decide what it means to learn with understanding and to teach for understanding. This research base describes how students themselves construct meaning for mathematical concepts and processes and how classrooms support that kind of learning.
