ABSTRACT
This chapter examines past research on the development of intelligent tutoring systems and explains samples of a "new breed" of software. It focuses on intelligent tutoring systems attempts to set a tone: Though artificial intelligence (AI) has much to offer, researchers should view its research as applied to education with as much skepticism as they would any other educational research enterprise. The chapter reviews several projects that illustrate the power of AI concepts and methodology for developing systems that present algebraic content in substantially new ways. Most research connecting AI with mathematics education has been to develop intelligent tutoring systems, which are programs that are intended to mimic the behavior of a competent tutor. The chapter explains aspects of several projects, all currently ongoing that illustrate the idea of "direct engagement" between students and computerized, algebraic environments. It describes the nature of the software is probably unfamiliar to a large segment of the mathematics education community.
