Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Presents two methods for replacing a series by one converging more rapidly: regrouping the terms of a series and manipulations of power series. Describes a general algorithm for approximating the natural logarithm of any number. (YP)

Reports on the findings of the Algorithms working group at the Ware, England, conference. Examines methods of introducing the algorithmic approach to mathematics via computer programing and using problems arising from content areas. Considers programing language and presents support for programming in mathematics curricula. (JM)

Provides four examples for testing the validity of logical arguments by using the method of truth trees. (YP)

Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

Shows a series of Euclidean equations using the Euclidean algorithm to get the greatest common divisor of two integers. Describes the use of the equations to generate a series of circles. Discusses computer generation of Euclidean circles and provides a BASIC program. (YP)

Raises and responds to questions about what and how to teach mathematics with the availability of calculators to all students. Discusses whether students need basic facts, mechanical skills, and knowledge of computational algorithms. Argues that students need to develop number sense and analytical skills using simple, symbolic, and graphing…

Presents an easy method for constructing magic squares from three-by-three to general squares. Provides a computer program generating odd-order magic squares. Six references are listed. (YP)

Reports on a study into the problem solving abilities of students in a Jamaican high school who were intentionally taught problem solving strategies during one-sixth of their mathematics instruction for one academic year. Results indicated no significant increases in their performance on a problem solving test. (TW)

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)

Investigates children's behaviors and conceptual achievements in the transition from informal calculation strategies to a written division algorithm. Describes five different strategies observed in the solution of division problems. Discusses the implications of the children's behavior. (YP)

This paper presents an examination of the construction of logic in multidigit subtraction. Interviews were conducted with 90 grade 2 and grade 3 students to determine whether they understood the logic of borrowing and whether the construction of the logic was related to procedural expertise or corresponding conceptual knowledge. Of 34 students…

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)