The contributions of the Persian scholar Karaji are described. Perhaps his greatest contributions were his arithmetization of algebra and the geometrical representation of algebraic operations. (MNS)

A method used by the ancient Babylonians to solve quadratic equations is presented. Illustrations are included from one Babylonian tablet. (MNS)

Rules from an old mathematics textbook are discussed. Suggested are approaches to using the materials with students, challenging them to come up with explanations of why the rules work. (MNS)

The solution of cubic equations is obtained by constructing intersecting conic sections. Details for a particular cubic are given. (MP)

The author argues that the idea of successive approximations is one of the most important in applied mathematics. The role of approximation in the development of the calendar is described. (SD)

The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)

One of the four cornerstones of the National Council of Teachers of Mathematics (NCTM) "Curriculum and Evaluation Standards for School Mathematics" asserts that connecting mathematics to other subjects in the curriculum and to the everyday world is an important goal of school mathematics. This yearbook is designed to help classroom…

This 1998 yearbook aims to stimulate and answer questions that all educators of mathematics need to consider to adapt school mathematics for the 21st century. The papers included in this book cover a wide variety of topics, including student-invented algorithms, the assessment of such algorithms, algorithms from history and other cultures, ways…

Some methods of proof of traditional algebra problems using geometric methods are explored. The techniques used come from the original Greek approaches to these mathematical questions. (MP)

Discussed is the benefit of the inclusion of historical material in a student's text. Several geometry problems are used as examples. A suggested list of problem sources is provided in the appendix. (YP)

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

Presented is the ancient Egyptian algorithm for the operations of multiplication and division of integers and fractions. Theorems involving unit fractions, proved by Fibonacci, justifying and extending the Egyptian or Ahmes' methods into the Hindu-Arabic numeric representational system are given. (MDH)

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…

Tracing the history of algebra within the U.S. secondary curriculum requires at the same time a review of the various reform movements relevant to secondary education, an acknowledgement of the sociological, political, and psychological perspectives driving these reforms, and most importantly, the perceived role of mathematics in the education of…