How set theory, combinatorics, probability, and the study of algorithms can be used in solving two problems is described in detail. Three computer programs are listed. (MNS)

Renaming fractions with the dot method is described with illustrations. It can be used to introduce renaming at the manipulative level in a meaningful way prior to moving to a more abstract level where prime factorization will be involved. (MNS)

Two worksheets are given, outlining algorithms to help students determine the day of the week an event will occur and to find the date for Easter. The activity provides computational practice. A computer program for determining Easter is also included. (MNS)

A modern adaptation of the historic lattice algorithm which can be used for multiplication and division is discussed. How it works is clearly illustrated. (MNS)

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

Presents a developmental taxonomy which promotes sequencing activities to enhance the potential of matching these activities with learner needs and readiness, suggesting that the order commonly found in the classroom needs to be inverted. The proposed taxonomy (story, skill, and algorithm) involves problem-solving emphasis in the classroom. (JN)

Described is a way to use knots to relate a three-dimensional object to a two-dimensional representation of the object. The results are used to produce an algorithm or rule to explain a general case. Included are examples, diagrams, procedures, and explanations. (KR)

The first aim in school might be to help children become more aware of the algorithmic processes they use; then, ensure that they can devise algorithms and define them. Many examples of how these aims can be met are given, including the use of calculators and computers. (MNS)

Discusses using what students already know about taking away objects when teaching subtraction and gives six lessons to develop language for discussing and recording subtraction situations that give meaning to the subtraction algorithm. (MKR)

Presented is a method where a quadratic equation is solved and from its roots the eigenvalues and corresponding eigenvectors are determined immediately. Included are the proposition, the procedure, and comments. (KR)

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

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…

Presented is a way to provide students with a review and an appreciation of the versatility of pointers in data structures by improvising with binary trees. Examples are described using the Pascal programing language. (KR)

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)

This article, which is organized around a single, well-known algorithm for root extraction, presents a way of incorporating dynamical systems into the teaching of mathematics. Included are sample exercises using complex numbers and the computer where students have the opportunity to do some analysis on this algorithm. (KR)