Mathematicians as Educators

18 NOTICES OF THE AMS VOLUME 44, NUMBER 1 The mathematical sciences professions are in a phase transition from which they may well emerge smaller and/or redistributed and much more dispersed. We are not an endangered species, but our health depends on being able to transcend our historic tendencies toward insularity, on our outreach to all of our sister and client communities. This message, in diverse forms, is widely heard today. The internal mathematical culture continues its deep investigation of the fundamental structures of number, space, dynamics,...now with the added exploratory and processing power of new technology. These investigations are guided partly by purely intellectual evolution, but largely also by the natural sciences, to which mathematics furnishes the language and concepts for description, analysis, modeling, simulation,.... In addition, mathematics provides design and simulation tools for engineering, technology, and for the organization and decision processes of industry. These diverse tools and functions of mathematical thinking are increasingly manifest in many professions and across the technical work force. The phase transition mentioned above involves many partial shifts of focus—from core mathematics toward applications and toward interdisciplinary work with the natural and social sciences, from academic to industrial and laboratory settings, from individual self-directed work to collaborative and multidisciplinary effort, from technical communication with co-specialists to translational communication across disciplinary and cultural boundaries,.... Mathematics education is fashioned to provide appropriate mathematical knowledge, understanding, and skills to diverse student populations. At the postsecondary level, such education is entrusted to two large communities. One is based in our system of two-year and community colleges. The other consists of academic mathematical scientists, most of whom have been trained principally to do mathematical research but for whom the economic base of their profession now is predominantly this educational mission. There has also been a small but distinguished group of scholars doing research and curriculum development in postsecondary mathematics in the tradition of Pólya—for example, Ed Dubinsky, Joan Ferrini-Mundy, Steve Monk, and Alan Schoenfeld.