Mathematics education research in undergraduate mathematics increased significantly during the 1990s, showing no signs of abating in the near future. Thus far, the research has often been associated with innovations in curriculum such as calculus reform, statistics education, and the use of computational and graphing technology in instruction. Mathematics education research, carefully conducted, is something far more fundamental and widely useful than might be implied by its use by the advocates of innovation in undergraduate mathematics education. Most simply, mathematics education research...