ABSTRACT
To discuss the teaching and learning of algebra with understanding, we must first look at the algebra that students too often encounter in their classrooms. The traditional image of algebra, based in more than a century of school algebra, is one of simplifying algebraic expressions, solving equations, learning the rules for manipulating symbols—the algebra that almost everyone, it seems, loves to hate. The algebra behind this image fails in virtually all the dimensions of understanding that Carpenter and Lehrer (chapter 2, this volume) have taken as a starting point for reform in the classroom. School algebra has traditionally been taught and learned as a set of procedures disconnected both from other mathematical knowledge and from students’ real worlds.
