ABSTRACT
Learning with understanding is central to reforming mathematics education because it provides a basis for students to apply their knowledge to learn new ideas and to solve new and unfamiliar problems. When students do not understand, they perceive each topic as an isolated skill, and they cannot apply their skills to solve problems not explicitly covered by instruction, nor extend their learning to new topics. As a consequence, unless students learn with understanding, whatever knowledge they acquire is likely to be of little use to them outside of school.
