An example is presented that can be used to introduce the study of limits of sequences through recursive formulas yielding square roots. (MP)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

"Chisanbop" is a Korean word which means finger calculation method. It is based on the Korean abacus, and its emphasis is on fives. By using Chisanbop techniques, one can add, subtract, multiply, and divide large numbers. Chisanbop can be taught most effectively to large groups in the second grade. (JN)

Introduces the method of ray tracing to analyze the refraction or reflection of real or virtual images from multiple optical devices. Discusses ray-tracing techniques for locating images using convex and concave lenses or mirrors. (MDH)

Attention is drawn to an ancient Greek method for finding the least common multiple (LCM) of two numbers. A link is established between this method and a well-known method of obtaining the highest common factor (HCF) numbers. This leads to consideration of some relationships between HCF and LCM. (Author/MK)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)

A common misconception among students setting up force-acceleration problems is to think of the expression "mass times acceleration" as a force itself. Presents a new formula to express the relationship between force, mass, and acceleration, and discusses its benefits. (MDH)

Establishes a rationale for teaching population genetics to students and inservice biology teachers. Suggests strategies for introducing students to the Hardy-Weinberg principle. (MDH)

Attention is called to the apparent widespread misunderstanding of algebraic notation by secondary school students, and how this may arise from some common approaches to teaching algebra to beginners is discussed. (MNS)

Children need more than activities to help them see that the relationship expressed in a formula is true. Giving them the underlying principles will contribute to better comprehension, retention, and transfer. (MNS)

The article describes the Mental Mathematics System, a number of formulas designed to develop mathematical skills in elementary and junior high school gifted and talented students. Formulas are provided for multiplication. The formulas for mental mathematics are noted to promote student interest in the subject. (SBH)

Describes numerical differentiation and the central difference formula in numerical analysis. Presents three computer programs that approximate the first derivative of a function utilizing the central difference formula. Analyzes conditions under which the approximation formula is exact. (MDH)

Argues that the derivation of the area of a circle using integral calculus is invalid. Describes the derivation of the area of a circle when the formula is not known by inscribing and circumscribing the circle with regular polygons whose areas converge to the same number. (MDH)

The general combinatorial problem of counting the number of regions into which the interior of a circle is divided by a family of lines is considered. A general formula is developed and its use is illustrated in two situations. (PK)

Classroom ideas for teaching area and perimeter concepts are presented. Squares, circles and other shapes are examined. Further explorations are suggested. (PK)