ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book examines several topics for possible inclusion in a modified algebra curriculum using the three criteria of intrinsic value, pedagogical value, and intrinsic excitement. It focuses on students' learning of variables, algebraic expressions, equations, and equation solving—with particular emphasis on the difficulties learners encounter with some of the structural features of school algebra, tracing some of those difficulties back to experiences in arithmetic. The book highlights the distinction that ought to be made between the syntactic and semantic aspects of algebra. It discusses the existence/nonexistence of theory in algebra research. The book considers the developments in intelligent tutoring systems and reviews several projects that illustrate the power of concepts and methodology from artificial intelligence for developing systems that present algebraic content in substantially new ways.
